Nonlinear microscopy 1
bull Introductionbull Wide-field and confocal (3D) microscopybull 2PEF microscopybull Applications neurosciences embryologybull Imaging depth in scattering mediabull SHG microscopybull Endogenous bio SHG2PEF contrast
Emmanuel BeaurepaireLab for optics and biosciences - Ecole Polytechnique - Palaiseau
wwwlobpolytechniquefr
Impulsions femtosecondes des concepts fondamentaux aux applications - Les Houches Janv 2009
Contributions D Deacutebarre N Olivier W Supatto MC Schanne-Klein JL Martin M Joffre M Strupler T Boulesteix AM Pena G Labroille R SPillai C Boudoux J Ogilvie E Farge N Desprat PA Pouille B Moulia N Peyrieacuteras L Duloquin PL Tharaux B
Crestani R Legouis T Tordjmann L Combettes S Charpak L Moreaux J Mertz
Nonlinear microscopy 2
bull THG microscopybull CARS microscopybull Microscopy with shaped broadband pulses bull Coherent microscopy with shaped beamsbull Epidetection of coherent signalsbull 3D microdissection with fs pulses
bull 1590 Zaccharias amp Hans Janssen (2 lentilles)bull 1665 Robert Hooke cellules (liegravege)bull 1632-1723 Anton van Leeuwenhoekrarr premiegravere description des micro-organismes cellules sanguines etc
laquo Renaissance de la microscopie raquoMicroscope confocal (1957 1980s) imagerie cellulaire 3D agrave lrsquoeacutechelle du micromegravetre
+ deacuteveloppement de marqueurs fluorescents morphologiques et fonctionnels (potentiel membranaire calcium hellip)
hellipmicroscopie subcellulaire in vivo rarr microscopie multiphoton (1990s)
bull XXe siegravecle Profondes avanceacutees en biologie (biologie moleacuteculaire geacuteneacutetiquehellip)rarr besoin de comprendre lrsquoorganisation spatiale des eacutevegravenements intracellulaires
Microscopie optique en biologie(bref raccourcihellip)
Field distribution in the focal region of an objective lens
E0
objective
Paraxial approximation not always validTransverse beam profile not always Gaussian
Field near focus of an aplanetic lens from an arbitrary pupil profile
Focal field distribution
Richards amp Wolf Proc Roy Soc A 253 358 (1959)Born amp Wolf Principles of optics (1980)
Debye-Wolf (Richards-Wolf) diffraction integral
Note relation between incident and refracted fields in an aplanetic system
Intensity law(energy conservation)
nk πω2=
θ zdA1 dA2
dA1 = dA1 cosθ
( ) ( ) ( )( )244sin0 uuuI prop
Point spread function (PSF) of single lens
( ) ( ) ( ) ( ) PSFdiuvJPvuI =primeprimeprimeprimeprime= int21
0
20 2exp2 ρρρρρ
v equiv r middot NA middot 2π λu equiv z middot NA2 middot 2π nλJ0 = 0th order Bessel functionρrsquo = θ middot n NA (radial coordinate in pupil)P(ρrsquo) = pupil function
Intensity distribution in the focal region of an objective with numerical aperture NA=n sin(α)
( )int=cstu
dvvuI is constant along zNote
NAnr
2sin2λ
αλδ =asymp
αn
αsinnNA =
Numerical aperture (NA)
( ) ( ) 2120 vvJvI prop
Born amp Wolf (1980) Principles of optics Muumlller (2006) Introd to confocal fluorescence microscopy
Wilson amp Sheppard (1984) Theory and Practice of Scanning Optical Microscopy
Simplified expression (within Kirchhoff Debye paraxial and scalar approximations)
lateral width
~λ2NA
axialwidth
~2nλNA2
Assuming P(ρrsquo) = 1
bull Lateral resolution ~λ2NA (related to width of PSF amp OTF)bull No true axial resolutionMissing cone of spatial frequencies the axial position of a thinfluorescent plane (laterally uniform) can not be determined
Standard fluorescence microscope (wide field)
( ) ( ) ( )
( ) ( )xyxPSFzyxO
zdydxdzzyyxxPSFzyxOZYXI
otimes=
primeprimeprimeprimeminusprimeminusprimeminus= intintintinfin
Image formation process
Can also be described in spatial frequency spaceby means of the optical transfer function (OTF)
( ) )( vuPSFFOTF vu =ΩΩ
Muumll
ler
Intro
d to
con
foca
lflu
or m
icro
sc (
2006
)
Lateral cut-off frequency (nλ)
Axi
al c
ut-o
ff fre
quen
cy(n
λ)
laquo missing cone raquo
OTF
Lamp
camera
F
Laser
spatial filter
detector
(Note scanning microscope)
3D imaging by (linear) confocal microscopy
488
nm
~500
nm
z
2det excexcconf PSFPSFPSFPSF asympsdot=
( ) ( ) ( )( )444sin0 uuuI prop
( )int=cstu
dvvuI peaks for upropz=0
PSFexc PSFconf
OTF wide field OTF confocal
λ=500nmNA=13
n=15log scale
Dia
spro
et a
l Bi
omed
Eng
Onl
ine
(200
6)M
uumllle
r In
trod
to c
onfo
calf
luor
esce
nce
mic
rosc
opy
(200
6)
rarrTrue axial resolution
Laser
spatial filter
detector
(Note scanning microscope)
3D imaging by (linear) confocal microscopy[+] Optical sectioning
⎩⎨⎧
propΔpropΔ
2NAnzNAr
λλ
[+] Many available fluorophores for biology
αsinnNA =
Wide field Confocal
Resolution
488
nm
~500
nm
z Excitation is not confined rarr photobleaching phototoxicityVery sensitive to scattering of visible light in tissues rarr limited penetration (~100microm)
4det
minuspropsdot= zPSFPSFPSF excconf
αn
3D microscopy in a biological tissue Diffraction-limited rArr relies on unscattered light
Howeverhellip visible light is strongly scattered in tissues
scattered photons
ballistic photons
DefScattering mean free path (Ls)= average distance between 2 scattering events (50-100 microm in biological tissues for visible light)
z
N0
N0 exp(-zLs) tissue
The number of ldquoballistic photonsrdquodecays exponentially with z
Ls
Confocal microscopy in scattering medium
bull Scattering of non-focal fluorescencebull Scattering of excitation light and of
focal fluorescence
rarr backgroundrarr signal attenuation
(focal point must be imaged on detector)
ExcitationFluoresc
Bbackground
(surface)
S
z
log (S+B)
transparentscattering
z
rArr Scattering limits imaging depthZmax ~ 50-150 microm
nonlinear excitation
F prop I 2PEF prop I2
1PEF1 photon excited
fluorescence
2PEF2 photon excited
fluorescence
Nonlinear (=multiphoton) microscopy
exci
tatio
n(v
isib
le)
exci
tatio
n(IR
)
[+] preserves sub-cellular resolutioninside scattering medium
ExcitationFluorescence
near IR λ excitation rarr better penetration
scattered IR produce ldquonordquo fluorescencerarr reduced background
2PEF microscopy in scattering medium
[+] Excitation is localized in 3Drarr reduced photoxicity
Zipf
elamp
Web
b (C
orne
ll U
niv)
linear nonlinear
S prop I2 (or I3)rArr excitationis confined
S prop I prop 1z2
rArr excitationis not confined ( )222 vuI
PSF =
Near-IR excitation λ asymp 07-12 microm[+] Reduced perturbabtion[+] Enhanced penetration in tissues
02 04 06 08 10 12 14 16 18 2001
1
10
100
Abs
orpt
ion
coef
ficie
nt (c
m-1)
Wavelength (microm)
Water (pure)Fat (pure)Hb02 (1mM)Hb (1mM)Melanin (1mM)Tryptophan (1mM)
Near-IR excitation reduces absorption and scattering laquo transparence window raquo of tissues
http
om
lco
gie
du
04 05 06 07 08 09 10 11 120
200
400
600
800
1000
1200
1400
Scat
terin
g co
effic
ient
(cm
-1)
Wavelength (microm)
confocal
2PEF SHGTHG
Multiphoton excitation tissue optics
Scattering mean free path (Ls) = average distance between 2 scattering events
Ls
g asymp 1 forward scatteringg asymp 0 isotropic scattering
θθcos=g
~100-200microm for λ asymp 07-12 microm
Scattering anisotropy
Biological tissues g ~ 08 ndash 095
F prop I
1PEF1 photon excited
fluorescence
exci
tatio
n(v
isib
le)
Zipf
elamp
Web
b (C
orne
ll U
niv)
linear nonlinear
S prop I2 (or I3)rArr excitationis confined
S prop I prop 1z2
rArr excitationis not confined
( )222 vuIPSF =
nonlinear excitation
2PEF SHG prop I2
2PEF2 photon excited
fluorescence
SHGsecond-harmonic
generation
THG prop I3
THGthird-harmonic
generation
CARScoherent anti-Stokes Raman
scattering
ωP ωSex
cita
tion
(IR)
CARS prop IP2 IS
[+] Several possible contrastmechanisms rarr different information
2PEF fluorescence SHG non-centrosymetryTHG χ(3) heterogeneitiesCARS vibration resonancehellip
[+] More robust in the presence of incoherent scattering (inside tissues)
2PEF penetration
100-600 microm
[+] Excitation is localized in 3Drarr reduced photoxicity
Nonlinear (=multiphoton) microscopies
g
e
g
e
Eeg
σabs asymp 10-16cm2 σ2p-abs asymp 10-49 cm4 sphoton
Usual unit Goumlppert-Mayer(1 GM = 10-50 cm4 sphoton)
1 event s 1 event 10 million years
Standard molecule in bright daylight
1-photon 2-photon
Absorption cross-section
Note Focusing a 1mm2 beam to a 1microm2 area increases the intensity squared by a factor (106)^2 rarr still not enough to enable rapid imaging (2-10 micros pixel dwell time) with such small cross-sections
22PEF2
12
2PEF21
p IτTσI
τTσ
TτF
TτF ⎟
⎠⎞
⎜⎝⎛=⎟
⎠⎞
⎜⎝⎛==
pI
Fluorescence during pulse
Averagefluorescence
laquo gain raquo Tτ
TiSaph laser
gain asymp 105T asymp 10 ns(100 MHz)τ asymp 100 fs
Gain with pulsed excitation
τ asymp 10-13 s T asymp 10-8 s
Pulsed lasers are used for optimal multiphoton excitation with minimal average power
time
pulses are typically τ ~100 femtoseconds FWHM
2P fluorescence depends on the average squared intensity (rather than on )2I ( )2I
Example withsquare pulses
Fp = frac12 σ2PEF Ip2 σ2PEF equiv η σ2p-abs (η radiative quantum efficiency)
More generally for pulsed excitation
( )22 IIτTgP= with gP depending on temporal shape
(066 for a Gaussian pulse shape)
( )22 II = second-order temporal coherence
wr
wz
2PEF cross-section orders of magnitude
σ2PEF = η σ2p-abs ~ 10-48 cm4 sphoton
202PEF2
10 IσF τ= T
20
0π
P2Iw
=
θω
ω
sinnλ032
=rw
)cos-(1nλ530
z θ=
ω
ωw
wr wz radius at 1e
NA2λ
asymp
2NAλn13
asymp
zr ww22
3
2πV ⎟
⎠⎞
⎜⎝⎛=
PSF (point spread
function)
Focal volume Gaussian-shape fit to
diffraction theory
Typically 2 microm times 04 microm
Usual unit Goumlppert-Mayer(1 GM = 10-50 cm4 sphoton)
Example one molecule in focus
bull P = 1 mW asymp 1015 photonss224 cm sphotons10asymp
sphotons105asymp
bull σ2PEF = 100 GM
λ=1 μm n=13 NA=1 σ2PEF=100 GM
C=1 μM rarr N=1000 molecules
rarr F ~ 2 times 107 photonss
Example 2 several molecules
CVγIσF 202PEF2
1τ= T
average fluorescence produced by one molecule
in excitation volume
pulsed excitation
2PEF microscopy implementation(source scanning objective dispersion compensation)
700-1200 nm~80 MHz~100 fs
source
No need to produce a descanned image of the the focal spot on a spatial filter simpler than a confocal microscope (except for the laser source)
LASER
Beam scanning
Laser in
Laser
out
Point Scanning
to microscope
Δt
Typical pixel time ~2-10 micros (100-400 kHz)Typical line duration ~1 ms (1 kHz)Typical image acq time ~05-2 s
Some methods for faster scanningbull X-axis resonant scanning
http
pa
rker
lab
bio
ucie
du
128 micros
sinusoidalx-scan
pixel clockline sync
y-scan
frame sync66 ms
laser
y-galvo
32-sidedpolygon
obj
telescope1
tele
scop
e2
PMTbull X-axis polygon mirror
These 2 approaches canbe used to record images
at video rates
Limitation signal level
Multipoint excitation canalso be used in certain
cases
http
ce
llser
vm
edy
ale
edu
imag
ing
Dureacutee de vie ~ 1ns
photonss 10F 9max lt
Autres facteursbull Photoblanchimentbull Photo-ionisation bull laquo inter-system crossing raquo
10 ns
100 fs ltlt 1 ns
(limiteacute par la moleacutecule)
photonss 10F 8max lt
(taux de reacutepeacutetition de lrsquooscillateur)
1 photon de fluorescence max par molecule par
impulsion
Facteurs limitant le niveau de signal
M B
lanc
hard
-Des
ce(U
niv
Ren
nes I
)
Engineered fluorophores with enhanced 2PEF
2PEF action cross-sections
10-100 GMldquoQuantum dotsrdquo
104 GM
Endogenous fluorophores (NADH etc)
Standard fluorophores (Rhodaminehellip) 01-10 GM
10-3 - 10-1 GM
Fluorescent proteins (GFP etc)
100-1000 GMZi
pfel
Web
b (C
orne
llU
niv
)
Example 150 fs rarr (5000 fs2) rarr 177 fs80 fs rarr (5000 fs2) rarr 190 fs10 fs rarr (5000 fs2) rarr ~1 ps 80 fs rarr (20000 fs2) rarr 697 fs150 fs rarr (20000 fs2) rarr 403 fs
Dispersion of optics in a multiphoton microscope 2000-20000 fs2
Implementation prism pairs gratings chirped mirrors SLM-based pulse shaper
( )2200 2ln41 τϕττ primeprime+=Pulse broadening
τ0 = initial duration (transform-limited pulse)φrsquorsquo = group delay dispersion (fs2)
Dispersion compensation
In practice compensation is necessary mostly for pulses ltlt 100 fs
Note1 2PEF imaging is typically done with 100fs pulsesShort pulses are interesting for spectroscopy (next lesson) but may induce additional toxicityNote2 managing 10fs pulses at the focus of high NA objective is not trivial Radially varying group delay can be a few 10s fs in some objectives
2PEF prop 1τ
PSF degradation example for aqueous sample
60times NA 12water immersion
40times NA 13oil immersion
rarr Use water-immersion objectives (index matching)
PSFz PSFz
Index mismatch cause PSF spreading and signal loss
Diaspro Ed Confocal and 2P Microscopy Foundations Applications and Advances (2001)Jacobsen Hell et al Refractive-index-induced aberrations in 2P confocal fluorescence microscopy J Microsc 176 226 (1995)Booth amp Wilson ldquoRefractive-index-mismatch induced aberrations in single-photon and 2P microscopyrdquo J Biomed Opt 6 266 (2001)
For small aberrations
( ) ( )2221 ΔΦminusasymp λπrefaber II
mean-square deformationof the wave front
( )2ΔΦ
rarr rapid impact on NL signal
Incidence on signal level
NeuroscienceYuste Denk (1995) Dendritic spines as basic functional units of neuronal integration Nature 375 682-684Svoboda Tank Denk (1996) Direct measurement of coupling between dendritic spines and shafts Science 272 716-719Svoboda Denk Kleinfeld Tank (1997) In vivo dendritic calcium dynamics in neocortical pyramidal neurons Nature 385 161-5
2PEF microscopy in biology some fields of application
Immunology
Developmental biology
ReviewsSvoboda amp Yasuda (2006) Principles of 2P excitation microscopy and its applications to neuroscience Neuron 50 823-839Mertz (2004) Nonlinear microscopy new techniques and applications Curr Opin Neurobiol 14 610-616
ReviewCalahan MD amp Gutman GA (2006) The sense of place in the immune system Nat Immunol 7 329-332
McMahon A Supatto W Fraser SE and Stathopoulos A (2008) Dynamic analyses of Drosophila gastrulation provide insights into collective cell migration Science 3221546-50
laserTiSaphir
rarr 400 μm
50 microm
Application example in neurosciences in vivo 2PEF imaging of an olfactory neuron
50 microm
S C
harp
ak e
t al
PNA
S 98
123
0 (2
001)
Les PA spontaneacutes enregistreacutes dans le soma (trace du bas) induisent des entreacutees de calcium dans le bouquet dendritique
Pb marquage cellules multiples rarr marqueurs geacuteneacutetiques agrave base de proteacuteines fluorescentesex laquo cameleons raquo (constructions 2XFPs+cmd sensibles au calcium) etc
[Ca2+]i imaging
S C
harp
ak e
t al
Ner
urop
hysi
olog
ieet
nou
velle
s mic
rosc
opie
s (I
NSE
RM
-Par
is V
)
Nat
Met
h 2
932
200
5
100microm Chl
omel
eon
Prot
ein
(sen
stiv
eto
chl
orid
e io
ns)
mou
se n
eoco
rtex
Hel
mch
enet
al
(200
5) N
at M
eth
2 9
32-9
40
Two-photon-excited fluorescence (2PEF)
[+] Genetically encoded probes fluorescent proteins (GFPhellip)
Nonlinear microscopy of tissues 2PEF
GFP
~ns
700-
1000
nm
350-
600+
nm
Some important fields of application of 2PEF microscopy
Neurosciences in vivo neuronal activityImmunology lymphocyte trafficking
GFP labeling of nuclei
2PEF λ=920 nm 2 simage 10 mW 1 image every 30 s
100 microm
yolk
vitelline membrane
nucleilipid droplets
Live embryo imaging 2PEF microscopy
Supatto et al (2005) PNASSquirrell et al (1999) Nat Biotechnol
LOB Polytechnique Curie
GFP labeling of nuclei
2PEF λ=920 nm
Live embryo imaging 2PEF microscopy
Caltech bioimaging centerMcMahon Supatto et al (2008) Science
Example quantitative study of individualcollective cell motions in a developing embryo
1 XYZ image every 10s
z
LOB Polytechnique Curie
[+] Endogenous fluorescents species
elastin(rat artery wall fresh)
Bou
lest
eix
et a
l (2
006)
C
ytom
etry
69A
~ns
700-
1000
nm
350-
600+
nm
Two-photon-excited fluorescence (2PEF)
Nonlinear microscopy of tissues 2PEF
Mouse ear skin
(fresh)
Excitation 720nm 800nm 900nm Detection 350-505 505-560 560-650 + spectral unmixing
Note NADH fluorescence is an
indicator of metabolic state
Rad
osev
itch
Hill
man
et a
l (2
008)
O
pt L
ett
33 2
164
NADH fluorescent NAD+ non-fluorescent
zmax
P0
( ))ex(s0 LzexpP minus
z
( )[ ] ( )zLzPTS exs Φsdotminussdotprop
2)(0 expτ
Signal
excitation detection
typically ~500 μm(layer 23 neocortex)
α - fluorophore efficiencyand detector noise
tissue scattering length average laser power
Φ - collected fraction of the generated fluorescence
inverse laser duty cycle
( )τα )(ln max)(
max TzPLz exs Φ=
Rat brain Ls~200microm
If limited by detector noise (no background)
zmax~50-200 μm with endogenous signals
What limits the imaging depthConfined excitation even in scattering media hellip but the number of ballistic excitation photons decreases exponentially with depth
PNAS 98 1230 (2001)
( )τα )(ln max)(
max TzPLz exs Φ=
A How to increase collection efficiency (Φ)
How to increase imaging depth
zmax
( )( )221 cos1
NA
NA
α
α
prop
minus=Φ
αNA
(1) first idea increase NA
This workshellip
Field-of-view (FOV)
(2) hellipbut what if sample is scattering
Scattered fluorescence seemsto originate from an
extended source
Field of view (related to the angular acceptance of the detection path) defines the depth where collection efficiency starts to drop
At large depths (diffusive light)
Oheim et al (2001) J Neurosci Meth 112 205Beaurepaire amp Mertz (2002) Appl Opt 41 5376
An objective with low magnification and high NA is advantageous for collecting scattered fluorescence
( ) 22 minussdotpropΦ zrFOV
Typical multiphoton microscope
laquo non-descanned raquo detection(close to objective)
700-1200 nm~80 MHz~100 fs
source
Diaspro et al (2006) Biomed Eng online
B
A
TiSapph
Reg Amp
z rarr
z rarr
T τ ~ 1times105
T τ ~ 4times107
fmax rTS
fmax rRA
Δz asymp ln(rTSrRA)2 asymp 2-3 scattering lengths Δz
rTS = 80 MHz
rRA = 200 kHz
log F
log FTemporal redistribution of the
same excitation power
At large depths contrast (amp resolution)
loss
hellip in vivoexperiment
( )2balscat II +
Theer amp Denk (2006) JOSA A 23 3139
2PEF imaging depth fundamental limit
Note Zmax increases with staining heterogeneity Zmax is increased by ~Ls when stained fraction is reduced 6times
Zmax reached when
( ) intint ge+focusat
balfocusofout
balscat III 22
Contribution of the different planes Model accounting for the temporal distribution of scattered light and assuming that scattering is mostly forward-directed
Influence of pulse duration rarr Using pulse duration of 20fs instead of 200fs should increase the SB ratio by 25times resulting in an increase of 05 scattering MFP to the depth limit
( )τα )(ln max)(
max TzPLz exs Φ=
How to increase imaging depth
zmax
bull Regenerative amplification multiplies Tτ by 400rarr Equivalent to multiplying P by 20
bull Implement wavefront correction to correct for specimen-induced aberrations (adaptive optics)
bull Design background rejection schemes to remove light generated out-of-focus when doing large depth imaging
B Improving excitation
bull Low mag objective multiplies Φ by 10(Only equivalent to multiplying P by 3)
bull And always non-descanned detection
A Improving collection Φ
Theer amp Denk OL2003
2PEF from a thin fluorescent slab as a function of slab defocus Ratio betweensignal detected with an unaberrated and an aberrated phase
2PEF images of a labeled glomerulus (from mouse olfactory bulb)
Wavefront correction in microscopy
Φ-Φ
Φ
Possible strategiesMeasure aberrated wavefront with wavefront sensor rarr implementation eg Denk PNAS 2006
Iterative sensorless approach with merit functioneg Wright et al OE 2007 (applied to CARS)
Model-based sensorless approach eg Deacutebarre Botcherby Booth Wilson OE 2008 (applied to structured illumination microscopy)
reference
astronomy ophtalmology microscopy
For small aberrations
( ) ( )2221 ΔΦminusasymp λπrefaber II
mean-square deformationof the wave front
( )2ΔΦ
rarr rapid impact on NL signal
LOB
-X
low-coherence interferometry+ wave-front sensing
4 images (I1hellipI4) recorded with reference path length shifts of 0 λ4 λ4 and 3λ4 For each pixel a complex amplitude A is calculated by
Reference
Sample
Low-coherence sourceTiS 915nm 100fs
CCD
( ) ( ) ⎟⎠⎞⎜
⎝⎛ ΔΔminus++=
22ln2expcos τνπδϕsrsrD iiiiI
z-resolution ~ 20 micromνΔ FWHM of source power spectral density
νΔprop 1
δϕ applied phase shift
τΔ delay due to path difference
+ ldquocompatiblerdquo with 2PEF microscopy
obj
(conjug with objective back focal plane)
Feieraband et al (2004) Opt Lett 29 2255Ruumlckel et al (2006) PNAS 103 17137Ruumlckel et al (2007) JOSA A 25 3517
δϕ
τΔ
6times 2PEF signal improvement
(2006) PNAS 103 17137
1P excitation 2P excitation
2PEF SHG prop I2
2PEF SHG
3PEF THG prop I3
excitation(IR)
F prop I
Fluoexcitation(visible) ωP ωS
3P excitation
3PEF
CARS prop IP2 IS
THG CARS
Different contrast mechanisms rarr different information
In particular SHG second harmonic generation ndash sensitive to symmetry at the sub-microm scaleTHG third harmonic generation ndash detects interfaces and microm-size inclusionsCARS laquononlinear Ramanraquo ndash chemical specificity
SHG THG specifically obtained from certain structures(little spectroscopic information)
Alternative contrast modes SHG THG CARS
E(ω) P(ω)
E(ω)
P(ω)
P(3ω)
SHG
THG
P(2ω)
Harmonic signal depends on the nature of the emitting medium
P(2ω)=frac12χ(2)(minus2ωωω) E(ω)E(ω)P(3ω)=frac14χ(3)(minus3ωωωω) E(ω)E(ω)E(ω)
Nonlinear microscopy harmonic generation
P = P(ω) + P(2)(2ω) + middot middot middot + P(n)(nω)= PL + PNL
avec P(n)(nω) =
Polarisable medium excited by an intense field components of order ngt1 in the induced polarization
rarr Emission at harmonic frequencies (nonlinear scattering)
non zero χ(2) =gt non centrosymmetric mediumχ(3) non zero everywhere (but weak)
Multiphoton microscope rarr combined contrast modes
2PEFsignal
SHGsignal
Osc
illato
r
THGsignal
Example of push-pull laquo harmonophore raquo molecule for SHG
(SHG)
Example stylbene derivative
hellip and amphiphilic version (for lipid membrane labeling)
M Blanchard-Desce (Univ Rennes)
SHG = coherent process (ne 2PEF)rarr possibility of constructive and destructive interferences
Example (labeled vesicle) parallel molecules rarr SHG
antiparallel molecules rarr no SHG (centrosymmetric medium)
Mertz amp Moreaux OL 2001
Constructive interference rarr enhanced signal Destructive interfeacuterence rarr null signal
Molecules emitting in phase Molecules emitting with opposite phases
ϕ1 = 0
ϕ2 = 0
ϕ1 = 0
ϕ2 = π
SHG
SHG
Excitation2PEF
Note in contrast 2PEF emission does not
depend on symmetry
SHG microscopy adapted for
membrane imaging
hellipand some endogenousstructures (see later)
Mor
eaux
Mer
tz e
t al
Bio
phys
J 8
0 1
568
(200
1)
SHG 2PEF
Wavelength (nm)400 450 500 550 600 650
Pow
er (a
u)
00
05
10
430 435 440 445 450
SH
G P
ower
(au
)
00
05
10
fluorescence
SHG
Spectrum radiated from a GUV labeledwith the styryl dye Di-6-ASPBS
Phase matching in (coherent) nonlinear optics
zLc
If Δkne0 (dispersion) I2ω(z) prop sin2Δkz2coherent signal buildup is limited to Lc
If Δk=0 (phase-matching case) I2ω(z) prop z2
Δk = k2ω - 2kω = wave vector mismatch
laquoClassicalraquo example SHG by plane wave propagating in a nonlinear medium
Note if Δkne0 phase-matching
can be forced in a birefringent crystal eg
where ne(2ω)ltno(ω)
keθ(2ω)=2ko(ω)neθ(2ω)=2no(ω)
The same applies for other NL processes
such as THG
Lc = coherence length
But what happens in a tightly focused geometry
bull Presence of transverse componentsbull Many possible k
kω = 2π nω λ
I Field near focus from arbitrary pupil profile (Cf Richards amp Wolf 1959 Born amp Wolf 1980)
III Far-field signal (Cf Novotny amp Hecht 2006)
II Induced polarization density near focus
For a homogeneous isotropic medium
expressed using Greenrsquos function
Signal generation in coherent NL microscopy
Example for THG
Solve wave equation taking into account NL polarizations created at various locations in the focal volume + coherent superposition in the detector plane
( )int int ΘΦΘpropmax
0
2
0
22(det) sinα π
RREFFddPDetected power
Field near focus phase distribution
Phase anomaly of focused beams (Gouy phase)LG Gouy CR Acad Sciences Paris 1890
Intensity near focus
minusπ (Gouy shift)
0Phase near focus
Cal
culN
Oliv
ier (
LOB
)
Approximation of tightly focused field for modeling nonlinear interactions GaussianGaussian amplitude and reduced axial wave vector
( ) xexp 2
2
2
22
⎟⎟⎠
⎞⎜⎜⎝
⎛minusminus
+minusminusasymp zki
wz
wyxiEzyxE
zrωωω ξ
wr wz 1e radii of the focal ellipse
2221 rwkωξ minusasymp
CfM
orea
ux S
andr
e M
ertz
(200
0) J
OSA
B 1
7 1
685
For a linearly x-polarized beam near focus
z (nm)
z
ωξ k
2 Iξ
ωω πω nk 2=
880nm NA=09
ω 2ω
0
-πPha
se a
nom
aly
Axial direction
)(cos 1 ξθ minus=slope prop (ξminus1)
Normalized intensitysquared
SHG from a labeled membrane Gouy shift deflects emission off-axis
θ
k2ω
ξ kω ξ kω
(ξlt1)
Mertz Moreaux et al (2001) Biophys J
Sample and field structure govern emission diagrams
emax asymp 06w0
Exemple of coherence effectobservation of SHG laquo hot spots raquo whenlabeled vesicules are in close proximity
Possible application sub-microm distance
measurement
Mertz Moreaux et al (2001) Biophys J
⎟⎟⎠
⎞⎜⎜⎝
⎛Θasymp
PEF
mHG
PEF
mHG NPP
22 σσ
N number of radiating molecules
Θ parameter describing signal reduction due to the sub-micrometer arrangement of the emitters within the focal volume (typ 10-2 for SHG)
222 INP PEFPEF σprop
Signal level in 2PEFmHG imaging
mmHGmHG INP σ2 Θprop
~ 10-4
(pour SHG)
rarr mHG signal strongly depends on the density of emitters
(SHG THG)
Intrinsic 2PEFSHG signals in cells and tissues
SHG = coherent second-ordernonlinear signal
no centrosymmetrySHG prop (density)2
rArr Dense and orderedmacromolecular structures
Zipfel et al (2003) PNAS 100 7075 (2003)
ldquoLive tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and SHGrdquo
- collagen fibrils
- sarcomeres
- astroglial fibers
- polarized microT bundles
cellulose starch hellip
Myofilaments = endogenous SHG source
Myocytes(Frog heart)
Boulesteix et al (2004) Opt Lett
Plot
niko
vet
al (
2006
) Bio
phys
J
SHG imaging of muscle structures
23 s acquisition
Applications sarcomere contraction measurements study of myogenesis
4 6 80
20
40
60
SHG
sig
nal (
phot
ons)
Length (microm)
sarcomere
constant variable
Saxitoxin (8 nM) 214 plusmn 002 microm
Control 231 plusmn 002 microm
rArr contracture at rest 7
N = C
R -O
H R
Possible molecularorigin the dense (crystalline) packingof peptide bonds such as amide group
Collagen triple-helix
Fibrils
Fibers
Macromolecular Organization
SHG is obtained from fibrillar collagen
SHGis observed
No SHG
Collagen I II III V XI hellip form fibrils
Collagen IV VIII X hellip form networks
rarr SHG = probe of macromolecular structuration
50 nm
Combined 2PEFSHG imaging of intact tissue
2PEFelastin
lamellae
SHGcollagenfibrils
Unstained carotid artery (Rat)λexc= 860nm
Boulesteix et al (2006) Cytometry A 69
yz
x
yz
x
yz
x
yz
x
yz
x
yz
x
yz
x
x
y
x
y
Lumen
Media
Intima
Adventitia
Endothelial cellsInternal elasticlamella
External elasticlamella
Fibroblast
Smoothmuscle cell
( ) ( ) ( )( )244sin0 uuuI prop
Point spread function (PSF) of single lens
( ) ( ) ( ) ( ) PSFdiuvJPvuI =primeprimeprimeprimeprime= int21
0
20 2exp2 ρρρρρ
v equiv r middot NA middot 2π λu equiv z middot NA2 middot 2π nλJ0 = 0th order Bessel functionρrsquo = θ middot n NA (radial coordinate in pupil)P(ρrsquo) = pupil function
Intensity distribution in the focal region of an objective with numerical aperture NA=n sin(α)
( )int=cstu
dvvuI is constant along zNote
NAnr
2sin2λ
αλδ =asymp
αn
αsinnNA =
Numerical aperture (NA)
( ) ( ) 2120 vvJvI prop
Born amp Wolf (1980) Principles of optics Muumlller (2006) Introd to confocal fluorescence microscopy
Wilson amp Sheppard (1984) Theory and Practice of Scanning Optical Microscopy
Simplified expression (within Kirchhoff Debye paraxial and scalar approximations)
lateral width
~λ2NA
axialwidth
~2nλNA2
Assuming P(ρrsquo) = 1
bull Lateral resolution ~λ2NA (related to width of PSF amp OTF)bull No true axial resolutionMissing cone of spatial frequencies the axial position of a thinfluorescent plane (laterally uniform) can not be determined
Standard fluorescence microscope (wide field)
( ) ( ) ( )
( ) ( )xyxPSFzyxO
zdydxdzzyyxxPSFzyxOZYXI
otimes=
primeprimeprimeprimeminusprimeminusprimeminus= intintintinfin
Image formation process
Can also be described in spatial frequency spaceby means of the optical transfer function (OTF)
( ) )( vuPSFFOTF vu =ΩΩ
Muumll
ler
Intro
d to
con
foca
lflu
or m
icro
sc (
2006
)
Lateral cut-off frequency (nλ)
Axi
al c
ut-o
ff fre
quen
cy(n
λ)
laquo missing cone raquo
OTF
Lamp
camera
F
Laser
spatial filter
detector
(Note scanning microscope)
3D imaging by (linear) confocal microscopy
488
nm
~500
nm
z
2det excexcconf PSFPSFPSFPSF asympsdot=
( ) ( ) ( )( )444sin0 uuuI prop
( )int=cstu
dvvuI peaks for upropz=0
PSFexc PSFconf
OTF wide field OTF confocal
λ=500nmNA=13
n=15log scale
Dia
spro
et a
l Bi
omed
Eng
Onl
ine
(200
6)M
uumllle
r In
trod
to c
onfo
calf
luor
esce
nce
mic
rosc
opy
(200
6)
rarrTrue axial resolution
Laser
spatial filter
detector
(Note scanning microscope)
3D imaging by (linear) confocal microscopy[+] Optical sectioning
⎩⎨⎧
propΔpropΔ
2NAnzNAr
λλ
[+] Many available fluorophores for biology
αsinnNA =
Wide field Confocal
Resolution
488
nm
~500
nm
z Excitation is not confined rarr photobleaching phototoxicityVery sensitive to scattering of visible light in tissues rarr limited penetration (~100microm)
4det
minuspropsdot= zPSFPSFPSF excconf
αn
3D microscopy in a biological tissue Diffraction-limited rArr relies on unscattered light
Howeverhellip visible light is strongly scattered in tissues
scattered photons
ballistic photons
DefScattering mean free path (Ls)= average distance between 2 scattering events (50-100 microm in biological tissues for visible light)
z
N0
N0 exp(-zLs) tissue
The number of ldquoballistic photonsrdquodecays exponentially with z
Ls
Confocal microscopy in scattering medium
bull Scattering of non-focal fluorescencebull Scattering of excitation light and of
focal fluorescence
rarr backgroundrarr signal attenuation
(focal point must be imaged on detector)
ExcitationFluoresc
Bbackground
(surface)
S
z
log (S+B)
transparentscattering
z
rArr Scattering limits imaging depthZmax ~ 50-150 microm
nonlinear excitation
F prop I 2PEF prop I2
1PEF1 photon excited
fluorescence
2PEF2 photon excited
fluorescence
Nonlinear (=multiphoton) microscopy
exci
tatio
n(v
isib
le)
exci
tatio
n(IR
)
[+] preserves sub-cellular resolutioninside scattering medium
ExcitationFluorescence
near IR λ excitation rarr better penetration
scattered IR produce ldquonordquo fluorescencerarr reduced background
2PEF microscopy in scattering medium
[+] Excitation is localized in 3Drarr reduced photoxicity
Zipf
elamp
Web
b (C
orne
ll U
niv)
linear nonlinear
S prop I2 (or I3)rArr excitationis confined
S prop I prop 1z2
rArr excitationis not confined ( )222 vuI
PSF =
Near-IR excitation λ asymp 07-12 microm[+] Reduced perturbabtion[+] Enhanced penetration in tissues
02 04 06 08 10 12 14 16 18 2001
1
10
100
Abs
orpt
ion
coef
ficie
nt (c
m-1)
Wavelength (microm)
Water (pure)Fat (pure)Hb02 (1mM)Hb (1mM)Melanin (1mM)Tryptophan (1mM)
Near-IR excitation reduces absorption and scattering laquo transparence window raquo of tissues
http
om
lco
gie
du
04 05 06 07 08 09 10 11 120
200
400
600
800
1000
1200
1400
Scat
terin
g co
effic
ient
(cm
-1)
Wavelength (microm)
confocal
2PEF SHGTHG
Multiphoton excitation tissue optics
Scattering mean free path (Ls) = average distance between 2 scattering events
Ls
g asymp 1 forward scatteringg asymp 0 isotropic scattering
θθcos=g
~100-200microm for λ asymp 07-12 microm
Scattering anisotropy
Biological tissues g ~ 08 ndash 095
F prop I
1PEF1 photon excited
fluorescence
exci
tatio
n(v
isib
le)
Zipf
elamp
Web
b (C
orne
ll U
niv)
linear nonlinear
S prop I2 (or I3)rArr excitationis confined
S prop I prop 1z2
rArr excitationis not confined
( )222 vuIPSF =
nonlinear excitation
2PEF SHG prop I2
2PEF2 photon excited
fluorescence
SHGsecond-harmonic
generation
THG prop I3
THGthird-harmonic
generation
CARScoherent anti-Stokes Raman
scattering
ωP ωSex
cita
tion
(IR)
CARS prop IP2 IS
[+] Several possible contrastmechanisms rarr different information
2PEF fluorescence SHG non-centrosymetryTHG χ(3) heterogeneitiesCARS vibration resonancehellip
[+] More robust in the presence of incoherent scattering (inside tissues)
2PEF penetration
100-600 microm
[+] Excitation is localized in 3Drarr reduced photoxicity
Nonlinear (=multiphoton) microscopies
g
e
g
e
Eeg
σabs asymp 10-16cm2 σ2p-abs asymp 10-49 cm4 sphoton
Usual unit Goumlppert-Mayer(1 GM = 10-50 cm4 sphoton)
1 event s 1 event 10 million years
Standard molecule in bright daylight
1-photon 2-photon
Absorption cross-section
Note Focusing a 1mm2 beam to a 1microm2 area increases the intensity squared by a factor (106)^2 rarr still not enough to enable rapid imaging (2-10 micros pixel dwell time) with such small cross-sections
22PEF2
12
2PEF21
p IτTσI
τTσ
TτF
TτF ⎟
⎠⎞
⎜⎝⎛=⎟
⎠⎞
⎜⎝⎛==
pI
Fluorescence during pulse
Averagefluorescence
laquo gain raquo Tτ
TiSaph laser
gain asymp 105T asymp 10 ns(100 MHz)τ asymp 100 fs
Gain with pulsed excitation
τ asymp 10-13 s T asymp 10-8 s
Pulsed lasers are used for optimal multiphoton excitation with minimal average power
time
pulses are typically τ ~100 femtoseconds FWHM
2P fluorescence depends on the average squared intensity (rather than on )2I ( )2I
Example withsquare pulses
Fp = frac12 σ2PEF Ip2 σ2PEF equiv η σ2p-abs (η radiative quantum efficiency)
More generally for pulsed excitation
( )22 IIτTgP= with gP depending on temporal shape
(066 for a Gaussian pulse shape)
( )22 II = second-order temporal coherence
wr
wz
2PEF cross-section orders of magnitude
σ2PEF = η σ2p-abs ~ 10-48 cm4 sphoton
202PEF2
10 IσF τ= T
20
0π
P2Iw
=
θω
ω
sinnλ032
=rw
)cos-(1nλ530
z θ=
ω
ωw
wr wz radius at 1e
NA2λ
asymp
2NAλn13
asymp
zr ww22
3
2πV ⎟
⎠⎞
⎜⎝⎛=
PSF (point spread
function)
Focal volume Gaussian-shape fit to
diffraction theory
Typically 2 microm times 04 microm
Usual unit Goumlppert-Mayer(1 GM = 10-50 cm4 sphoton)
Example one molecule in focus
bull P = 1 mW asymp 1015 photonss224 cm sphotons10asymp
sphotons105asymp
bull σ2PEF = 100 GM
λ=1 μm n=13 NA=1 σ2PEF=100 GM
C=1 μM rarr N=1000 molecules
rarr F ~ 2 times 107 photonss
Example 2 several molecules
CVγIσF 202PEF2
1τ= T
average fluorescence produced by one molecule
in excitation volume
pulsed excitation
2PEF microscopy implementation(source scanning objective dispersion compensation)
700-1200 nm~80 MHz~100 fs
source
No need to produce a descanned image of the the focal spot on a spatial filter simpler than a confocal microscope (except for the laser source)
LASER
Beam scanning
Laser in
Laser
out
Point Scanning
to microscope
Δt
Typical pixel time ~2-10 micros (100-400 kHz)Typical line duration ~1 ms (1 kHz)Typical image acq time ~05-2 s
Some methods for faster scanningbull X-axis resonant scanning
http
pa
rker
lab
bio
ucie
du
128 micros
sinusoidalx-scan
pixel clockline sync
y-scan
frame sync66 ms
laser
y-galvo
32-sidedpolygon
obj
telescope1
tele
scop
e2
PMTbull X-axis polygon mirror
These 2 approaches canbe used to record images
at video rates
Limitation signal level
Multipoint excitation canalso be used in certain
cases
http
ce
llser
vm
edy
ale
edu
imag
ing
Dureacutee de vie ~ 1ns
photonss 10F 9max lt
Autres facteursbull Photoblanchimentbull Photo-ionisation bull laquo inter-system crossing raquo
10 ns
100 fs ltlt 1 ns
(limiteacute par la moleacutecule)
photonss 10F 8max lt
(taux de reacutepeacutetition de lrsquooscillateur)
1 photon de fluorescence max par molecule par
impulsion
Facteurs limitant le niveau de signal
M B
lanc
hard
-Des
ce(U
niv
Ren
nes I
)
Engineered fluorophores with enhanced 2PEF
2PEF action cross-sections
10-100 GMldquoQuantum dotsrdquo
104 GM
Endogenous fluorophores (NADH etc)
Standard fluorophores (Rhodaminehellip) 01-10 GM
10-3 - 10-1 GM
Fluorescent proteins (GFP etc)
100-1000 GMZi
pfel
Web
b (C
orne
llU
niv
)
Example 150 fs rarr (5000 fs2) rarr 177 fs80 fs rarr (5000 fs2) rarr 190 fs10 fs rarr (5000 fs2) rarr ~1 ps 80 fs rarr (20000 fs2) rarr 697 fs150 fs rarr (20000 fs2) rarr 403 fs
Dispersion of optics in a multiphoton microscope 2000-20000 fs2
Implementation prism pairs gratings chirped mirrors SLM-based pulse shaper
( )2200 2ln41 τϕττ primeprime+=Pulse broadening
τ0 = initial duration (transform-limited pulse)φrsquorsquo = group delay dispersion (fs2)
Dispersion compensation
In practice compensation is necessary mostly for pulses ltlt 100 fs
Note1 2PEF imaging is typically done with 100fs pulsesShort pulses are interesting for spectroscopy (next lesson) but may induce additional toxicityNote2 managing 10fs pulses at the focus of high NA objective is not trivial Radially varying group delay can be a few 10s fs in some objectives
2PEF prop 1τ
PSF degradation example for aqueous sample
60times NA 12water immersion
40times NA 13oil immersion
rarr Use water-immersion objectives (index matching)
PSFz PSFz
Index mismatch cause PSF spreading and signal loss
Diaspro Ed Confocal and 2P Microscopy Foundations Applications and Advances (2001)Jacobsen Hell et al Refractive-index-induced aberrations in 2P confocal fluorescence microscopy J Microsc 176 226 (1995)Booth amp Wilson ldquoRefractive-index-mismatch induced aberrations in single-photon and 2P microscopyrdquo J Biomed Opt 6 266 (2001)
For small aberrations
( ) ( )2221 ΔΦminusasymp λπrefaber II
mean-square deformationof the wave front
( )2ΔΦ
rarr rapid impact on NL signal
Incidence on signal level
NeuroscienceYuste Denk (1995) Dendritic spines as basic functional units of neuronal integration Nature 375 682-684Svoboda Tank Denk (1996) Direct measurement of coupling between dendritic spines and shafts Science 272 716-719Svoboda Denk Kleinfeld Tank (1997) In vivo dendritic calcium dynamics in neocortical pyramidal neurons Nature 385 161-5
2PEF microscopy in biology some fields of application
Immunology
Developmental biology
ReviewsSvoboda amp Yasuda (2006) Principles of 2P excitation microscopy and its applications to neuroscience Neuron 50 823-839Mertz (2004) Nonlinear microscopy new techniques and applications Curr Opin Neurobiol 14 610-616
ReviewCalahan MD amp Gutman GA (2006) The sense of place in the immune system Nat Immunol 7 329-332
McMahon A Supatto W Fraser SE and Stathopoulos A (2008) Dynamic analyses of Drosophila gastrulation provide insights into collective cell migration Science 3221546-50
laserTiSaphir
rarr 400 μm
50 microm
Application example in neurosciences in vivo 2PEF imaging of an olfactory neuron
50 microm
S C
harp
ak e
t al
PNA
S 98
123
0 (2
001)
Les PA spontaneacutes enregistreacutes dans le soma (trace du bas) induisent des entreacutees de calcium dans le bouquet dendritique
Pb marquage cellules multiples rarr marqueurs geacuteneacutetiques agrave base de proteacuteines fluorescentesex laquo cameleons raquo (constructions 2XFPs+cmd sensibles au calcium) etc
[Ca2+]i imaging
S C
harp
ak e
t al
Ner
urop
hysi
olog
ieet
nou
velle
s mic
rosc
opie
s (I
NSE
RM
-Par
is V
)
Nat
Met
h 2
932
200
5
100microm Chl
omel
eon
Prot
ein
(sen
stiv
eto
chl
orid
e io
ns)
mou
se n
eoco
rtex
Hel
mch
enet
al
(200
5) N
at M
eth
2 9
32-9
40
Two-photon-excited fluorescence (2PEF)
[+] Genetically encoded probes fluorescent proteins (GFPhellip)
Nonlinear microscopy of tissues 2PEF
GFP
~ns
700-
1000
nm
350-
600+
nm
Some important fields of application of 2PEF microscopy
Neurosciences in vivo neuronal activityImmunology lymphocyte trafficking
GFP labeling of nuclei
2PEF λ=920 nm 2 simage 10 mW 1 image every 30 s
100 microm
yolk
vitelline membrane
nucleilipid droplets
Live embryo imaging 2PEF microscopy
Supatto et al (2005) PNASSquirrell et al (1999) Nat Biotechnol
LOB Polytechnique Curie
GFP labeling of nuclei
2PEF λ=920 nm
Live embryo imaging 2PEF microscopy
Caltech bioimaging centerMcMahon Supatto et al (2008) Science
Example quantitative study of individualcollective cell motions in a developing embryo
1 XYZ image every 10s
z
LOB Polytechnique Curie
[+] Endogenous fluorescents species
elastin(rat artery wall fresh)
Bou
lest
eix
et a
l (2
006)
C
ytom
etry
69A
~ns
700-
1000
nm
350-
600+
nm
Two-photon-excited fluorescence (2PEF)
Nonlinear microscopy of tissues 2PEF
Mouse ear skin
(fresh)
Excitation 720nm 800nm 900nm Detection 350-505 505-560 560-650 + spectral unmixing
Note NADH fluorescence is an
indicator of metabolic state
Rad
osev
itch
Hill
man
et a
l (2
008)
O
pt L
ett
33 2
164
NADH fluorescent NAD+ non-fluorescent
zmax
P0
( ))ex(s0 LzexpP minus
z
( )[ ] ( )zLzPTS exs Φsdotminussdotprop
2)(0 expτ
Signal
excitation detection
typically ~500 μm(layer 23 neocortex)
α - fluorophore efficiencyand detector noise
tissue scattering length average laser power
Φ - collected fraction of the generated fluorescence
inverse laser duty cycle
( )τα )(ln max)(
max TzPLz exs Φ=
Rat brain Ls~200microm
If limited by detector noise (no background)
zmax~50-200 μm with endogenous signals
What limits the imaging depthConfined excitation even in scattering media hellip but the number of ballistic excitation photons decreases exponentially with depth
PNAS 98 1230 (2001)
( )τα )(ln max)(
max TzPLz exs Φ=
A How to increase collection efficiency (Φ)
How to increase imaging depth
zmax
( )( )221 cos1
NA
NA
α
α
prop
minus=Φ
αNA
(1) first idea increase NA
This workshellip
Field-of-view (FOV)
(2) hellipbut what if sample is scattering
Scattered fluorescence seemsto originate from an
extended source
Field of view (related to the angular acceptance of the detection path) defines the depth where collection efficiency starts to drop
At large depths (diffusive light)
Oheim et al (2001) J Neurosci Meth 112 205Beaurepaire amp Mertz (2002) Appl Opt 41 5376
An objective with low magnification and high NA is advantageous for collecting scattered fluorescence
( ) 22 minussdotpropΦ zrFOV
Typical multiphoton microscope
laquo non-descanned raquo detection(close to objective)
700-1200 nm~80 MHz~100 fs
source
Diaspro et al (2006) Biomed Eng online
B
A
TiSapph
Reg Amp
z rarr
z rarr
T τ ~ 1times105
T τ ~ 4times107
fmax rTS
fmax rRA
Δz asymp ln(rTSrRA)2 asymp 2-3 scattering lengths Δz
rTS = 80 MHz
rRA = 200 kHz
log F
log FTemporal redistribution of the
same excitation power
At large depths contrast (amp resolution)
loss
hellip in vivoexperiment
( )2balscat II +
Theer amp Denk (2006) JOSA A 23 3139
2PEF imaging depth fundamental limit
Note Zmax increases with staining heterogeneity Zmax is increased by ~Ls when stained fraction is reduced 6times
Zmax reached when
( ) intint ge+focusat
balfocusofout
balscat III 22
Contribution of the different planes Model accounting for the temporal distribution of scattered light and assuming that scattering is mostly forward-directed
Influence of pulse duration rarr Using pulse duration of 20fs instead of 200fs should increase the SB ratio by 25times resulting in an increase of 05 scattering MFP to the depth limit
( )τα )(ln max)(
max TzPLz exs Φ=
How to increase imaging depth
zmax
bull Regenerative amplification multiplies Tτ by 400rarr Equivalent to multiplying P by 20
bull Implement wavefront correction to correct for specimen-induced aberrations (adaptive optics)
bull Design background rejection schemes to remove light generated out-of-focus when doing large depth imaging
B Improving excitation
bull Low mag objective multiplies Φ by 10(Only equivalent to multiplying P by 3)
bull And always non-descanned detection
A Improving collection Φ
Theer amp Denk OL2003
2PEF from a thin fluorescent slab as a function of slab defocus Ratio betweensignal detected with an unaberrated and an aberrated phase
2PEF images of a labeled glomerulus (from mouse olfactory bulb)
Wavefront correction in microscopy
Φ-Φ
Φ
Possible strategiesMeasure aberrated wavefront with wavefront sensor rarr implementation eg Denk PNAS 2006
Iterative sensorless approach with merit functioneg Wright et al OE 2007 (applied to CARS)
Model-based sensorless approach eg Deacutebarre Botcherby Booth Wilson OE 2008 (applied to structured illumination microscopy)
reference
astronomy ophtalmology microscopy
For small aberrations
( ) ( )2221 ΔΦminusasymp λπrefaber II
mean-square deformationof the wave front
( )2ΔΦ
rarr rapid impact on NL signal
LOB
-X
low-coherence interferometry+ wave-front sensing
4 images (I1hellipI4) recorded with reference path length shifts of 0 λ4 λ4 and 3λ4 For each pixel a complex amplitude A is calculated by
Reference
Sample
Low-coherence sourceTiS 915nm 100fs
CCD
( ) ( ) ⎟⎠⎞⎜
⎝⎛ ΔΔminus++=
22ln2expcos τνπδϕsrsrD iiiiI
z-resolution ~ 20 micromνΔ FWHM of source power spectral density
νΔprop 1
δϕ applied phase shift
τΔ delay due to path difference
+ ldquocompatiblerdquo with 2PEF microscopy
obj
(conjug with objective back focal plane)
Feieraband et al (2004) Opt Lett 29 2255Ruumlckel et al (2006) PNAS 103 17137Ruumlckel et al (2007) JOSA A 25 3517
δϕ
τΔ
6times 2PEF signal improvement
(2006) PNAS 103 17137
1P excitation 2P excitation
2PEF SHG prop I2
2PEF SHG
3PEF THG prop I3
excitation(IR)
F prop I
Fluoexcitation(visible) ωP ωS
3P excitation
3PEF
CARS prop IP2 IS
THG CARS
Different contrast mechanisms rarr different information
In particular SHG second harmonic generation ndash sensitive to symmetry at the sub-microm scaleTHG third harmonic generation ndash detects interfaces and microm-size inclusionsCARS laquononlinear Ramanraquo ndash chemical specificity
SHG THG specifically obtained from certain structures(little spectroscopic information)
Alternative contrast modes SHG THG CARS
E(ω) P(ω)
E(ω)
P(ω)
P(3ω)
SHG
THG
P(2ω)
Harmonic signal depends on the nature of the emitting medium
P(2ω)=frac12χ(2)(minus2ωωω) E(ω)E(ω)P(3ω)=frac14χ(3)(minus3ωωωω) E(ω)E(ω)E(ω)
Nonlinear microscopy harmonic generation
P = P(ω) + P(2)(2ω) + middot middot middot + P(n)(nω)= PL + PNL
avec P(n)(nω) =
Polarisable medium excited by an intense field components of order ngt1 in the induced polarization
rarr Emission at harmonic frequencies (nonlinear scattering)
non zero χ(2) =gt non centrosymmetric mediumχ(3) non zero everywhere (but weak)
Multiphoton microscope rarr combined contrast modes
2PEFsignal
SHGsignal
Osc
illato
r
THGsignal
Example of push-pull laquo harmonophore raquo molecule for SHG
(SHG)
Example stylbene derivative
hellip and amphiphilic version (for lipid membrane labeling)
M Blanchard-Desce (Univ Rennes)
SHG = coherent process (ne 2PEF)rarr possibility of constructive and destructive interferences
Example (labeled vesicle) parallel molecules rarr SHG
antiparallel molecules rarr no SHG (centrosymmetric medium)
Mertz amp Moreaux OL 2001
Constructive interference rarr enhanced signal Destructive interfeacuterence rarr null signal
Molecules emitting in phase Molecules emitting with opposite phases
ϕ1 = 0
ϕ2 = 0
ϕ1 = 0
ϕ2 = π
SHG
SHG
Excitation2PEF
Note in contrast 2PEF emission does not
depend on symmetry
SHG microscopy adapted for
membrane imaging
hellipand some endogenousstructures (see later)
Mor
eaux
Mer
tz e
t al
Bio
phys
J 8
0 1
568
(200
1)
SHG 2PEF
Wavelength (nm)400 450 500 550 600 650
Pow
er (a
u)
00
05
10
430 435 440 445 450
SH
G P
ower
(au
)
00
05
10
fluorescence
SHG
Spectrum radiated from a GUV labeledwith the styryl dye Di-6-ASPBS
Phase matching in (coherent) nonlinear optics
zLc
If Δkne0 (dispersion) I2ω(z) prop sin2Δkz2coherent signal buildup is limited to Lc
If Δk=0 (phase-matching case) I2ω(z) prop z2
Δk = k2ω - 2kω = wave vector mismatch
laquoClassicalraquo example SHG by plane wave propagating in a nonlinear medium
Note if Δkne0 phase-matching
can be forced in a birefringent crystal eg
where ne(2ω)ltno(ω)
keθ(2ω)=2ko(ω)neθ(2ω)=2no(ω)
The same applies for other NL processes
such as THG
Lc = coherence length
But what happens in a tightly focused geometry
bull Presence of transverse componentsbull Many possible k
kω = 2π nω λ
I Field near focus from arbitrary pupil profile (Cf Richards amp Wolf 1959 Born amp Wolf 1980)
III Far-field signal (Cf Novotny amp Hecht 2006)
II Induced polarization density near focus
For a homogeneous isotropic medium
expressed using Greenrsquos function
Signal generation in coherent NL microscopy
Example for THG
Solve wave equation taking into account NL polarizations created at various locations in the focal volume + coherent superposition in the detector plane
( )int int ΘΦΘpropmax
0
2
0
22(det) sinα π
RREFFddPDetected power
Field near focus phase distribution
Phase anomaly of focused beams (Gouy phase)LG Gouy CR Acad Sciences Paris 1890
Intensity near focus
minusπ (Gouy shift)
0Phase near focus
Cal
culN
Oliv
ier (
LOB
)
Approximation of tightly focused field for modeling nonlinear interactions GaussianGaussian amplitude and reduced axial wave vector
( ) xexp 2
2
2
22
⎟⎟⎠
⎞⎜⎜⎝
⎛minusminus
+minusminusasymp zki
wz
wyxiEzyxE
zrωωω ξ
wr wz 1e radii of the focal ellipse
2221 rwkωξ minusasymp
CfM
orea
ux S
andr
e M
ertz
(200
0) J
OSA
B 1
7 1
685
For a linearly x-polarized beam near focus
z (nm)
z
ωξ k
2 Iξ
ωω πω nk 2=
880nm NA=09
ω 2ω
0
-πPha
se a
nom
aly
Axial direction
)(cos 1 ξθ minus=slope prop (ξminus1)
Normalized intensitysquared
SHG from a labeled membrane Gouy shift deflects emission off-axis
θ
k2ω
ξ kω ξ kω
(ξlt1)
Mertz Moreaux et al (2001) Biophys J
Sample and field structure govern emission diagrams
emax asymp 06w0
Exemple of coherence effectobservation of SHG laquo hot spots raquo whenlabeled vesicules are in close proximity
Possible application sub-microm distance
measurement
Mertz Moreaux et al (2001) Biophys J
⎟⎟⎠
⎞⎜⎜⎝
⎛Θasymp
PEF
mHG
PEF
mHG NPP
22 σσ
N number of radiating molecules
Θ parameter describing signal reduction due to the sub-micrometer arrangement of the emitters within the focal volume (typ 10-2 for SHG)
222 INP PEFPEF σprop
Signal level in 2PEFmHG imaging
mmHGmHG INP σ2 Θprop
~ 10-4
(pour SHG)
rarr mHG signal strongly depends on the density of emitters
(SHG THG)
Intrinsic 2PEFSHG signals in cells and tissues
SHG = coherent second-ordernonlinear signal
no centrosymmetrySHG prop (density)2
rArr Dense and orderedmacromolecular structures
Zipfel et al (2003) PNAS 100 7075 (2003)
ldquoLive tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and SHGrdquo
- collagen fibrils
- sarcomeres
- astroglial fibers
- polarized microT bundles
cellulose starch hellip
Myofilaments = endogenous SHG source
Myocytes(Frog heart)
Boulesteix et al (2004) Opt Lett
Plot
niko
vet
al (
2006
) Bio
phys
J
SHG imaging of muscle structures
23 s acquisition
Applications sarcomere contraction measurements study of myogenesis
4 6 80
20
40
60
SHG
sig
nal (
phot
ons)
Length (microm)
sarcomere
constant variable
Saxitoxin (8 nM) 214 plusmn 002 microm
Control 231 plusmn 002 microm
rArr contracture at rest 7
N = C
R -O
H R
Possible molecularorigin the dense (crystalline) packingof peptide bonds such as amide group
Collagen triple-helix
Fibrils
Fibers
Macromolecular Organization
SHG is obtained from fibrillar collagen
SHGis observed
No SHG
Collagen I II III V XI hellip form fibrils
Collagen IV VIII X hellip form networks
rarr SHG = probe of macromolecular structuration
50 nm
Combined 2PEFSHG imaging of intact tissue
2PEFelastin
lamellae
SHGcollagenfibrils
Unstained carotid artery (Rat)λexc= 860nm
Boulesteix et al (2006) Cytometry A 69
yz
x
yz
x
yz
x
yz
x
yz
x
yz
x
yz
x
x
y
x
y
Lumen
Media
Intima
Adventitia
Endothelial cellsInternal elasticlamella
External elasticlamella
Fibroblast
Smoothmuscle cell
3D microscopy in a biological tissue Diffraction-limited rArr relies on unscattered light
Howeverhellip visible light is strongly scattered in tissues
scattered photons
ballistic photons
DefScattering mean free path (Ls)= average distance between 2 scattering events (50-100 microm in biological tissues for visible light)
z
N0
N0 exp(-zLs) tissue
The number of ldquoballistic photonsrdquodecays exponentially with z
Ls
Confocal microscopy in scattering medium
bull Scattering of non-focal fluorescencebull Scattering of excitation light and of
focal fluorescence
rarr backgroundrarr signal attenuation
(focal point must be imaged on detector)
ExcitationFluoresc
Bbackground
(surface)
S
z
log (S+B)
transparentscattering
z
rArr Scattering limits imaging depthZmax ~ 50-150 microm
nonlinear excitation
F prop I 2PEF prop I2
1PEF1 photon excited
fluorescence
2PEF2 photon excited
fluorescence
Nonlinear (=multiphoton) microscopy
exci
tatio
n(v
isib
le)
exci
tatio
n(IR
)
[+] preserves sub-cellular resolutioninside scattering medium
ExcitationFluorescence
near IR λ excitation rarr better penetration
scattered IR produce ldquonordquo fluorescencerarr reduced background
2PEF microscopy in scattering medium
[+] Excitation is localized in 3Drarr reduced photoxicity
Zipf
elamp
Web
b (C
orne
ll U
niv)
linear nonlinear
S prop I2 (or I3)rArr excitationis confined
S prop I prop 1z2
rArr excitationis not confined ( )222 vuI
PSF =
Near-IR excitation λ asymp 07-12 microm[+] Reduced perturbabtion[+] Enhanced penetration in tissues
02 04 06 08 10 12 14 16 18 2001
1
10
100
Abs
orpt
ion
coef
ficie
nt (c
m-1)
Wavelength (microm)
Water (pure)Fat (pure)Hb02 (1mM)Hb (1mM)Melanin (1mM)Tryptophan (1mM)
Near-IR excitation reduces absorption and scattering laquo transparence window raquo of tissues
http
om
lco
gie
du
04 05 06 07 08 09 10 11 120
200
400
600
800
1000
1200
1400
Scat
terin
g co
effic
ient
(cm
-1)
Wavelength (microm)
confocal
2PEF SHGTHG
Multiphoton excitation tissue optics
Scattering mean free path (Ls) = average distance between 2 scattering events
Ls
g asymp 1 forward scatteringg asymp 0 isotropic scattering
θθcos=g
~100-200microm for λ asymp 07-12 microm
Scattering anisotropy
Biological tissues g ~ 08 ndash 095
F prop I
1PEF1 photon excited
fluorescence
exci
tatio
n(v
isib
le)
Zipf
elamp
Web
b (C
orne
ll U
niv)
linear nonlinear
S prop I2 (or I3)rArr excitationis confined
S prop I prop 1z2
rArr excitationis not confined
( )222 vuIPSF =
nonlinear excitation
2PEF SHG prop I2
2PEF2 photon excited
fluorescence
SHGsecond-harmonic
generation
THG prop I3
THGthird-harmonic
generation
CARScoherent anti-Stokes Raman
scattering
ωP ωSex
cita
tion
(IR)
CARS prop IP2 IS
[+] Several possible contrastmechanisms rarr different information
2PEF fluorescence SHG non-centrosymetryTHG χ(3) heterogeneitiesCARS vibration resonancehellip
[+] More robust in the presence of incoherent scattering (inside tissues)
2PEF penetration
100-600 microm
[+] Excitation is localized in 3Drarr reduced photoxicity
Nonlinear (=multiphoton) microscopies
g
e
g
e
Eeg
σabs asymp 10-16cm2 σ2p-abs asymp 10-49 cm4 sphoton
Usual unit Goumlppert-Mayer(1 GM = 10-50 cm4 sphoton)
1 event s 1 event 10 million years
Standard molecule in bright daylight
1-photon 2-photon
Absorption cross-section
Note Focusing a 1mm2 beam to a 1microm2 area increases the intensity squared by a factor (106)^2 rarr still not enough to enable rapid imaging (2-10 micros pixel dwell time) with such small cross-sections
22PEF2
12
2PEF21
p IτTσI
τTσ
TτF
TτF ⎟
⎠⎞
⎜⎝⎛=⎟
⎠⎞
⎜⎝⎛==
pI
Fluorescence during pulse
Averagefluorescence
laquo gain raquo Tτ
TiSaph laser
gain asymp 105T asymp 10 ns(100 MHz)τ asymp 100 fs
Gain with pulsed excitation
τ asymp 10-13 s T asymp 10-8 s
Pulsed lasers are used for optimal multiphoton excitation with minimal average power
time
pulses are typically τ ~100 femtoseconds FWHM
2P fluorescence depends on the average squared intensity (rather than on )2I ( )2I
Example withsquare pulses
Fp = frac12 σ2PEF Ip2 σ2PEF equiv η σ2p-abs (η radiative quantum efficiency)
More generally for pulsed excitation
( )22 IIτTgP= with gP depending on temporal shape
(066 for a Gaussian pulse shape)
( )22 II = second-order temporal coherence
wr
wz
2PEF cross-section orders of magnitude
σ2PEF = η σ2p-abs ~ 10-48 cm4 sphoton
202PEF2
10 IσF τ= T
20
0π
P2Iw
=
θω
ω
sinnλ032
=rw
)cos-(1nλ530
z θ=
ω
ωw
wr wz radius at 1e
NA2λ
asymp
2NAλn13
asymp
zr ww22
3
2πV ⎟
⎠⎞
⎜⎝⎛=
PSF (point spread
function)
Focal volume Gaussian-shape fit to
diffraction theory
Typically 2 microm times 04 microm
Usual unit Goumlppert-Mayer(1 GM = 10-50 cm4 sphoton)
Example one molecule in focus
bull P = 1 mW asymp 1015 photonss224 cm sphotons10asymp
sphotons105asymp
bull σ2PEF = 100 GM
λ=1 μm n=13 NA=1 σ2PEF=100 GM
C=1 μM rarr N=1000 molecules
rarr F ~ 2 times 107 photonss
Example 2 several molecules
CVγIσF 202PEF2
1τ= T
average fluorescence produced by one molecule
in excitation volume
pulsed excitation
2PEF microscopy implementation(source scanning objective dispersion compensation)
700-1200 nm~80 MHz~100 fs
source
No need to produce a descanned image of the the focal spot on a spatial filter simpler than a confocal microscope (except for the laser source)
LASER
Beam scanning
Laser in
Laser
out
Point Scanning
to microscope
Δt
Typical pixel time ~2-10 micros (100-400 kHz)Typical line duration ~1 ms (1 kHz)Typical image acq time ~05-2 s
Some methods for faster scanningbull X-axis resonant scanning
http
pa
rker
lab
bio
ucie
du
128 micros
sinusoidalx-scan
pixel clockline sync
y-scan
frame sync66 ms
laser
y-galvo
32-sidedpolygon
obj
telescope1
tele
scop
e2
PMTbull X-axis polygon mirror
These 2 approaches canbe used to record images
at video rates
Limitation signal level
Multipoint excitation canalso be used in certain
cases
http
ce
llser
vm
edy
ale
edu
imag
ing
Dureacutee de vie ~ 1ns
photonss 10F 9max lt
Autres facteursbull Photoblanchimentbull Photo-ionisation bull laquo inter-system crossing raquo
10 ns
100 fs ltlt 1 ns
(limiteacute par la moleacutecule)
photonss 10F 8max lt
(taux de reacutepeacutetition de lrsquooscillateur)
1 photon de fluorescence max par molecule par
impulsion
Facteurs limitant le niveau de signal
M B
lanc
hard
-Des
ce(U
niv
Ren
nes I
)
Engineered fluorophores with enhanced 2PEF
2PEF action cross-sections
10-100 GMldquoQuantum dotsrdquo
104 GM
Endogenous fluorophores (NADH etc)
Standard fluorophores (Rhodaminehellip) 01-10 GM
10-3 - 10-1 GM
Fluorescent proteins (GFP etc)
100-1000 GMZi
pfel
Web
b (C
orne
llU
niv
)
Example 150 fs rarr (5000 fs2) rarr 177 fs80 fs rarr (5000 fs2) rarr 190 fs10 fs rarr (5000 fs2) rarr ~1 ps 80 fs rarr (20000 fs2) rarr 697 fs150 fs rarr (20000 fs2) rarr 403 fs
Dispersion of optics in a multiphoton microscope 2000-20000 fs2
Implementation prism pairs gratings chirped mirrors SLM-based pulse shaper
( )2200 2ln41 τϕττ primeprime+=Pulse broadening
τ0 = initial duration (transform-limited pulse)φrsquorsquo = group delay dispersion (fs2)
Dispersion compensation
In practice compensation is necessary mostly for pulses ltlt 100 fs
Note1 2PEF imaging is typically done with 100fs pulsesShort pulses are interesting for spectroscopy (next lesson) but may induce additional toxicityNote2 managing 10fs pulses at the focus of high NA objective is not trivial Radially varying group delay can be a few 10s fs in some objectives
2PEF prop 1τ
PSF degradation example for aqueous sample
60times NA 12water immersion
40times NA 13oil immersion
rarr Use water-immersion objectives (index matching)
PSFz PSFz
Index mismatch cause PSF spreading and signal loss
Diaspro Ed Confocal and 2P Microscopy Foundations Applications and Advances (2001)Jacobsen Hell et al Refractive-index-induced aberrations in 2P confocal fluorescence microscopy J Microsc 176 226 (1995)Booth amp Wilson ldquoRefractive-index-mismatch induced aberrations in single-photon and 2P microscopyrdquo J Biomed Opt 6 266 (2001)
For small aberrations
( ) ( )2221 ΔΦminusasymp λπrefaber II
mean-square deformationof the wave front
( )2ΔΦ
rarr rapid impact on NL signal
Incidence on signal level
NeuroscienceYuste Denk (1995) Dendritic spines as basic functional units of neuronal integration Nature 375 682-684Svoboda Tank Denk (1996) Direct measurement of coupling between dendritic spines and shafts Science 272 716-719Svoboda Denk Kleinfeld Tank (1997) In vivo dendritic calcium dynamics in neocortical pyramidal neurons Nature 385 161-5
2PEF microscopy in biology some fields of application
Immunology
Developmental biology
ReviewsSvoboda amp Yasuda (2006) Principles of 2P excitation microscopy and its applications to neuroscience Neuron 50 823-839Mertz (2004) Nonlinear microscopy new techniques and applications Curr Opin Neurobiol 14 610-616
ReviewCalahan MD amp Gutman GA (2006) The sense of place in the immune system Nat Immunol 7 329-332
McMahon A Supatto W Fraser SE and Stathopoulos A (2008) Dynamic analyses of Drosophila gastrulation provide insights into collective cell migration Science 3221546-50
laserTiSaphir
rarr 400 μm
50 microm
Application example in neurosciences in vivo 2PEF imaging of an olfactory neuron
50 microm
S C
harp
ak e
t al
PNA
S 98
123
0 (2
001)
Les PA spontaneacutes enregistreacutes dans le soma (trace du bas) induisent des entreacutees de calcium dans le bouquet dendritique
Pb marquage cellules multiples rarr marqueurs geacuteneacutetiques agrave base de proteacuteines fluorescentesex laquo cameleons raquo (constructions 2XFPs+cmd sensibles au calcium) etc
[Ca2+]i imaging
S C
harp
ak e
t al
Ner
urop
hysi
olog
ieet
nou
velle
s mic
rosc
opie
s (I
NSE
RM
-Par
is V
)
Nat
Met
h 2
932
200
5
100microm Chl
omel
eon
Prot
ein
(sen
stiv
eto
chl
orid
e io
ns)
mou
se n
eoco
rtex
Hel
mch
enet
al
(200
5) N
at M
eth
2 9
32-9
40
Two-photon-excited fluorescence (2PEF)
[+] Genetically encoded probes fluorescent proteins (GFPhellip)
Nonlinear microscopy of tissues 2PEF
GFP
~ns
700-
1000
nm
350-
600+
nm
Some important fields of application of 2PEF microscopy
Neurosciences in vivo neuronal activityImmunology lymphocyte trafficking
GFP labeling of nuclei
2PEF λ=920 nm 2 simage 10 mW 1 image every 30 s
100 microm
yolk
vitelline membrane
nucleilipid droplets
Live embryo imaging 2PEF microscopy
Supatto et al (2005) PNASSquirrell et al (1999) Nat Biotechnol
LOB Polytechnique Curie
GFP labeling of nuclei
2PEF λ=920 nm
Live embryo imaging 2PEF microscopy
Caltech bioimaging centerMcMahon Supatto et al (2008) Science
Example quantitative study of individualcollective cell motions in a developing embryo
1 XYZ image every 10s
z
LOB Polytechnique Curie
[+] Endogenous fluorescents species
elastin(rat artery wall fresh)
Bou
lest
eix
et a
l (2
006)
C
ytom
etry
69A
~ns
700-
1000
nm
350-
600+
nm
Two-photon-excited fluorescence (2PEF)
Nonlinear microscopy of tissues 2PEF
Mouse ear skin
(fresh)
Excitation 720nm 800nm 900nm Detection 350-505 505-560 560-650 + spectral unmixing
Note NADH fluorescence is an
indicator of metabolic state
Rad
osev
itch
Hill
man
et a
l (2
008)
O
pt L
ett
33 2
164
NADH fluorescent NAD+ non-fluorescent
zmax
P0
( ))ex(s0 LzexpP minus
z
( )[ ] ( )zLzPTS exs Φsdotminussdotprop
2)(0 expτ
Signal
excitation detection
typically ~500 μm(layer 23 neocortex)
α - fluorophore efficiencyand detector noise
tissue scattering length average laser power
Φ - collected fraction of the generated fluorescence
inverse laser duty cycle
( )τα )(ln max)(
max TzPLz exs Φ=
Rat brain Ls~200microm
If limited by detector noise (no background)
zmax~50-200 μm with endogenous signals
What limits the imaging depthConfined excitation even in scattering media hellip but the number of ballistic excitation photons decreases exponentially with depth
PNAS 98 1230 (2001)
( )τα )(ln max)(
max TzPLz exs Φ=
A How to increase collection efficiency (Φ)
How to increase imaging depth
zmax
( )( )221 cos1
NA
NA
α
α
prop
minus=Φ
αNA
(1) first idea increase NA
This workshellip
Field-of-view (FOV)
(2) hellipbut what if sample is scattering
Scattered fluorescence seemsto originate from an
extended source
Field of view (related to the angular acceptance of the detection path) defines the depth where collection efficiency starts to drop
At large depths (diffusive light)
Oheim et al (2001) J Neurosci Meth 112 205Beaurepaire amp Mertz (2002) Appl Opt 41 5376
An objective with low magnification and high NA is advantageous for collecting scattered fluorescence
( ) 22 minussdotpropΦ zrFOV
Typical multiphoton microscope
laquo non-descanned raquo detection(close to objective)
700-1200 nm~80 MHz~100 fs
source
Diaspro et al (2006) Biomed Eng online
B
A
TiSapph
Reg Amp
z rarr
z rarr
T τ ~ 1times105
T τ ~ 4times107
fmax rTS
fmax rRA
Δz asymp ln(rTSrRA)2 asymp 2-3 scattering lengths Δz
rTS = 80 MHz
rRA = 200 kHz
log F
log FTemporal redistribution of the
same excitation power
At large depths contrast (amp resolution)
loss
hellip in vivoexperiment
( )2balscat II +
Theer amp Denk (2006) JOSA A 23 3139
2PEF imaging depth fundamental limit
Note Zmax increases with staining heterogeneity Zmax is increased by ~Ls when stained fraction is reduced 6times
Zmax reached when
( ) intint ge+focusat
balfocusofout
balscat III 22
Contribution of the different planes Model accounting for the temporal distribution of scattered light and assuming that scattering is mostly forward-directed
Influence of pulse duration rarr Using pulse duration of 20fs instead of 200fs should increase the SB ratio by 25times resulting in an increase of 05 scattering MFP to the depth limit
( )τα )(ln max)(
max TzPLz exs Φ=
How to increase imaging depth
zmax
bull Regenerative amplification multiplies Tτ by 400rarr Equivalent to multiplying P by 20
bull Implement wavefront correction to correct for specimen-induced aberrations (adaptive optics)
bull Design background rejection schemes to remove light generated out-of-focus when doing large depth imaging
B Improving excitation
bull Low mag objective multiplies Φ by 10(Only equivalent to multiplying P by 3)
bull And always non-descanned detection
A Improving collection Φ
Theer amp Denk OL2003
2PEF from a thin fluorescent slab as a function of slab defocus Ratio betweensignal detected with an unaberrated and an aberrated phase
2PEF images of a labeled glomerulus (from mouse olfactory bulb)
Wavefront correction in microscopy
Φ-Φ
Φ
Possible strategiesMeasure aberrated wavefront with wavefront sensor rarr implementation eg Denk PNAS 2006
Iterative sensorless approach with merit functioneg Wright et al OE 2007 (applied to CARS)
Model-based sensorless approach eg Deacutebarre Botcherby Booth Wilson OE 2008 (applied to structured illumination microscopy)
reference
astronomy ophtalmology microscopy
For small aberrations
( ) ( )2221 ΔΦminusasymp λπrefaber II
mean-square deformationof the wave front
( )2ΔΦ
rarr rapid impact on NL signal
LOB
-X
low-coherence interferometry+ wave-front sensing
4 images (I1hellipI4) recorded with reference path length shifts of 0 λ4 λ4 and 3λ4 For each pixel a complex amplitude A is calculated by
Reference
Sample
Low-coherence sourceTiS 915nm 100fs
CCD
( ) ( ) ⎟⎠⎞⎜
⎝⎛ ΔΔminus++=
22ln2expcos τνπδϕsrsrD iiiiI
z-resolution ~ 20 micromνΔ FWHM of source power spectral density
νΔprop 1
δϕ applied phase shift
τΔ delay due to path difference
+ ldquocompatiblerdquo with 2PEF microscopy
obj
(conjug with objective back focal plane)
Feieraband et al (2004) Opt Lett 29 2255Ruumlckel et al (2006) PNAS 103 17137Ruumlckel et al (2007) JOSA A 25 3517
δϕ
τΔ
6times 2PEF signal improvement
(2006) PNAS 103 17137
1P excitation 2P excitation
2PEF SHG prop I2
2PEF SHG
3PEF THG prop I3
excitation(IR)
F prop I
Fluoexcitation(visible) ωP ωS
3P excitation
3PEF
CARS prop IP2 IS
THG CARS
Different contrast mechanisms rarr different information
In particular SHG second harmonic generation ndash sensitive to symmetry at the sub-microm scaleTHG third harmonic generation ndash detects interfaces and microm-size inclusionsCARS laquononlinear Ramanraquo ndash chemical specificity
SHG THG specifically obtained from certain structures(little spectroscopic information)
Alternative contrast modes SHG THG CARS
E(ω) P(ω)
E(ω)
P(ω)
P(3ω)
SHG
THG
P(2ω)
Harmonic signal depends on the nature of the emitting medium
P(2ω)=frac12χ(2)(minus2ωωω) E(ω)E(ω)P(3ω)=frac14χ(3)(minus3ωωωω) E(ω)E(ω)E(ω)
Nonlinear microscopy harmonic generation
P = P(ω) + P(2)(2ω) + middot middot middot + P(n)(nω)= PL + PNL
avec P(n)(nω) =
Polarisable medium excited by an intense field components of order ngt1 in the induced polarization
rarr Emission at harmonic frequencies (nonlinear scattering)
non zero χ(2) =gt non centrosymmetric mediumχ(3) non zero everywhere (but weak)
Multiphoton microscope rarr combined contrast modes
2PEFsignal
SHGsignal
Osc
illato
r
THGsignal
Example of push-pull laquo harmonophore raquo molecule for SHG
(SHG)
Example stylbene derivative
hellip and amphiphilic version (for lipid membrane labeling)
M Blanchard-Desce (Univ Rennes)
SHG = coherent process (ne 2PEF)rarr possibility of constructive and destructive interferences
Example (labeled vesicle) parallel molecules rarr SHG
antiparallel molecules rarr no SHG (centrosymmetric medium)
Mertz amp Moreaux OL 2001
Constructive interference rarr enhanced signal Destructive interfeacuterence rarr null signal
Molecules emitting in phase Molecules emitting with opposite phases
ϕ1 = 0
ϕ2 = 0
ϕ1 = 0
ϕ2 = π
SHG
SHG
Excitation2PEF
Note in contrast 2PEF emission does not
depend on symmetry
SHG microscopy adapted for
membrane imaging
hellipand some endogenousstructures (see later)
Mor
eaux
Mer
tz e
t al
Bio
phys
J 8
0 1
568
(200
1)
SHG 2PEF
Wavelength (nm)400 450 500 550 600 650
Pow
er (a
u)
00
05
10
430 435 440 445 450
SH
G P
ower
(au
)
00
05
10
fluorescence
SHG
Spectrum radiated from a GUV labeledwith the styryl dye Di-6-ASPBS
Phase matching in (coherent) nonlinear optics
zLc
If Δkne0 (dispersion) I2ω(z) prop sin2Δkz2coherent signal buildup is limited to Lc
If Δk=0 (phase-matching case) I2ω(z) prop z2
Δk = k2ω - 2kω = wave vector mismatch
laquoClassicalraquo example SHG by plane wave propagating in a nonlinear medium
Note if Δkne0 phase-matching
can be forced in a birefringent crystal eg
where ne(2ω)ltno(ω)
keθ(2ω)=2ko(ω)neθ(2ω)=2no(ω)
The same applies for other NL processes
such as THG
Lc = coherence length
But what happens in a tightly focused geometry
bull Presence of transverse componentsbull Many possible k
kω = 2π nω λ
I Field near focus from arbitrary pupil profile (Cf Richards amp Wolf 1959 Born amp Wolf 1980)
III Far-field signal (Cf Novotny amp Hecht 2006)
II Induced polarization density near focus
For a homogeneous isotropic medium
expressed using Greenrsquos function
Signal generation in coherent NL microscopy
Example for THG
Solve wave equation taking into account NL polarizations created at various locations in the focal volume + coherent superposition in the detector plane
( )int int ΘΦΘpropmax
0
2
0
22(det) sinα π
RREFFddPDetected power
Field near focus phase distribution
Phase anomaly of focused beams (Gouy phase)LG Gouy CR Acad Sciences Paris 1890
Intensity near focus
minusπ (Gouy shift)
0Phase near focus
Cal
culN
Oliv
ier (
LOB
)
Approximation of tightly focused field for modeling nonlinear interactions GaussianGaussian amplitude and reduced axial wave vector
( ) xexp 2
2
2
22
⎟⎟⎠
⎞⎜⎜⎝
⎛minusminus
+minusminusasymp zki
wz
wyxiEzyxE
zrωωω ξ
wr wz 1e radii of the focal ellipse
2221 rwkωξ minusasymp
CfM
orea
ux S
andr
e M
ertz
(200
0) J
OSA
B 1
7 1
685
For a linearly x-polarized beam near focus
z (nm)
z
ωξ k
2 Iξ
ωω πω nk 2=
880nm NA=09
ω 2ω
0
-πPha
se a
nom
aly
Axial direction
)(cos 1 ξθ minus=slope prop (ξminus1)
Normalized intensitysquared
SHG from a labeled membrane Gouy shift deflects emission off-axis
θ
k2ω
ξ kω ξ kω
(ξlt1)
Mertz Moreaux et al (2001) Biophys J
Sample and field structure govern emission diagrams
emax asymp 06w0
Exemple of coherence effectobservation of SHG laquo hot spots raquo whenlabeled vesicules are in close proximity
Possible application sub-microm distance
measurement
Mertz Moreaux et al (2001) Biophys J
⎟⎟⎠
⎞⎜⎜⎝
⎛Θasymp
PEF
mHG
PEF
mHG NPP
22 σσ
N number of radiating molecules
Θ parameter describing signal reduction due to the sub-micrometer arrangement of the emitters within the focal volume (typ 10-2 for SHG)
222 INP PEFPEF σprop
Signal level in 2PEFmHG imaging
mmHGmHG INP σ2 Θprop
~ 10-4
(pour SHG)
rarr mHG signal strongly depends on the density of emitters
(SHG THG)
Intrinsic 2PEFSHG signals in cells and tissues
SHG = coherent second-ordernonlinear signal
no centrosymmetrySHG prop (density)2
rArr Dense and orderedmacromolecular structures
Zipfel et al (2003) PNAS 100 7075 (2003)
ldquoLive tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and SHGrdquo
- collagen fibrils
- sarcomeres
- astroglial fibers
- polarized microT bundles
cellulose starch hellip
Myofilaments = endogenous SHG source
Myocytes(Frog heart)
Boulesteix et al (2004) Opt Lett
Plot
niko
vet
al (
2006
) Bio
phys
J
SHG imaging of muscle structures
23 s acquisition
Applications sarcomere contraction measurements study of myogenesis
4 6 80
20
40
60
SHG
sig
nal (
phot
ons)
Length (microm)
sarcomere
constant variable
Saxitoxin (8 nM) 214 plusmn 002 microm
Control 231 plusmn 002 microm
rArr contracture at rest 7
N = C
R -O
H R
Possible molecularorigin the dense (crystalline) packingof peptide bonds such as amide group
Collagen triple-helix
Fibrils
Fibers
Macromolecular Organization
SHG is obtained from fibrillar collagen
SHGis observed
No SHG
Collagen I II III V XI hellip form fibrils
Collagen IV VIII X hellip form networks
rarr SHG = probe of macromolecular structuration
50 nm
Combined 2PEFSHG imaging of intact tissue
2PEFelastin
lamellae
SHGcollagenfibrils
Unstained carotid artery (Rat)λexc= 860nm
Boulesteix et al (2006) Cytometry A 69
yz
x
yz
x
yz
x
yz
x
yz
x
yz
x
yz
x
x
y
x
y
Lumen
Media
Intima
Adventitia
Endothelial cellsInternal elasticlamella
External elasticlamella
Fibroblast
Smoothmuscle cell
F prop I
1PEF1 photon excited
fluorescence
exci
tatio
n(v
isib
le)
Zipf
elamp
Web
b (C
orne
ll U
niv)
linear nonlinear
S prop I2 (or I3)rArr excitationis confined
S prop I prop 1z2
rArr excitationis not confined
( )222 vuIPSF =
nonlinear excitation
2PEF SHG prop I2
2PEF2 photon excited
fluorescence
SHGsecond-harmonic
generation
THG prop I3
THGthird-harmonic
generation
CARScoherent anti-Stokes Raman
scattering
ωP ωSex
cita
tion
(IR)
CARS prop IP2 IS
[+] Several possible contrastmechanisms rarr different information
2PEF fluorescence SHG non-centrosymetryTHG χ(3) heterogeneitiesCARS vibration resonancehellip
[+] More robust in the presence of incoherent scattering (inside tissues)
2PEF penetration
100-600 microm
[+] Excitation is localized in 3Drarr reduced photoxicity
Nonlinear (=multiphoton) microscopies
g
e
g
e
Eeg
σabs asymp 10-16cm2 σ2p-abs asymp 10-49 cm4 sphoton
Usual unit Goumlppert-Mayer(1 GM = 10-50 cm4 sphoton)
1 event s 1 event 10 million years
Standard molecule in bright daylight
1-photon 2-photon
Absorption cross-section
Note Focusing a 1mm2 beam to a 1microm2 area increases the intensity squared by a factor (106)^2 rarr still not enough to enable rapid imaging (2-10 micros pixel dwell time) with such small cross-sections
22PEF2
12
2PEF21
p IτTσI
τTσ
TτF
TτF ⎟
⎠⎞
⎜⎝⎛=⎟
⎠⎞
⎜⎝⎛==
pI
Fluorescence during pulse
Averagefluorescence
laquo gain raquo Tτ
TiSaph laser
gain asymp 105T asymp 10 ns(100 MHz)τ asymp 100 fs
Gain with pulsed excitation
τ asymp 10-13 s T asymp 10-8 s
Pulsed lasers are used for optimal multiphoton excitation with minimal average power
time
pulses are typically τ ~100 femtoseconds FWHM
2P fluorescence depends on the average squared intensity (rather than on )2I ( )2I
Example withsquare pulses
Fp = frac12 σ2PEF Ip2 σ2PEF equiv η σ2p-abs (η radiative quantum efficiency)
More generally for pulsed excitation
( )22 IIτTgP= with gP depending on temporal shape
(066 for a Gaussian pulse shape)
( )22 II = second-order temporal coherence
wr
wz
2PEF cross-section orders of magnitude
σ2PEF = η σ2p-abs ~ 10-48 cm4 sphoton
202PEF2
10 IσF τ= T
20
0π
P2Iw
=
θω
ω
sinnλ032
=rw
)cos-(1nλ530
z θ=
ω
ωw
wr wz radius at 1e
NA2λ
asymp
2NAλn13
asymp
zr ww22
3
2πV ⎟
⎠⎞
⎜⎝⎛=
PSF (point spread
function)
Focal volume Gaussian-shape fit to
diffraction theory
Typically 2 microm times 04 microm
Usual unit Goumlppert-Mayer(1 GM = 10-50 cm4 sphoton)
Example one molecule in focus
bull P = 1 mW asymp 1015 photonss224 cm sphotons10asymp
sphotons105asymp
bull σ2PEF = 100 GM
λ=1 μm n=13 NA=1 σ2PEF=100 GM
C=1 μM rarr N=1000 molecules
rarr F ~ 2 times 107 photonss
Example 2 several molecules
CVγIσF 202PEF2
1τ= T
average fluorescence produced by one molecule
in excitation volume
pulsed excitation
2PEF microscopy implementation(source scanning objective dispersion compensation)
700-1200 nm~80 MHz~100 fs
source
No need to produce a descanned image of the the focal spot on a spatial filter simpler than a confocal microscope (except for the laser source)
LASER
Beam scanning
Laser in
Laser
out
Point Scanning
to microscope
Δt
Typical pixel time ~2-10 micros (100-400 kHz)Typical line duration ~1 ms (1 kHz)Typical image acq time ~05-2 s
Some methods for faster scanningbull X-axis resonant scanning
http
pa
rker
lab
bio
ucie
du
128 micros
sinusoidalx-scan
pixel clockline sync
y-scan
frame sync66 ms
laser
y-galvo
32-sidedpolygon
obj
telescope1
tele
scop
e2
PMTbull X-axis polygon mirror
These 2 approaches canbe used to record images
at video rates
Limitation signal level
Multipoint excitation canalso be used in certain
cases
http
ce
llser
vm
edy
ale
edu
imag
ing
Dureacutee de vie ~ 1ns
photonss 10F 9max lt
Autres facteursbull Photoblanchimentbull Photo-ionisation bull laquo inter-system crossing raquo
10 ns
100 fs ltlt 1 ns
(limiteacute par la moleacutecule)
photonss 10F 8max lt
(taux de reacutepeacutetition de lrsquooscillateur)
1 photon de fluorescence max par molecule par
impulsion
Facteurs limitant le niveau de signal
M B
lanc
hard
-Des
ce(U
niv
Ren
nes I
)
Engineered fluorophores with enhanced 2PEF
2PEF action cross-sections
10-100 GMldquoQuantum dotsrdquo
104 GM
Endogenous fluorophores (NADH etc)
Standard fluorophores (Rhodaminehellip) 01-10 GM
10-3 - 10-1 GM
Fluorescent proteins (GFP etc)
100-1000 GMZi
pfel
Web
b (C
orne
llU
niv
)
Example 150 fs rarr (5000 fs2) rarr 177 fs80 fs rarr (5000 fs2) rarr 190 fs10 fs rarr (5000 fs2) rarr ~1 ps 80 fs rarr (20000 fs2) rarr 697 fs150 fs rarr (20000 fs2) rarr 403 fs
Dispersion of optics in a multiphoton microscope 2000-20000 fs2
Implementation prism pairs gratings chirped mirrors SLM-based pulse shaper
( )2200 2ln41 τϕττ primeprime+=Pulse broadening
τ0 = initial duration (transform-limited pulse)φrsquorsquo = group delay dispersion (fs2)
Dispersion compensation
In practice compensation is necessary mostly for pulses ltlt 100 fs
Note1 2PEF imaging is typically done with 100fs pulsesShort pulses are interesting for spectroscopy (next lesson) but may induce additional toxicityNote2 managing 10fs pulses at the focus of high NA objective is not trivial Radially varying group delay can be a few 10s fs in some objectives
2PEF prop 1τ
PSF degradation example for aqueous sample
60times NA 12water immersion
40times NA 13oil immersion
rarr Use water-immersion objectives (index matching)
PSFz PSFz
Index mismatch cause PSF spreading and signal loss
Diaspro Ed Confocal and 2P Microscopy Foundations Applications and Advances (2001)Jacobsen Hell et al Refractive-index-induced aberrations in 2P confocal fluorescence microscopy J Microsc 176 226 (1995)Booth amp Wilson ldquoRefractive-index-mismatch induced aberrations in single-photon and 2P microscopyrdquo J Biomed Opt 6 266 (2001)
For small aberrations
( ) ( )2221 ΔΦminusasymp λπrefaber II
mean-square deformationof the wave front
( )2ΔΦ
rarr rapid impact on NL signal
Incidence on signal level
NeuroscienceYuste Denk (1995) Dendritic spines as basic functional units of neuronal integration Nature 375 682-684Svoboda Tank Denk (1996) Direct measurement of coupling between dendritic spines and shafts Science 272 716-719Svoboda Denk Kleinfeld Tank (1997) In vivo dendritic calcium dynamics in neocortical pyramidal neurons Nature 385 161-5
2PEF microscopy in biology some fields of application
Immunology
Developmental biology
ReviewsSvoboda amp Yasuda (2006) Principles of 2P excitation microscopy and its applications to neuroscience Neuron 50 823-839Mertz (2004) Nonlinear microscopy new techniques and applications Curr Opin Neurobiol 14 610-616
ReviewCalahan MD amp Gutman GA (2006) The sense of place in the immune system Nat Immunol 7 329-332
McMahon A Supatto W Fraser SE and Stathopoulos A (2008) Dynamic analyses of Drosophila gastrulation provide insights into collective cell migration Science 3221546-50
laserTiSaphir
rarr 400 μm
50 microm
Application example in neurosciences in vivo 2PEF imaging of an olfactory neuron
50 microm
S C
harp
ak e
t al
PNA
S 98
123
0 (2
001)
Les PA spontaneacutes enregistreacutes dans le soma (trace du bas) induisent des entreacutees de calcium dans le bouquet dendritique
Pb marquage cellules multiples rarr marqueurs geacuteneacutetiques agrave base de proteacuteines fluorescentesex laquo cameleons raquo (constructions 2XFPs+cmd sensibles au calcium) etc
[Ca2+]i imaging
S C
harp
ak e
t al
Ner
urop
hysi
olog
ieet
nou
velle
s mic
rosc
opie
s (I
NSE
RM
-Par
is V
)
Nat
Met
h 2
932
200
5
100microm Chl
omel
eon
Prot
ein
(sen
stiv
eto
chl
orid
e io
ns)
mou
se n
eoco
rtex
Hel
mch
enet
al
(200
5) N
at M
eth
2 9
32-9
40
Two-photon-excited fluorescence (2PEF)
[+] Genetically encoded probes fluorescent proteins (GFPhellip)
Nonlinear microscopy of tissues 2PEF
GFP
~ns
700-
1000
nm
350-
600+
nm
Some important fields of application of 2PEF microscopy
Neurosciences in vivo neuronal activityImmunology lymphocyte trafficking
GFP labeling of nuclei
2PEF λ=920 nm 2 simage 10 mW 1 image every 30 s
100 microm
yolk
vitelline membrane
nucleilipid droplets
Live embryo imaging 2PEF microscopy
Supatto et al (2005) PNASSquirrell et al (1999) Nat Biotechnol
LOB Polytechnique Curie
GFP labeling of nuclei
2PEF λ=920 nm
Live embryo imaging 2PEF microscopy
Caltech bioimaging centerMcMahon Supatto et al (2008) Science
Example quantitative study of individualcollective cell motions in a developing embryo
1 XYZ image every 10s
z
LOB Polytechnique Curie
[+] Endogenous fluorescents species
elastin(rat artery wall fresh)
Bou
lest
eix
et a
l (2
006)
C
ytom
etry
69A
~ns
700-
1000
nm
350-
600+
nm
Two-photon-excited fluorescence (2PEF)
Nonlinear microscopy of tissues 2PEF
Mouse ear skin
(fresh)
Excitation 720nm 800nm 900nm Detection 350-505 505-560 560-650 + spectral unmixing
Note NADH fluorescence is an
indicator of metabolic state
Rad
osev
itch
Hill
man
et a
l (2
008)
O
pt L
ett
33 2
164
NADH fluorescent NAD+ non-fluorescent
zmax
P0
( ))ex(s0 LzexpP minus
z
( )[ ] ( )zLzPTS exs Φsdotminussdotprop
2)(0 expτ
Signal
excitation detection
typically ~500 μm(layer 23 neocortex)
α - fluorophore efficiencyand detector noise
tissue scattering length average laser power
Φ - collected fraction of the generated fluorescence
inverse laser duty cycle
( )τα )(ln max)(
max TzPLz exs Φ=
Rat brain Ls~200microm
If limited by detector noise (no background)
zmax~50-200 μm with endogenous signals
What limits the imaging depthConfined excitation even in scattering media hellip but the number of ballistic excitation photons decreases exponentially with depth
PNAS 98 1230 (2001)
( )τα )(ln max)(
max TzPLz exs Φ=
A How to increase collection efficiency (Φ)
How to increase imaging depth
zmax
( )( )221 cos1
NA
NA
α
α
prop
minus=Φ
αNA
(1) first idea increase NA
This workshellip
Field-of-view (FOV)
(2) hellipbut what if sample is scattering
Scattered fluorescence seemsto originate from an
extended source
Field of view (related to the angular acceptance of the detection path) defines the depth where collection efficiency starts to drop
At large depths (diffusive light)
Oheim et al (2001) J Neurosci Meth 112 205Beaurepaire amp Mertz (2002) Appl Opt 41 5376
An objective with low magnification and high NA is advantageous for collecting scattered fluorescence
( ) 22 minussdotpropΦ zrFOV
Typical multiphoton microscope
laquo non-descanned raquo detection(close to objective)
700-1200 nm~80 MHz~100 fs
source
Diaspro et al (2006) Biomed Eng online
B
A
TiSapph
Reg Amp
z rarr
z rarr
T τ ~ 1times105
T τ ~ 4times107
fmax rTS
fmax rRA
Δz asymp ln(rTSrRA)2 asymp 2-3 scattering lengths Δz
rTS = 80 MHz
rRA = 200 kHz
log F
log FTemporal redistribution of the
same excitation power
At large depths contrast (amp resolution)
loss
hellip in vivoexperiment
( )2balscat II +
Theer amp Denk (2006) JOSA A 23 3139
2PEF imaging depth fundamental limit
Note Zmax increases with staining heterogeneity Zmax is increased by ~Ls when stained fraction is reduced 6times
Zmax reached when
( ) intint ge+focusat
balfocusofout
balscat III 22
Contribution of the different planes Model accounting for the temporal distribution of scattered light and assuming that scattering is mostly forward-directed
Influence of pulse duration rarr Using pulse duration of 20fs instead of 200fs should increase the SB ratio by 25times resulting in an increase of 05 scattering MFP to the depth limit
( )τα )(ln max)(
max TzPLz exs Φ=
How to increase imaging depth
zmax
bull Regenerative amplification multiplies Tτ by 400rarr Equivalent to multiplying P by 20
bull Implement wavefront correction to correct for specimen-induced aberrations (adaptive optics)
bull Design background rejection schemes to remove light generated out-of-focus when doing large depth imaging
B Improving excitation
bull Low mag objective multiplies Φ by 10(Only equivalent to multiplying P by 3)
bull And always non-descanned detection
A Improving collection Φ
Theer amp Denk OL2003
2PEF from a thin fluorescent slab as a function of slab defocus Ratio betweensignal detected with an unaberrated and an aberrated phase
2PEF images of a labeled glomerulus (from mouse olfactory bulb)
Wavefront correction in microscopy
Φ-Φ
Φ
Possible strategiesMeasure aberrated wavefront with wavefront sensor rarr implementation eg Denk PNAS 2006
Iterative sensorless approach with merit functioneg Wright et al OE 2007 (applied to CARS)
Model-based sensorless approach eg Deacutebarre Botcherby Booth Wilson OE 2008 (applied to structured illumination microscopy)
reference
astronomy ophtalmology microscopy
For small aberrations
( ) ( )2221 ΔΦminusasymp λπrefaber II
mean-square deformationof the wave front
( )2ΔΦ
rarr rapid impact on NL signal
LOB
-X
low-coherence interferometry+ wave-front sensing
4 images (I1hellipI4) recorded with reference path length shifts of 0 λ4 λ4 and 3λ4 For each pixel a complex amplitude A is calculated by
Reference
Sample
Low-coherence sourceTiS 915nm 100fs
CCD
( ) ( ) ⎟⎠⎞⎜
⎝⎛ ΔΔminus++=
22ln2expcos τνπδϕsrsrD iiiiI
z-resolution ~ 20 micromνΔ FWHM of source power spectral density
νΔprop 1
δϕ applied phase shift
τΔ delay due to path difference
+ ldquocompatiblerdquo with 2PEF microscopy
obj
(conjug with objective back focal plane)
Feieraband et al (2004) Opt Lett 29 2255Ruumlckel et al (2006) PNAS 103 17137Ruumlckel et al (2007) JOSA A 25 3517
δϕ
τΔ
6times 2PEF signal improvement
(2006) PNAS 103 17137
1P excitation 2P excitation
2PEF SHG prop I2
2PEF SHG
3PEF THG prop I3
excitation(IR)
F prop I
Fluoexcitation(visible) ωP ωS
3P excitation
3PEF
CARS prop IP2 IS
THG CARS
Different contrast mechanisms rarr different information
In particular SHG second harmonic generation ndash sensitive to symmetry at the sub-microm scaleTHG third harmonic generation ndash detects interfaces and microm-size inclusionsCARS laquononlinear Ramanraquo ndash chemical specificity
SHG THG specifically obtained from certain structures(little spectroscopic information)
Alternative contrast modes SHG THG CARS
E(ω) P(ω)
E(ω)
P(ω)
P(3ω)
SHG
THG
P(2ω)
Harmonic signal depends on the nature of the emitting medium
P(2ω)=frac12χ(2)(minus2ωωω) E(ω)E(ω)P(3ω)=frac14χ(3)(minus3ωωωω) E(ω)E(ω)E(ω)
Nonlinear microscopy harmonic generation
P = P(ω) + P(2)(2ω) + middot middot middot + P(n)(nω)= PL + PNL
avec P(n)(nω) =
Polarisable medium excited by an intense field components of order ngt1 in the induced polarization
rarr Emission at harmonic frequencies (nonlinear scattering)
non zero χ(2) =gt non centrosymmetric mediumχ(3) non zero everywhere (but weak)
Multiphoton microscope rarr combined contrast modes
2PEFsignal
SHGsignal
Osc
illato
r
THGsignal
Example of push-pull laquo harmonophore raquo molecule for SHG
(SHG)
Example stylbene derivative
hellip and amphiphilic version (for lipid membrane labeling)
M Blanchard-Desce (Univ Rennes)
SHG = coherent process (ne 2PEF)rarr possibility of constructive and destructive interferences
Example (labeled vesicle) parallel molecules rarr SHG
antiparallel molecules rarr no SHG (centrosymmetric medium)
Mertz amp Moreaux OL 2001
Constructive interference rarr enhanced signal Destructive interfeacuterence rarr null signal
Molecules emitting in phase Molecules emitting with opposite phases
ϕ1 = 0
ϕ2 = 0
ϕ1 = 0
ϕ2 = π
SHG
SHG
Excitation2PEF
Note in contrast 2PEF emission does not
depend on symmetry
SHG microscopy adapted for
membrane imaging
hellipand some endogenousstructures (see later)
Mor
eaux
Mer
tz e
t al
Bio
phys
J 8
0 1
568
(200
1)
SHG 2PEF
Wavelength (nm)400 450 500 550 600 650
Pow
er (a
u)
00
05
10
430 435 440 445 450
SH
G P
ower
(au
)
00
05
10
fluorescence
SHG
Spectrum radiated from a GUV labeledwith the styryl dye Di-6-ASPBS
Phase matching in (coherent) nonlinear optics
zLc
If Δkne0 (dispersion) I2ω(z) prop sin2Δkz2coherent signal buildup is limited to Lc
If Δk=0 (phase-matching case) I2ω(z) prop z2
Δk = k2ω - 2kω = wave vector mismatch
laquoClassicalraquo example SHG by plane wave propagating in a nonlinear medium
Note if Δkne0 phase-matching
can be forced in a birefringent crystal eg
where ne(2ω)ltno(ω)
keθ(2ω)=2ko(ω)neθ(2ω)=2no(ω)
The same applies for other NL processes
such as THG
Lc = coherence length
But what happens in a tightly focused geometry
bull Presence of transverse componentsbull Many possible k
kω = 2π nω λ
I Field near focus from arbitrary pupil profile (Cf Richards amp Wolf 1959 Born amp Wolf 1980)
III Far-field signal (Cf Novotny amp Hecht 2006)
II Induced polarization density near focus
For a homogeneous isotropic medium
expressed using Greenrsquos function
Signal generation in coherent NL microscopy
Example for THG
Solve wave equation taking into account NL polarizations created at various locations in the focal volume + coherent superposition in the detector plane
( )int int ΘΦΘpropmax
0
2
0
22(det) sinα π
RREFFddPDetected power
Field near focus phase distribution
Phase anomaly of focused beams (Gouy phase)LG Gouy CR Acad Sciences Paris 1890
Intensity near focus
minusπ (Gouy shift)
0Phase near focus
Cal
culN
Oliv
ier (
LOB
)
Approximation of tightly focused field for modeling nonlinear interactions GaussianGaussian amplitude and reduced axial wave vector
( ) xexp 2
2
2
22
⎟⎟⎠
⎞⎜⎜⎝
⎛minusminus
+minusminusasymp zki
wz
wyxiEzyxE
zrωωω ξ
wr wz 1e radii of the focal ellipse
2221 rwkωξ minusasymp
CfM
orea
ux S
andr
e M
ertz
(200
0) J
OSA
B 1
7 1
685
For a linearly x-polarized beam near focus
z (nm)
z
ωξ k
2 Iξ
ωω πω nk 2=
880nm NA=09
ω 2ω
0
-πPha
se a
nom
aly
Axial direction
)(cos 1 ξθ minus=slope prop (ξminus1)
Normalized intensitysquared
SHG from a labeled membrane Gouy shift deflects emission off-axis
θ
k2ω
ξ kω ξ kω
(ξlt1)
Mertz Moreaux et al (2001) Biophys J
Sample and field structure govern emission diagrams
emax asymp 06w0
Exemple of coherence effectobservation of SHG laquo hot spots raquo whenlabeled vesicules are in close proximity
Possible application sub-microm distance
measurement
Mertz Moreaux et al (2001) Biophys J
⎟⎟⎠
⎞⎜⎜⎝
⎛Θasymp
PEF
mHG
PEF
mHG NPP
22 σσ
N number of radiating molecules
Θ parameter describing signal reduction due to the sub-micrometer arrangement of the emitters within the focal volume (typ 10-2 for SHG)
222 INP PEFPEF σprop
Signal level in 2PEFmHG imaging
mmHGmHG INP σ2 Θprop
~ 10-4
(pour SHG)
rarr mHG signal strongly depends on the density of emitters
(SHG THG)
Intrinsic 2PEFSHG signals in cells and tissues
SHG = coherent second-ordernonlinear signal
no centrosymmetrySHG prop (density)2
rArr Dense and orderedmacromolecular structures
Zipfel et al (2003) PNAS 100 7075 (2003)
ldquoLive tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and SHGrdquo
- collagen fibrils
- sarcomeres
- astroglial fibers
- polarized microT bundles
cellulose starch hellip
Myofilaments = endogenous SHG source
Myocytes(Frog heart)
Boulesteix et al (2004) Opt Lett
Plot
niko
vet
al (
2006
) Bio
phys
J
SHG imaging of muscle structures
23 s acquisition
Applications sarcomere contraction measurements study of myogenesis
4 6 80
20
40
60
SHG
sig
nal (
phot
ons)
Length (microm)
sarcomere
constant variable
Saxitoxin (8 nM) 214 plusmn 002 microm
Control 231 plusmn 002 microm
rArr contracture at rest 7
N = C
R -O
H R
Possible molecularorigin the dense (crystalline) packingof peptide bonds such as amide group
Collagen triple-helix
Fibrils
Fibers
Macromolecular Organization
SHG is obtained from fibrillar collagen
SHGis observed
No SHG
Collagen I II III V XI hellip form fibrils
Collagen IV VIII X hellip form networks
rarr SHG = probe of macromolecular structuration
50 nm
Combined 2PEFSHG imaging of intact tissue
2PEFelastin
lamellae
SHGcollagenfibrils
Unstained carotid artery (Rat)λexc= 860nm
Boulesteix et al (2006) Cytometry A 69
yz
x
yz
x
yz
x
yz
x
yz
x
yz
x
yz
x
x
y
x
y
Lumen
Media
Intima
Adventitia
Endothelial cellsInternal elasticlamella
External elasticlamella
Fibroblast
Smoothmuscle cell
2PEF microscopy implementation(source scanning objective dispersion compensation)
700-1200 nm~80 MHz~100 fs
source
No need to produce a descanned image of the the focal spot on a spatial filter simpler than a confocal microscope (except for the laser source)
LASER
Beam scanning
Laser in
Laser
out
Point Scanning
to microscope
Δt
Typical pixel time ~2-10 micros (100-400 kHz)Typical line duration ~1 ms (1 kHz)Typical image acq time ~05-2 s
Some methods for faster scanningbull X-axis resonant scanning
http
pa
rker
lab
bio
ucie
du
128 micros
sinusoidalx-scan
pixel clockline sync
y-scan
frame sync66 ms
laser
y-galvo
32-sidedpolygon
obj
telescope1
tele
scop
e2
PMTbull X-axis polygon mirror
These 2 approaches canbe used to record images
at video rates
Limitation signal level
Multipoint excitation canalso be used in certain
cases
http
ce
llser
vm
edy
ale
edu
imag
ing
Dureacutee de vie ~ 1ns
photonss 10F 9max lt
Autres facteursbull Photoblanchimentbull Photo-ionisation bull laquo inter-system crossing raquo
10 ns
100 fs ltlt 1 ns
(limiteacute par la moleacutecule)
photonss 10F 8max lt
(taux de reacutepeacutetition de lrsquooscillateur)
1 photon de fluorescence max par molecule par
impulsion
Facteurs limitant le niveau de signal
M B
lanc
hard
-Des
ce(U
niv
Ren
nes I
)
Engineered fluorophores with enhanced 2PEF
2PEF action cross-sections
10-100 GMldquoQuantum dotsrdquo
104 GM
Endogenous fluorophores (NADH etc)
Standard fluorophores (Rhodaminehellip) 01-10 GM
10-3 - 10-1 GM
Fluorescent proteins (GFP etc)
100-1000 GMZi
pfel
Web
b (C
orne
llU
niv
)
Example 150 fs rarr (5000 fs2) rarr 177 fs80 fs rarr (5000 fs2) rarr 190 fs10 fs rarr (5000 fs2) rarr ~1 ps 80 fs rarr (20000 fs2) rarr 697 fs150 fs rarr (20000 fs2) rarr 403 fs
Dispersion of optics in a multiphoton microscope 2000-20000 fs2
Implementation prism pairs gratings chirped mirrors SLM-based pulse shaper
( )2200 2ln41 τϕττ primeprime+=Pulse broadening
τ0 = initial duration (transform-limited pulse)φrsquorsquo = group delay dispersion (fs2)
Dispersion compensation
In practice compensation is necessary mostly for pulses ltlt 100 fs
Note1 2PEF imaging is typically done with 100fs pulsesShort pulses are interesting for spectroscopy (next lesson) but may induce additional toxicityNote2 managing 10fs pulses at the focus of high NA objective is not trivial Radially varying group delay can be a few 10s fs in some objectives
2PEF prop 1τ
PSF degradation example for aqueous sample
60times NA 12water immersion
40times NA 13oil immersion
rarr Use water-immersion objectives (index matching)
PSFz PSFz
Index mismatch cause PSF spreading and signal loss
Diaspro Ed Confocal and 2P Microscopy Foundations Applications and Advances (2001)Jacobsen Hell et al Refractive-index-induced aberrations in 2P confocal fluorescence microscopy J Microsc 176 226 (1995)Booth amp Wilson ldquoRefractive-index-mismatch induced aberrations in single-photon and 2P microscopyrdquo J Biomed Opt 6 266 (2001)
For small aberrations
( ) ( )2221 ΔΦminusasymp λπrefaber II
mean-square deformationof the wave front
( )2ΔΦ
rarr rapid impact on NL signal
Incidence on signal level
NeuroscienceYuste Denk (1995) Dendritic spines as basic functional units of neuronal integration Nature 375 682-684Svoboda Tank Denk (1996) Direct measurement of coupling between dendritic spines and shafts Science 272 716-719Svoboda Denk Kleinfeld Tank (1997) In vivo dendritic calcium dynamics in neocortical pyramidal neurons Nature 385 161-5
2PEF microscopy in biology some fields of application
Immunology
Developmental biology
ReviewsSvoboda amp Yasuda (2006) Principles of 2P excitation microscopy and its applications to neuroscience Neuron 50 823-839Mertz (2004) Nonlinear microscopy new techniques and applications Curr Opin Neurobiol 14 610-616
ReviewCalahan MD amp Gutman GA (2006) The sense of place in the immune system Nat Immunol 7 329-332
McMahon A Supatto W Fraser SE and Stathopoulos A (2008) Dynamic analyses of Drosophila gastrulation provide insights into collective cell migration Science 3221546-50
laserTiSaphir
rarr 400 μm
50 microm
Application example in neurosciences in vivo 2PEF imaging of an olfactory neuron
50 microm
S C
harp
ak e
t al
PNA
S 98
123
0 (2
001)
Les PA spontaneacutes enregistreacutes dans le soma (trace du bas) induisent des entreacutees de calcium dans le bouquet dendritique
Pb marquage cellules multiples rarr marqueurs geacuteneacutetiques agrave base de proteacuteines fluorescentesex laquo cameleons raquo (constructions 2XFPs+cmd sensibles au calcium) etc
[Ca2+]i imaging
S C
harp
ak e
t al
Ner
urop
hysi
olog
ieet
nou
velle
s mic
rosc
opie
s (I
NSE
RM
-Par
is V
)
Nat
Met
h 2
932
200
5
100microm Chl
omel
eon
Prot
ein
(sen
stiv
eto
chl
orid
e io
ns)
mou
se n
eoco
rtex
Hel
mch
enet
al
(200
5) N
at M
eth
2 9
32-9
40
Two-photon-excited fluorescence (2PEF)
[+] Genetically encoded probes fluorescent proteins (GFPhellip)
Nonlinear microscopy of tissues 2PEF
GFP
~ns
700-
1000
nm
350-
600+
nm
Some important fields of application of 2PEF microscopy
Neurosciences in vivo neuronal activityImmunology lymphocyte trafficking
GFP labeling of nuclei
2PEF λ=920 nm 2 simage 10 mW 1 image every 30 s
100 microm
yolk
vitelline membrane
nucleilipid droplets
Live embryo imaging 2PEF microscopy
Supatto et al (2005) PNASSquirrell et al (1999) Nat Biotechnol
LOB Polytechnique Curie
GFP labeling of nuclei
2PEF λ=920 nm
Live embryo imaging 2PEF microscopy
Caltech bioimaging centerMcMahon Supatto et al (2008) Science
Example quantitative study of individualcollective cell motions in a developing embryo
1 XYZ image every 10s
z
LOB Polytechnique Curie
[+] Endogenous fluorescents species
elastin(rat artery wall fresh)
Bou
lest
eix
et a
l (2
006)
C
ytom
etry
69A
~ns
700-
1000
nm
350-
600+
nm
Two-photon-excited fluorescence (2PEF)
Nonlinear microscopy of tissues 2PEF
Mouse ear skin
(fresh)
Excitation 720nm 800nm 900nm Detection 350-505 505-560 560-650 + spectral unmixing
Note NADH fluorescence is an
indicator of metabolic state
Rad
osev
itch
Hill
man
et a
l (2
008)
O
pt L
ett
33 2
164
NADH fluorescent NAD+ non-fluorescent
zmax
P0
( ))ex(s0 LzexpP minus
z
( )[ ] ( )zLzPTS exs Φsdotminussdotprop
2)(0 expτ
Signal
excitation detection
typically ~500 μm(layer 23 neocortex)
α - fluorophore efficiencyand detector noise
tissue scattering length average laser power
Φ - collected fraction of the generated fluorescence
inverse laser duty cycle
( )τα )(ln max)(
max TzPLz exs Φ=
Rat brain Ls~200microm
If limited by detector noise (no background)
zmax~50-200 μm with endogenous signals
What limits the imaging depthConfined excitation even in scattering media hellip but the number of ballistic excitation photons decreases exponentially with depth
PNAS 98 1230 (2001)
( )τα )(ln max)(
max TzPLz exs Φ=
A How to increase collection efficiency (Φ)
How to increase imaging depth
zmax
( )( )221 cos1
NA
NA
α
α
prop
minus=Φ
αNA
(1) first idea increase NA
This workshellip
Field-of-view (FOV)
(2) hellipbut what if sample is scattering
Scattered fluorescence seemsto originate from an
extended source
Field of view (related to the angular acceptance of the detection path) defines the depth where collection efficiency starts to drop
At large depths (diffusive light)
Oheim et al (2001) J Neurosci Meth 112 205Beaurepaire amp Mertz (2002) Appl Opt 41 5376
An objective with low magnification and high NA is advantageous for collecting scattered fluorescence
( ) 22 minussdotpropΦ zrFOV
Typical multiphoton microscope
laquo non-descanned raquo detection(close to objective)
700-1200 nm~80 MHz~100 fs
source
Diaspro et al (2006) Biomed Eng online
B
A
TiSapph
Reg Amp
z rarr
z rarr
T τ ~ 1times105
T τ ~ 4times107
fmax rTS
fmax rRA
Δz asymp ln(rTSrRA)2 asymp 2-3 scattering lengths Δz
rTS = 80 MHz
rRA = 200 kHz
log F
log FTemporal redistribution of the
same excitation power
At large depths contrast (amp resolution)
loss
hellip in vivoexperiment
( )2balscat II +
Theer amp Denk (2006) JOSA A 23 3139
2PEF imaging depth fundamental limit
Note Zmax increases with staining heterogeneity Zmax is increased by ~Ls when stained fraction is reduced 6times
Zmax reached when
( ) intint ge+focusat
balfocusofout
balscat III 22
Contribution of the different planes Model accounting for the temporal distribution of scattered light and assuming that scattering is mostly forward-directed
Influence of pulse duration rarr Using pulse duration of 20fs instead of 200fs should increase the SB ratio by 25times resulting in an increase of 05 scattering MFP to the depth limit
( )τα )(ln max)(
max TzPLz exs Φ=
How to increase imaging depth
zmax
bull Regenerative amplification multiplies Tτ by 400rarr Equivalent to multiplying P by 20
bull Implement wavefront correction to correct for specimen-induced aberrations (adaptive optics)
bull Design background rejection schemes to remove light generated out-of-focus when doing large depth imaging
B Improving excitation
bull Low mag objective multiplies Φ by 10(Only equivalent to multiplying P by 3)
bull And always non-descanned detection
A Improving collection Φ
Theer amp Denk OL2003
2PEF from a thin fluorescent slab as a function of slab defocus Ratio betweensignal detected with an unaberrated and an aberrated phase
2PEF images of a labeled glomerulus (from mouse olfactory bulb)
Wavefront correction in microscopy
Φ-Φ
Φ
Possible strategiesMeasure aberrated wavefront with wavefront sensor rarr implementation eg Denk PNAS 2006
Iterative sensorless approach with merit functioneg Wright et al OE 2007 (applied to CARS)
Model-based sensorless approach eg Deacutebarre Botcherby Booth Wilson OE 2008 (applied to structured illumination microscopy)
reference
astronomy ophtalmology microscopy
For small aberrations
( ) ( )2221 ΔΦminusasymp λπrefaber II
mean-square deformationof the wave front
( )2ΔΦ
rarr rapid impact on NL signal
LOB
-X
low-coherence interferometry+ wave-front sensing
4 images (I1hellipI4) recorded with reference path length shifts of 0 λ4 λ4 and 3λ4 For each pixel a complex amplitude A is calculated by
Reference
Sample
Low-coherence sourceTiS 915nm 100fs
CCD
( ) ( ) ⎟⎠⎞⎜
⎝⎛ ΔΔminus++=
22ln2expcos τνπδϕsrsrD iiiiI
z-resolution ~ 20 micromνΔ FWHM of source power spectral density
νΔprop 1
δϕ applied phase shift
τΔ delay due to path difference
+ ldquocompatiblerdquo with 2PEF microscopy
obj
(conjug with objective back focal plane)
Feieraband et al (2004) Opt Lett 29 2255Ruumlckel et al (2006) PNAS 103 17137Ruumlckel et al (2007) JOSA A 25 3517
δϕ
τΔ
6times 2PEF signal improvement
(2006) PNAS 103 17137
1P excitation 2P excitation
2PEF SHG prop I2
2PEF SHG
3PEF THG prop I3
excitation(IR)
F prop I
Fluoexcitation(visible) ωP ωS
3P excitation
3PEF
CARS prop IP2 IS
THG CARS
Different contrast mechanisms rarr different information
In particular SHG second harmonic generation ndash sensitive to symmetry at the sub-microm scaleTHG third harmonic generation ndash detects interfaces and microm-size inclusionsCARS laquononlinear Ramanraquo ndash chemical specificity
SHG THG specifically obtained from certain structures(little spectroscopic information)
Alternative contrast modes SHG THG CARS
E(ω) P(ω)
E(ω)
P(ω)
P(3ω)
SHG
THG
P(2ω)
Harmonic signal depends on the nature of the emitting medium
P(2ω)=frac12χ(2)(minus2ωωω) E(ω)E(ω)P(3ω)=frac14χ(3)(minus3ωωωω) E(ω)E(ω)E(ω)
Nonlinear microscopy harmonic generation
P = P(ω) + P(2)(2ω) + middot middot middot + P(n)(nω)= PL + PNL
avec P(n)(nω) =
Polarisable medium excited by an intense field components of order ngt1 in the induced polarization
rarr Emission at harmonic frequencies (nonlinear scattering)
non zero χ(2) =gt non centrosymmetric mediumχ(3) non zero everywhere (but weak)
Multiphoton microscope rarr combined contrast modes
2PEFsignal
SHGsignal
Osc
illato
r
THGsignal
Example of push-pull laquo harmonophore raquo molecule for SHG
(SHG)
Example stylbene derivative
hellip and amphiphilic version (for lipid membrane labeling)
M Blanchard-Desce (Univ Rennes)
SHG = coherent process (ne 2PEF)rarr possibility of constructive and destructive interferences
Example (labeled vesicle) parallel molecules rarr SHG
antiparallel molecules rarr no SHG (centrosymmetric medium)
Mertz amp Moreaux OL 2001
Constructive interference rarr enhanced signal Destructive interfeacuterence rarr null signal
Molecules emitting in phase Molecules emitting with opposite phases
ϕ1 = 0
ϕ2 = 0
ϕ1 = 0
ϕ2 = π
SHG
SHG
Excitation2PEF
Note in contrast 2PEF emission does not
depend on symmetry
SHG microscopy adapted for
membrane imaging
hellipand some endogenousstructures (see later)
Mor
eaux
Mer
tz e
t al
Bio
phys
J 8
0 1
568
(200
1)
SHG 2PEF
Wavelength (nm)400 450 500 550 600 650
Pow
er (a
u)
00
05
10
430 435 440 445 450
SH
G P
ower
(au
)
00
05
10
fluorescence
SHG
Spectrum radiated from a GUV labeledwith the styryl dye Di-6-ASPBS
Phase matching in (coherent) nonlinear optics
zLc
If Δkne0 (dispersion) I2ω(z) prop sin2Δkz2coherent signal buildup is limited to Lc
If Δk=0 (phase-matching case) I2ω(z) prop z2
Δk = k2ω - 2kω = wave vector mismatch
laquoClassicalraquo example SHG by plane wave propagating in a nonlinear medium
Note if Δkne0 phase-matching
can be forced in a birefringent crystal eg
where ne(2ω)ltno(ω)
keθ(2ω)=2ko(ω)neθ(2ω)=2no(ω)
The same applies for other NL processes
such as THG
Lc = coherence length
But what happens in a tightly focused geometry
bull Presence of transverse componentsbull Many possible k
kω = 2π nω λ
I Field near focus from arbitrary pupil profile (Cf Richards amp Wolf 1959 Born amp Wolf 1980)
III Far-field signal (Cf Novotny amp Hecht 2006)
II Induced polarization density near focus
For a homogeneous isotropic medium
expressed using Greenrsquos function
Signal generation in coherent NL microscopy
Example for THG
Solve wave equation taking into account NL polarizations created at various locations in the focal volume + coherent superposition in the detector plane
( )int int ΘΦΘpropmax
0
2
0
22(det) sinα π
RREFFddPDetected power
Field near focus phase distribution
Phase anomaly of focused beams (Gouy phase)LG Gouy CR Acad Sciences Paris 1890
Intensity near focus
minusπ (Gouy shift)
0Phase near focus
Cal
culN
Oliv
ier (
LOB
)
Approximation of tightly focused field for modeling nonlinear interactions GaussianGaussian amplitude and reduced axial wave vector
( ) xexp 2
2
2
22
⎟⎟⎠
⎞⎜⎜⎝
⎛minusminus
+minusminusasymp zki
wz
wyxiEzyxE
zrωωω ξ
wr wz 1e radii of the focal ellipse
2221 rwkωξ minusasymp
CfM
orea
ux S
andr
e M
ertz
(200
0) J
OSA
B 1
7 1
685
For a linearly x-polarized beam near focus
z (nm)
z
ωξ k
2 Iξ
ωω πω nk 2=
880nm NA=09
ω 2ω
0
-πPha
se a
nom
aly
Axial direction
)(cos 1 ξθ minus=slope prop (ξminus1)
Normalized intensitysquared
SHG from a labeled membrane Gouy shift deflects emission off-axis
θ
k2ω
ξ kω ξ kω
(ξlt1)
Mertz Moreaux et al (2001) Biophys J
Sample and field structure govern emission diagrams
emax asymp 06w0
Exemple of coherence effectobservation of SHG laquo hot spots raquo whenlabeled vesicules are in close proximity
Possible application sub-microm distance
measurement
Mertz Moreaux et al (2001) Biophys J
⎟⎟⎠
⎞⎜⎜⎝
⎛Θasymp
PEF
mHG
PEF
mHG NPP
22 σσ
N number of radiating molecules
Θ parameter describing signal reduction due to the sub-micrometer arrangement of the emitters within the focal volume (typ 10-2 for SHG)
222 INP PEFPEF σprop
Signal level in 2PEFmHG imaging
mmHGmHG INP σ2 Θprop
~ 10-4
(pour SHG)
rarr mHG signal strongly depends on the density of emitters
(SHG THG)
Intrinsic 2PEFSHG signals in cells and tissues
SHG = coherent second-ordernonlinear signal
no centrosymmetrySHG prop (density)2
rArr Dense and orderedmacromolecular structures
Zipfel et al (2003) PNAS 100 7075 (2003)
ldquoLive tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and SHGrdquo
- collagen fibrils
- sarcomeres
- astroglial fibers
- polarized microT bundles
cellulose starch hellip
Myofilaments = endogenous SHG source
Myocytes(Frog heart)
Boulesteix et al (2004) Opt Lett
Plot
niko
vet
al (
2006
) Bio
phys
J
SHG imaging of muscle structures
23 s acquisition
Applications sarcomere contraction measurements study of myogenesis
4 6 80
20
40
60
SHG
sig
nal (
phot
ons)
Length (microm)
sarcomere
constant variable
Saxitoxin (8 nM) 214 plusmn 002 microm
Control 231 plusmn 002 microm
rArr contracture at rest 7
N = C
R -O
H R
Possible molecularorigin the dense (crystalline) packingof peptide bonds such as amide group
Collagen triple-helix
Fibrils
Fibers
Macromolecular Organization
SHG is obtained from fibrillar collagen
SHGis observed
No SHG
Collagen I II III V XI hellip form fibrils
Collagen IV VIII X hellip form networks
rarr SHG = probe of macromolecular structuration
50 nm
Combined 2PEFSHG imaging of intact tissue
2PEFelastin
lamellae
SHGcollagenfibrils
Unstained carotid artery (Rat)λexc= 860nm
Boulesteix et al (2006) Cytometry A 69
yz
x
yz
x
yz
x
yz
x
yz
x
yz
x
yz
x
x
y
x
y
Lumen
Media
Intima
Adventitia
Endothelial cellsInternal elasticlamella
External elasticlamella
Fibroblast
Smoothmuscle cell
M B
lanc
hard
-Des
ce(U
niv
Ren
nes I
)
Engineered fluorophores with enhanced 2PEF
2PEF action cross-sections
10-100 GMldquoQuantum dotsrdquo
104 GM
Endogenous fluorophores (NADH etc)
Standard fluorophores (Rhodaminehellip) 01-10 GM
10-3 - 10-1 GM
Fluorescent proteins (GFP etc)
100-1000 GMZi
pfel
Web
b (C
orne
llU
niv
)
Example 150 fs rarr (5000 fs2) rarr 177 fs80 fs rarr (5000 fs2) rarr 190 fs10 fs rarr (5000 fs2) rarr ~1 ps 80 fs rarr (20000 fs2) rarr 697 fs150 fs rarr (20000 fs2) rarr 403 fs
Dispersion of optics in a multiphoton microscope 2000-20000 fs2
Implementation prism pairs gratings chirped mirrors SLM-based pulse shaper
( )2200 2ln41 τϕττ primeprime+=Pulse broadening
τ0 = initial duration (transform-limited pulse)φrsquorsquo = group delay dispersion (fs2)
Dispersion compensation
In practice compensation is necessary mostly for pulses ltlt 100 fs
Note1 2PEF imaging is typically done with 100fs pulsesShort pulses are interesting for spectroscopy (next lesson) but may induce additional toxicityNote2 managing 10fs pulses at the focus of high NA objective is not trivial Radially varying group delay can be a few 10s fs in some objectives
2PEF prop 1τ
PSF degradation example for aqueous sample
60times NA 12water immersion
40times NA 13oil immersion
rarr Use water-immersion objectives (index matching)
PSFz PSFz
Index mismatch cause PSF spreading and signal loss
Diaspro Ed Confocal and 2P Microscopy Foundations Applications and Advances (2001)Jacobsen Hell et al Refractive-index-induced aberrations in 2P confocal fluorescence microscopy J Microsc 176 226 (1995)Booth amp Wilson ldquoRefractive-index-mismatch induced aberrations in single-photon and 2P microscopyrdquo J Biomed Opt 6 266 (2001)
For small aberrations
( ) ( )2221 ΔΦminusasymp λπrefaber II
mean-square deformationof the wave front
( )2ΔΦ
rarr rapid impact on NL signal
Incidence on signal level
NeuroscienceYuste Denk (1995) Dendritic spines as basic functional units of neuronal integration Nature 375 682-684Svoboda Tank Denk (1996) Direct measurement of coupling between dendritic spines and shafts Science 272 716-719Svoboda Denk Kleinfeld Tank (1997) In vivo dendritic calcium dynamics in neocortical pyramidal neurons Nature 385 161-5
2PEF microscopy in biology some fields of application
Immunology
Developmental biology
ReviewsSvoboda amp Yasuda (2006) Principles of 2P excitation microscopy and its applications to neuroscience Neuron 50 823-839Mertz (2004) Nonlinear microscopy new techniques and applications Curr Opin Neurobiol 14 610-616
ReviewCalahan MD amp Gutman GA (2006) The sense of place in the immune system Nat Immunol 7 329-332
McMahon A Supatto W Fraser SE and Stathopoulos A (2008) Dynamic analyses of Drosophila gastrulation provide insights into collective cell migration Science 3221546-50
laserTiSaphir
rarr 400 μm
50 microm
Application example in neurosciences in vivo 2PEF imaging of an olfactory neuron
50 microm
S C
harp
ak e
t al
PNA
S 98
123
0 (2
001)
Les PA spontaneacutes enregistreacutes dans le soma (trace du bas) induisent des entreacutees de calcium dans le bouquet dendritique
Pb marquage cellules multiples rarr marqueurs geacuteneacutetiques agrave base de proteacuteines fluorescentesex laquo cameleons raquo (constructions 2XFPs+cmd sensibles au calcium) etc
[Ca2+]i imaging
S C
harp
ak e
t al
Ner
urop
hysi
olog
ieet
nou
velle
s mic
rosc
opie
s (I
NSE
RM
-Par
is V
)
Nat
Met
h 2
932
200
5
100microm Chl
omel
eon
Prot
ein
(sen
stiv
eto
chl
orid
e io
ns)
mou
se n
eoco
rtex
Hel
mch
enet
al
(200
5) N
at M
eth
2 9
32-9
40
Two-photon-excited fluorescence (2PEF)
[+] Genetically encoded probes fluorescent proteins (GFPhellip)
Nonlinear microscopy of tissues 2PEF
GFP
~ns
700-
1000
nm
350-
600+
nm
Some important fields of application of 2PEF microscopy
Neurosciences in vivo neuronal activityImmunology lymphocyte trafficking
GFP labeling of nuclei
2PEF λ=920 nm 2 simage 10 mW 1 image every 30 s
100 microm
yolk
vitelline membrane
nucleilipid droplets
Live embryo imaging 2PEF microscopy
Supatto et al (2005) PNASSquirrell et al (1999) Nat Biotechnol
LOB Polytechnique Curie
GFP labeling of nuclei
2PEF λ=920 nm
Live embryo imaging 2PEF microscopy
Caltech bioimaging centerMcMahon Supatto et al (2008) Science
Example quantitative study of individualcollective cell motions in a developing embryo
1 XYZ image every 10s
z
LOB Polytechnique Curie
[+] Endogenous fluorescents species
elastin(rat artery wall fresh)
Bou
lest
eix
et a
l (2
006)
C
ytom
etry
69A
~ns
700-
1000
nm
350-
600+
nm
Two-photon-excited fluorescence (2PEF)
Nonlinear microscopy of tissues 2PEF
Mouse ear skin
(fresh)
Excitation 720nm 800nm 900nm Detection 350-505 505-560 560-650 + spectral unmixing
Note NADH fluorescence is an
indicator of metabolic state
Rad
osev
itch
Hill
man
et a
l (2
008)
O
pt L
ett
33 2
164
NADH fluorescent NAD+ non-fluorescent
zmax
P0
( ))ex(s0 LzexpP minus
z
( )[ ] ( )zLzPTS exs Φsdotminussdotprop
2)(0 expτ
Signal
excitation detection
typically ~500 μm(layer 23 neocortex)
α - fluorophore efficiencyand detector noise
tissue scattering length average laser power
Φ - collected fraction of the generated fluorescence
inverse laser duty cycle
( )τα )(ln max)(
max TzPLz exs Φ=
Rat brain Ls~200microm
If limited by detector noise (no background)
zmax~50-200 μm with endogenous signals
What limits the imaging depthConfined excitation even in scattering media hellip but the number of ballistic excitation photons decreases exponentially with depth
PNAS 98 1230 (2001)
( )τα )(ln max)(
max TzPLz exs Φ=
A How to increase collection efficiency (Φ)
How to increase imaging depth
zmax
( )( )221 cos1
NA
NA
α
α
prop
minus=Φ
αNA
(1) first idea increase NA
This workshellip
Field-of-view (FOV)
(2) hellipbut what if sample is scattering
Scattered fluorescence seemsto originate from an
extended source
Field of view (related to the angular acceptance of the detection path) defines the depth where collection efficiency starts to drop
At large depths (diffusive light)
Oheim et al (2001) J Neurosci Meth 112 205Beaurepaire amp Mertz (2002) Appl Opt 41 5376
An objective with low magnification and high NA is advantageous for collecting scattered fluorescence
( ) 22 minussdotpropΦ zrFOV
Typical multiphoton microscope
laquo non-descanned raquo detection(close to objective)
700-1200 nm~80 MHz~100 fs
source
Diaspro et al (2006) Biomed Eng online
B
A
TiSapph
Reg Amp
z rarr
z rarr
T τ ~ 1times105
T τ ~ 4times107
fmax rTS
fmax rRA
Δz asymp ln(rTSrRA)2 asymp 2-3 scattering lengths Δz
rTS = 80 MHz
rRA = 200 kHz
log F
log FTemporal redistribution of the
same excitation power
At large depths contrast (amp resolution)
loss
hellip in vivoexperiment
( )2balscat II +
Theer amp Denk (2006) JOSA A 23 3139
2PEF imaging depth fundamental limit
Note Zmax increases with staining heterogeneity Zmax is increased by ~Ls when stained fraction is reduced 6times
Zmax reached when
( ) intint ge+focusat
balfocusofout
balscat III 22
Contribution of the different planes Model accounting for the temporal distribution of scattered light and assuming that scattering is mostly forward-directed
Influence of pulse duration rarr Using pulse duration of 20fs instead of 200fs should increase the SB ratio by 25times resulting in an increase of 05 scattering MFP to the depth limit
( )τα )(ln max)(
max TzPLz exs Φ=
How to increase imaging depth
zmax
bull Regenerative amplification multiplies Tτ by 400rarr Equivalent to multiplying P by 20
bull Implement wavefront correction to correct for specimen-induced aberrations (adaptive optics)
bull Design background rejection schemes to remove light generated out-of-focus when doing large depth imaging
B Improving excitation
bull Low mag objective multiplies Φ by 10(Only equivalent to multiplying P by 3)
bull And always non-descanned detection
A Improving collection Φ
Theer amp Denk OL2003
2PEF from a thin fluorescent slab as a function of slab defocus Ratio betweensignal detected with an unaberrated and an aberrated phase
2PEF images of a labeled glomerulus (from mouse olfactory bulb)
Wavefront correction in microscopy
Φ-Φ
Φ
Possible strategiesMeasure aberrated wavefront with wavefront sensor rarr implementation eg Denk PNAS 2006
Iterative sensorless approach with merit functioneg Wright et al OE 2007 (applied to CARS)
Model-based sensorless approach eg Deacutebarre Botcherby Booth Wilson OE 2008 (applied to structured illumination microscopy)
reference
astronomy ophtalmology microscopy
For small aberrations
( ) ( )2221 ΔΦminusasymp λπrefaber II
mean-square deformationof the wave front
( )2ΔΦ
rarr rapid impact on NL signal
LOB
-X
low-coherence interferometry+ wave-front sensing
4 images (I1hellipI4) recorded with reference path length shifts of 0 λ4 λ4 and 3λ4 For each pixel a complex amplitude A is calculated by
Reference
Sample
Low-coherence sourceTiS 915nm 100fs
CCD
( ) ( ) ⎟⎠⎞⎜
⎝⎛ ΔΔminus++=
22ln2expcos τνπδϕsrsrD iiiiI
z-resolution ~ 20 micromνΔ FWHM of source power spectral density
νΔprop 1
δϕ applied phase shift
τΔ delay due to path difference
+ ldquocompatiblerdquo with 2PEF microscopy
obj
(conjug with objective back focal plane)
Feieraband et al (2004) Opt Lett 29 2255Ruumlckel et al (2006) PNAS 103 17137Ruumlckel et al (2007) JOSA A 25 3517
δϕ
τΔ
6times 2PEF signal improvement
(2006) PNAS 103 17137
1P excitation 2P excitation
2PEF SHG prop I2
2PEF SHG
3PEF THG prop I3
excitation(IR)
F prop I
Fluoexcitation(visible) ωP ωS
3P excitation
3PEF
CARS prop IP2 IS
THG CARS
Different contrast mechanisms rarr different information
In particular SHG second harmonic generation ndash sensitive to symmetry at the sub-microm scaleTHG third harmonic generation ndash detects interfaces and microm-size inclusionsCARS laquononlinear Ramanraquo ndash chemical specificity
SHG THG specifically obtained from certain structures(little spectroscopic information)
Alternative contrast modes SHG THG CARS
E(ω) P(ω)
E(ω)
P(ω)
P(3ω)
SHG
THG
P(2ω)
Harmonic signal depends on the nature of the emitting medium
P(2ω)=frac12χ(2)(minus2ωωω) E(ω)E(ω)P(3ω)=frac14χ(3)(minus3ωωωω) E(ω)E(ω)E(ω)
Nonlinear microscopy harmonic generation
P = P(ω) + P(2)(2ω) + middot middot middot + P(n)(nω)= PL + PNL
avec P(n)(nω) =
Polarisable medium excited by an intense field components of order ngt1 in the induced polarization
rarr Emission at harmonic frequencies (nonlinear scattering)
non zero χ(2) =gt non centrosymmetric mediumχ(3) non zero everywhere (but weak)
Multiphoton microscope rarr combined contrast modes
2PEFsignal
SHGsignal
Osc
illato
r
THGsignal
Example of push-pull laquo harmonophore raquo molecule for SHG
(SHG)
Example stylbene derivative
hellip and amphiphilic version (for lipid membrane labeling)
M Blanchard-Desce (Univ Rennes)
SHG = coherent process (ne 2PEF)rarr possibility of constructive and destructive interferences
Example (labeled vesicle) parallel molecules rarr SHG
antiparallel molecules rarr no SHG (centrosymmetric medium)
Mertz amp Moreaux OL 2001
Constructive interference rarr enhanced signal Destructive interfeacuterence rarr null signal
Molecules emitting in phase Molecules emitting with opposite phases
ϕ1 = 0
ϕ2 = 0
ϕ1 = 0
ϕ2 = π
SHG
SHG
Excitation2PEF
Note in contrast 2PEF emission does not
depend on symmetry
SHG microscopy adapted for
membrane imaging
hellipand some endogenousstructures (see later)
Mor
eaux
Mer
tz e
t al
Bio
phys
J 8
0 1
568
(200
1)
SHG 2PEF
Wavelength (nm)400 450 500 550 600 650
Pow
er (a
u)
00
05
10
430 435 440 445 450
SH
G P
ower
(au
)
00
05
10
fluorescence
SHG
Spectrum radiated from a GUV labeledwith the styryl dye Di-6-ASPBS
Phase matching in (coherent) nonlinear optics
zLc
If Δkne0 (dispersion) I2ω(z) prop sin2Δkz2coherent signal buildup is limited to Lc
If Δk=0 (phase-matching case) I2ω(z) prop z2
Δk = k2ω - 2kω = wave vector mismatch
laquoClassicalraquo example SHG by plane wave propagating in a nonlinear medium
Note if Δkne0 phase-matching
can be forced in a birefringent crystal eg
where ne(2ω)ltno(ω)
keθ(2ω)=2ko(ω)neθ(2ω)=2no(ω)
The same applies for other NL processes
such as THG
Lc = coherence length
But what happens in a tightly focused geometry
bull Presence of transverse componentsbull Many possible k
kω = 2π nω λ
I Field near focus from arbitrary pupil profile (Cf Richards amp Wolf 1959 Born amp Wolf 1980)
III Far-field signal (Cf Novotny amp Hecht 2006)
II Induced polarization density near focus
For a homogeneous isotropic medium
expressed using Greenrsquos function
Signal generation in coherent NL microscopy
Example for THG
Solve wave equation taking into account NL polarizations created at various locations in the focal volume + coherent superposition in the detector plane
( )int int ΘΦΘpropmax
0
2
0
22(det) sinα π
RREFFddPDetected power
Field near focus phase distribution
Phase anomaly of focused beams (Gouy phase)LG Gouy CR Acad Sciences Paris 1890
Intensity near focus
minusπ (Gouy shift)
0Phase near focus
Cal
culN
Oliv
ier (
LOB
)
Approximation of tightly focused field for modeling nonlinear interactions GaussianGaussian amplitude and reduced axial wave vector
( ) xexp 2
2
2
22
⎟⎟⎠
⎞⎜⎜⎝
⎛minusminus
+minusminusasymp zki
wz
wyxiEzyxE
zrωωω ξ
wr wz 1e radii of the focal ellipse
2221 rwkωξ minusasymp
CfM
orea
ux S
andr
e M
ertz
(200
0) J
OSA
B 1
7 1
685
For a linearly x-polarized beam near focus
z (nm)
z
ωξ k
2 Iξ
ωω πω nk 2=
880nm NA=09
ω 2ω
0
-πPha
se a
nom
aly
Axial direction
)(cos 1 ξθ minus=slope prop (ξminus1)
Normalized intensitysquared
SHG from a labeled membrane Gouy shift deflects emission off-axis
θ
k2ω
ξ kω ξ kω
(ξlt1)
Mertz Moreaux et al (2001) Biophys J
Sample and field structure govern emission diagrams
emax asymp 06w0
Exemple of coherence effectobservation of SHG laquo hot spots raquo whenlabeled vesicules are in close proximity
Possible application sub-microm distance
measurement
Mertz Moreaux et al (2001) Biophys J
⎟⎟⎠
⎞⎜⎜⎝
⎛Θasymp
PEF
mHG
PEF
mHG NPP
22 σσ
N number of radiating molecules
Θ parameter describing signal reduction due to the sub-micrometer arrangement of the emitters within the focal volume (typ 10-2 for SHG)
222 INP PEFPEF σprop
Signal level in 2PEFmHG imaging
mmHGmHG INP σ2 Θprop
~ 10-4
(pour SHG)
rarr mHG signal strongly depends on the density of emitters
(SHG THG)
Intrinsic 2PEFSHG signals in cells and tissues
SHG = coherent second-ordernonlinear signal
no centrosymmetrySHG prop (density)2
rArr Dense and orderedmacromolecular structures
Zipfel et al (2003) PNAS 100 7075 (2003)
ldquoLive tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and SHGrdquo
- collagen fibrils
- sarcomeres
- astroglial fibers
- polarized microT bundles
cellulose starch hellip
Myofilaments = endogenous SHG source
Myocytes(Frog heart)
Boulesteix et al (2004) Opt Lett
Plot
niko
vet
al (
2006
) Bio
phys
J
SHG imaging of muscle structures
23 s acquisition
Applications sarcomere contraction measurements study of myogenesis
4 6 80
20
40
60
SHG
sig
nal (
phot
ons)
Length (microm)
sarcomere
constant variable
Saxitoxin (8 nM) 214 plusmn 002 microm
Control 231 plusmn 002 microm
rArr contracture at rest 7
N = C
R -O
H R
Possible molecularorigin the dense (crystalline) packingof peptide bonds such as amide group
Collagen triple-helix
Fibrils
Fibers
Macromolecular Organization
SHG is obtained from fibrillar collagen
SHGis observed
No SHG
Collagen I II III V XI hellip form fibrils
Collagen IV VIII X hellip form networks
rarr SHG = probe of macromolecular structuration
50 nm
Combined 2PEFSHG imaging of intact tissue
2PEFelastin
lamellae
SHGcollagenfibrils
Unstained carotid artery (Rat)λexc= 860nm
Boulesteix et al (2006) Cytometry A 69
yz
x
yz
x
yz
x
yz
x
yz
x
yz
x
yz
x
x
y
x
y
Lumen
Media
Intima
Adventitia
Endothelial cellsInternal elasticlamella
External elasticlamella
Fibroblast
Smoothmuscle cell
laserTiSaphir
rarr 400 μm
50 microm
Application example in neurosciences in vivo 2PEF imaging of an olfactory neuron
50 microm
S C
harp
ak e
t al
PNA
S 98
123
0 (2
001)
Les PA spontaneacutes enregistreacutes dans le soma (trace du bas) induisent des entreacutees de calcium dans le bouquet dendritique
Pb marquage cellules multiples rarr marqueurs geacuteneacutetiques agrave base de proteacuteines fluorescentesex laquo cameleons raquo (constructions 2XFPs+cmd sensibles au calcium) etc
[Ca2+]i imaging
S C
harp
ak e
t al
Ner
urop
hysi
olog
ieet
nou
velle
s mic
rosc
opie
s (I
NSE
RM
-Par
is V
)
Nat
Met
h 2
932
200
5
100microm Chl
omel
eon
Prot
ein
(sen
stiv
eto
chl
orid
e io
ns)
mou
se n
eoco
rtex
Hel
mch
enet
al
(200
5) N
at M
eth
2 9
32-9
40
Two-photon-excited fluorescence (2PEF)
[+] Genetically encoded probes fluorescent proteins (GFPhellip)
Nonlinear microscopy of tissues 2PEF
GFP
~ns
700-
1000
nm
350-
600+
nm
Some important fields of application of 2PEF microscopy
Neurosciences in vivo neuronal activityImmunology lymphocyte trafficking
GFP labeling of nuclei
2PEF λ=920 nm 2 simage 10 mW 1 image every 30 s
100 microm
yolk
vitelline membrane
nucleilipid droplets
Live embryo imaging 2PEF microscopy
Supatto et al (2005) PNASSquirrell et al (1999) Nat Biotechnol
LOB Polytechnique Curie
GFP labeling of nuclei
2PEF λ=920 nm
Live embryo imaging 2PEF microscopy
Caltech bioimaging centerMcMahon Supatto et al (2008) Science
Example quantitative study of individualcollective cell motions in a developing embryo
1 XYZ image every 10s
z
LOB Polytechnique Curie
[+] Endogenous fluorescents species
elastin(rat artery wall fresh)
Bou
lest
eix
et a
l (2
006)
C
ytom
etry
69A
~ns
700-
1000
nm
350-
600+
nm
Two-photon-excited fluorescence (2PEF)
Nonlinear microscopy of tissues 2PEF
Mouse ear skin
(fresh)
Excitation 720nm 800nm 900nm Detection 350-505 505-560 560-650 + spectral unmixing
Note NADH fluorescence is an
indicator of metabolic state
Rad
osev
itch
Hill
man
et a
l (2
008)
O
pt L
ett
33 2
164
NADH fluorescent NAD+ non-fluorescent
zmax
P0
( ))ex(s0 LzexpP minus
z
( )[ ] ( )zLzPTS exs Φsdotminussdotprop
2)(0 expτ
Signal
excitation detection
typically ~500 μm(layer 23 neocortex)
α - fluorophore efficiencyand detector noise
tissue scattering length average laser power
Φ - collected fraction of the generated fluorescence
inverse laser duty cycle
( )τα )(ln max)(
max TzPLz exs Φ=
Rat brain Ls~200microm
If limited by detector noise (no background)
zmax~50-200 μm with endogenous signals
What limits the imaging depthConfined excitation even in scattering media hellip but the number of ballistic excitation photons decreases exponentially with depth
PNAS 98 1230 (2001)
( )τα )(ln max)(
max TzPLz exs Φ=
A How to increase collection efficiency (Φ)
How to increase imaging depth
zmax
( )( )221 cos1
NA
NA
α
α
prop
minus=Φ
αNA
(1) first idea increase NA
This workshellip
Field-of-view (FOV)
(2) hellipbut what if sample is scattering
Scattered fluorescence seemsto originate from an
extended source
Field of view (related to the angular acceptance of the detection path) defines the depth where collection efficiency starts to drop
At large depths (diffusive light)
Oheim et al (2001) J Neurosci Meth 112 205Beaurepaire amp Mertz (2002) Appl Opt 41 5376
An objective with low magnification and high NA is advantageous for collecting scattered fluorescence
( ) 22 minussdotpropΦ zrFOV
Typical multiphoton microscope
laquo non-descanned raquo detection(close to objective)
700-1200 nm~80 MHz~100 fs
source
Diaspro et al (2006) Biomed Eng online
B
A
TiSapph
Reg Amp
z rarr
z rarr
T τ ~ 1times105
T τ ~ 4times107
fmax rTS
fmax rRA
Δz asymp ln(rTSrRA)2 asymp 2-3 scattering lengths Δz
rTS = 80 MHz
rRA = 200 kHz
log F
log FTemporal redistribution of the
same excitation power
At large depths contrast (amp resolution)
loss
hellip in vivoexperiment
( )2balscat II +
Theer amp Denk (2006) JOSA A 23 3139
2PEF imaging depth fundamental limit
Note Zmax increases with staining heterogeneity Zmax is increased by ~Ls when stained fraction is reduced 6times
Zmax reached when
( ) intint ge+focusat
balfocusofout
balscat III 22
Contribution of the different planes Model accounting for the temporal distribution of scattered light and assuming that scattering is mostly forward-directed
Influence of pulse duration rarr Using pulse duration of 20fs instead of 200fs should increase the SB ratio by 25times resulting in an increase of 05 scattering MFP to the depth limit
( )τα )(ln max)(
max TzPLz exs Φ=
How to increase imaging depth
zmax
bull Regenerative amplification multiplies Tτ by 400rarr Equivalent to multiplying P by 20
bull Implement wavefront correction to correct for specimen-induced aberrations (adaptive optics)
bull Design background rejection schemes to remove light generated out-of-focus when doing large depth imaging
B Improving excitation
bull Low mag objective multiplies Φ by 10(Only equivalent to multiplying P by 3)
bull And always non-descanned detection
A Improving collection Φ
Theer amp Denk OL2003
2PEF from a thin fluorescent slab as a function of slab defocus Ratio betweensignal detected with an unaberrated and an aberrated phase
2PEF images of a labeled glomerulus (from mouse olfactory bulb)
Wavefront correction in microscopy
Φ-Φ
Φ
Possible strategiesMeasure aberrated wavefront with wavefront sensor rarr implementation eg Denk PNAS 2006
Iterative sensorless approach with merit functioneg Wright et al OE 2007 (applied to CARS)
Model-based sensorless approach eg Deacutebarre Botcherby Booth Wilson OE 2008 (applied to structured illumination microscopy)
reference
astronomy ophtalmology microscopy
For small aberrations
( ) ( )2221 ΔΦminusasymp λπrefaber II
mean-square deformationof the wave front
( )2ΔΦ
rarr rapid impact on NL signal
LOB
-X
low-coherence interferometry+ wave-front sensing
4 images (I1hellipI4) recorded with reference path length shifts of 0 λ4 λ4 and 3λ4 For each pixel a complex amplitude A is calculated by
Reference
Sample
Low-coherence sourceTiS 915nm 100fs
CCD
( ) ( ) ⎟⎠⎞⎜
⎝⎛ ΔΔminus++=
22ln2expcos τνπδϕsrsrD iiiiI
z-resolution ~ 20 micromνΔ FWHM of source power spectral density
νΔprop 1
δϕ applied phase shift
τΔ delay due to path difference
+ ldquocompatiblerdquo with 2PEF microscopy
obj
(conjug with objective back focal plane)
Feieraband et al (2004) Opt Lett 29 2255Ruumlckel et al (2006) PNAS 103 17137Ruumlckel et al (2007) JOSA A 25 3517
δϕ
τΔ
6times 2PEF signal improvement
(2006) PNAS 103 17137
1P excitation 2P excitation
2PEF SHG prop I2
2PEF SHG
3PEF THG prop I3
excitation(IR)
F prop I
Fluoexcitation(visible) ωP ωS
3P excitation
3PEF
CARS prop IP2 IS
THG CARS
Different contrast mechanisms rarr different information
In particular SHG second harmonic generation ndash sensitive to symmetry at the sub-microm scaleTHG third harmonic generation ndash detects interfaces and microm-size inclusionsCARS laquononlinear Ramanraquo ndash chemical specificity
SHG THG specifically obtained from certain structures(little spectroscopic information)
Alternative contrast modes SHG THG CARS
E(ω) P(ω)
E(ω)
P(ω)
P(3ω)
SHG
THG
P(2ω)
Harmonic signal depends on the nature of the emitting medium
P(2ω)=frac12χ(2)(minus2ωωω) E(ω)E(ω)P(3ω)=frac14χ(3)(minus3ωωωω) E(ω)E(ω)E(ω)
Nonlinear microscopy harmonic generation
P = P(ω) + P(2)(2ω) + middot middot middot + P(n)(nω)= PL + PNL
avec P(n)(nω) =
Polarisable medium excited by an intense field components of order ngt1 in the induced polarization
rarr Emission at harmonic frequencies (nonlinear scattering)
non zero χ(2) =gt non centrosymmetric mediumχ(3) non zero everywhere (but weak)
Multiphoton microscope rarr combined contrast modes
2PEFsignal
SHGsignal
Osc
illato
r
THGsignal
Example of push-pull laquo harmonophore raquo molecule for SHG
(SHG)
Example stylbene derivative
hellip and amphiphilic version (for lipid membrane labeling)
M Blanchard-Desce (Univ Rennes)
SHG = coherent process (ne 2PEF)rarr possibility of constructive and destructive interferences
Example (labeled vesicle) parallel molecules rarr SHG
antiparallel molecules rarr no SHG (centrosymmetric medium)
Mertz amp Moreaux OL 2001
Constructive interference rarr enhanced signal Destructive interfeacuterence rarr null signal
Molecules emitting in phase Molecules emitting with opposite phases
ϕ1 = 0
ϕ2 = 0
ϕ1 = 0
ϕ2 = π
SHG
SHG
Excitation2PEF
Note in contrast 2PEF emission does not
depend on symmetry
SHG microscopy adapted for
membrane imaging
hellipand some endogenousstructures (see later)
Mor
eaux
Mer
tz e
t al
Bio
phys
J 8
0 1
568
(200
1)
SHG 2PEF
Wavelength (nm)400 450 500 550 600 650
Pow
er (a
u)
00
05
10
430 435 440 445 450
SH
G P
ower
(au
)
00
05
10
fluorescence
SHG
Spectrum radiated from a GUV labeledwith the styryl dye Di-6-ASPBS
Phase matching in (coherent) nonlinear optics
zLc
If Δkne0 (dispersion) I2ω(z) prop sin2Δkz2coherent signal buildup is limited to Lc
If Δk=0 (phase-matching case) I2ω(z) prop z2
Δk = k2ω - 2kω = wave vector mismatch
laquoClassicalraquo example SHG by plane wave propagating in a nonlinear medium
Note if Δkne0 phase-matching
can be forced in a birefringent crystal eg
where ne(2ω)ltno(ω)
keθ(2ω)=2ko(ω)neθ(2ω)=2no(ω)
The same applies for other NL processes
such as THG
Lc = coherence length
But what happens in a tightly focused geometry
bull Presence of transverse componentsbull Many possible k
kω = 2π nω λ
I Field near focus from arbitrary pupil profile (Cf Richards amp Wolf 1959 Born amp Wolf 1980)
III Far-field signal (Cf Novotny amp Hecht 2006)
II Induced polarization density near focus
For a homogeneous isotropic medium
expressed using Greenrsquos function
Signal generation in coherent NL microscopy
Example for THG
Solve wave equation taking into account NL polarizations created at various locations in the focal volume + coherent superposition in the detector plane
( )int int ΘΦΘpropmax
0
2
0
22(det) sinα π
RREFFddPDetected power
Field near focus phase distribution
Phase anomaly of focused beams (Gouy phase)LG Gouy CR Acad Sciences Paris 1890
Intensity near focus
minusπ (Gouy shift)
0Phase near focus
Cal
culN
Oliv
ier (
LOB
)
Approximation of tightly focused field for modeling nonlinear interactions GaussianGaussian amplitude and reduced axial wave vector
( ) xexp 2
2
2
22
⎟⎟⎠
⎞⎜⎜⎝
⎛minusminus
+minusminusasymp zki
wz
wyxiEzyxE
zrωωω ξ
wr wz 1e radii of the focal ellipse
2221 rwkωξ minusasymp
CfM
orea
ux S
andr
e M
ertz
(200
0) J
OSA
B 1
7 1
685
For a linearly x-polarized beam near focus
z (nm)
z
ωξ k
2 Iξ
ωω πω nk 2=
880nm NA=09
ω 2ω
0
-πPha
se a
nom
aly
Axial direction
)(cos 1 ξθ minus=slope prop (ξminus1)
Normalized intensitysquared
SHG from a labeled membrane Gouy shift deflects emission off-axis
θ
k2ω
ξ kω ξ kω
(ξlt1)
Mertz Moreaux et al (2001) Biophys J
Sample and field structure govern emission diagrams
emax asymp 06w0
Exemple of coherence effectobservation of SHG laquo hot spots raquo whenlabeled vesicules are in close proximity
Possible application sub-microm distance
measurement
Mertz Moreaux et al (2001) Biophys J
⎟⎟⎠
⎞⎜⎜⎝
⎛Θasymp
PEF
mHG
PEF
mHG NPP
22 σσ
N number of radiating molecules
Θ parameter describing signal reduction due to the sub-micrometer arrangement of the emitters within the focal volume (typ 10-2 for SHG)
222 INP PEFPEF σprop
Signal level in 2PEFmHG imaging
mmHGmHG INP σ2 Θprop
~ 10-4
(pour SHG)
rarr mHG signal strongly depends on the density of emitters
(SHG THG)
Intrinsic 2PEFSHG signals in cells and tissues
SHG = coherent second-ordernonlinear signal
no centrosymmetrySHG prop (density)2
rArr Dense and orderedmacromolecular structures
Zipfel et al (2003) PNAS 100 7075 (2003)
ldquoLive tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and SHGrdquo
- collagen fibrils
- sarcomeres
- astroglial fibers
- polarized microT bundles
cellulose starch hellip
Myofilaments = endogenous SHG source
Myocytes(Frog heart)
Boulesteix et al (2004) Opt Lett
Plot
niko
vet
al (
2006
) Bio
phys
J
SHG imaging of muscle structures
23 s acquisition
Applications sarcomere contraction measurements study of myogenesis
4 6 80
20
40
60
SHG
sig
nal (
phot
ons)
Length (microm)
sarcomere
constant variable
Saxitoxin (8 nM) 214 plusmn 002 microm
Control 231 plusmn 002 microm
rArr contracture at rest 7
N = C
R -O
H R
Possible molecularorigin the dense (crystalline) packingof peptide bonds such as amide group
Collagen triple-helix
Fibrils
Fibers
Macromolecular Organization
SHG is obtained from fibrillar collagen
SHGis observed
No SHG
Collagen I II III V XI hellip form fibrils
Collagen IV VIII X hellip form networks
rarr SHG = probe of macromolecular structuration
50 nm
Combined 2PEFSHG imaging of intact tissue
2PEFelastin
lamellae
SHGcollagenfibrils
Unstained carotid artery (Rat)λexc= 860nm
Boulesteix et al (2006) Cytometry A 69
yz
x
yz
x
yz
x
yz
x
yz
x
yz
x
yz
x
x
y
x
y
Lumen
Media
Intima
Adventitia
Endothelial cellsInternal elasticlamella
External elasticlamella
Fibroblast
Smoothmuscle cell
[+] Endogenous fluorescents species
elastin(rat artery wall fresh)
Bou
lest
eix
et a
l (2
006)
C
ytom
etry
69A
~ns
700-
1000
nm
350-
600+
nm
Two-photon-excited fluorescence (2PEF)
Nonlinear microscopy of tissues 2PEF
Mouse ear skin
(fresh)
Excitation 720nm 800nm 900nm Detection 350-505 505-560 560-650 + spectral unmixing
Note NADH fluorescence is an
indicator of metabolic state
Rad
osev
itch
Hill
man
et a
l (2
008)
O
pt L
ett
33 2
164
NADH fluorescent NAD+ non-fluorescent
zmax
P0
( ))ex(s0 LzexpP minus
z
( )[ ] ( )zLzPTS exs Φsdotminussdotprop
2)(0 expτ
Signal
excitation detection
typically ~500 μm(layer 23 neocortex)
α - fluorophore efficiencyand detector noise
tissue scattering length average laser power
Φ - collected fraction of the generated fluorescence
inverse laser duty cycle
( )τα )(ln max)(
max TzPLz exs Φ=
Rat brain Ls~200microm
If limited by detector noise (no background)
zmax~50-200 μm with endogenous signals
What limits the imaging depthConfined excitation even in scattering media hellip but the number of ballistic excitation photons decreases exponentially with depth
PNAS 98 1230 (2001)
( )τα )(ln max)(
max TzPLz exs Φ=
A How to increase collection efficiency (Φ)
How to increase imaging depth
zmax
( )( )221 cos1
NA
NA
α
α
prop
minus=Φ
αNA
(1) first idea increase NA
This workshellip
Field-of-view (FOV)
(2) hellipbut what if sample is scattering
Scattered fluorescence seemsto originate from an
extended source
Field of view (related to the angular acceptance of the detection path) defines the depth where collection efficiency starts to drop
At large depths (diffusive light)
Oheim et al (2001) J Neurosci Meth 112 205Beaurepaire amp Mertz (2002) Appl Opt 41 5376
An objective with low magnification and high NA is advantageous for collecting scattered fluorescence
( ) 22 minussdotpropΦ zrFOV
Typical multiphoton microscope
laquo non-descanned raquo detection(close to objective)
700-1200 nm~80 MHz~100 fs
source
Diaspro et al (2006) Biomed Eng online
B
A
TiSapph
Reg Amp
z rarr
z rarr
T τ ~ 1times105
T τ ~ 4times107
fmax rTS
fmax rRA
Δz asymp ln(rTSrRA)2 asymp 2-3 scattering lengths Δz
rTS = 80 MHz
rRA = 200 kHz
log F
log FTemporal redistribution of the
same excitation power
At large depths contrast (amp resolution)
loss
hellip in vivoexperiment
( )2balscat II +
Theer amp Denk (2006) JOSA A 23 3139
2PEF imaging depth fundamental limit
Note Zmax increases with staining heterogeneity Zmax is increased by ~Ls when stained fraction is reduced 6times
Zmax reached when
( ) intint ge+focusat
balfocusofout
balscat III 22
Contribution of the different planes Model accounting for the temporal distribution of scattered light and assuming that scattering is mostly forward-directed
Influence of pulse duration rarr Using pulse duration of 20fs instead of 200fs should increase the SB ratio by 25times resulting in an increase of 05 scattering MFP to the depth limit
( )τα )(ln max)(
max TzPLz exs Φ=
How to increase imaging depth
zmax
bull Regenerative amplification multiplies Tτ by 400rarr Equivalent to multiplying P by 20
bull Implement wavefront correction to correct for specimen-induced aberrations (adaptive optics)
bull Design background rejection schemes to remove light generated out-of-focus when doing large depth imaging
B Improving excitation
bull Low mag objective multiplies Φ by 10(Only equivalent to multiplying P by 3)
bull And always non-descanned detection
A Improving collection Φ
Theer amp Denk OL2003
2PEF from a thin fluorescent slab as a function of slab defocus Ratio betweensignal detected with an unaberrated and an aberrated phase
2PEF images of a labeled glomerulus (from mouse olfactory bulb)
Wavefront correction in microscopy
Φ-Φ
Φ
Possible strategiesMeasure aberrated wavefront with wavefront sensor rarr implementation eg Denk PNAS 2006
Iterative sensorless approach with merit functioneg Wright et al OE 2007 (applied to CARS)
Model-based sensorless approach eg Deacutebarre Botcherby Booth Wilson OE 2008 (applied to structured illumination microscopy)
reference
astronomy ophtalmology microscopy
For small aberrations
( ) ( )2221 ΔΦminusasymp λπrefaber II
mean-square deformationof the wave front
( )2ΔΦ
rarr rapid impact on NL signal
LOB
-X
low-coherence interferometry+ wave-front sensing
4 images (I1hellipI4) recorded with reference path length shifts of 0 λ4 λ4 and 3λ4 For each pixel a complex amplitude A is calculated by
Reference
Sample
Low-coherence sourceTiS 915nm 100fs
CCD
( ) ( ) ⎟⎠⎞⎜
⎝⎛ ΔΔminus++=
22ln2expcos τνπδϕsrsrD iiiiI
z-resolution ~ 20 micromνΔ FWHM of source power spectral density
νΔprop 1
δϕ applied phase shift
τΔ delay due to path difference
+ ldquocompatiblerdquo with 2PEF microscopy
obj
(conjug with objective back focal plane)
Feieraband et al (2004) Opt Lett 29 2255Ruumlckel et al (2006) PNAS 103 17137Ruumlckel et al (2007) JOSA A 25 3517
δϕ
τΔ
6times 2PEF signal improvement
(2006) PNAS 103 17137
1P excitation 2P excitation
2PEF SHG prop I2
2PEF SHG
3PEF THG prop I3
excitation(IR)
F prop I
Fluoexcitation(visible) ωP ωS
3P excitation
3PEF
CARS prop IP2 IS
THG CARS
Different contrast mechanisms rarr different information
In particular SHG second harmonic generation ndash sensitive to symmetry at the sub-microm scaleTHG third harmonic generation ndash detects interfaces and microm-size inclusionsCARS laquononlinear Ramanraquo ndash chemical specificity
SHG THG specifically obtained from certain structures(little spectroscopic information)
Alternative contrast modes SHG THG CARS
E(ω) P(ω)
E(ω)
P(ω)
P(3ω)
SHG
THG
P(2ω)
Harmonic signal depends on the nature of the emitting medium
P(2ω)=frac12χ(2)(minus2ωωω) E(ω)E(ω)P(3ω)=frac14χ(3)(minus3ωωωω) E(ω)E(ω)E(ω)
Nonlinear microscopy harmonic generation
P = P(ω) + P(2)(2ω) + middot middot middot + P(n)(nω)= PL + PNL
avec P(n)(nω) =
Polarisable medium excited by an intense field components of order ngt1 in the induced polarization
rarr Emission at harmonic frequencies (nonlinear scattering)
non zero χ(2) =gt non centrosymmetric mediumχ(3) non zero everywhere (but weak)
Multiphoton microscope rarr combined contrast modes
2PEFsignal
SHGsignal
Osc
illato
r
THGsignal
Example of push-pull laquo harmonophore raquo molecule for SHG
(SHG)
Example stylbene derivative
hellip and amphiphilic version (for lipid membrane labeling)
M Blanchard-Desce (Univ Rennes)
SHG = coherent process (ne 2PEF)rarr possibility of constructive and destructive interferences
Example (labeled vesicle) parallel molecules rarr SHG
antiparallel molecules rarr no SHG (centrosymmetric medium)
Mertz amp Moreaux OL 2001
Constructive interference rarr enhanced signal Destructive interfeacuterence rarr null signal
Molecules emitting in phase Molecules emitting with opposite phases
ϕ1 = 0
ϕ2 = 0
ϕ1 = 0
ϕ2 = π
SHG
SHG
Excitation2PEF
Note in contrast 2PEF emission does not
depend on symmetry
SHG microscopy adapted for
membrane imaging
hellipand some endogenousstructures (see later)
Mor
eaux
Mer
tz e
t al
Bio
phys
J 8
0 1
568
(200
1)
SHG 2PEF
Wavelength (nm)400 450 500 550 600 650
Pow
er (a
u)
00
05
10
430 435 440 445 450
SH
G P
ower
(au
)
00
05
10
fluorescence
SHG
Spectrum radiated from a GUV labeledwith the styryl dye Di-6-ASPBS
Phase matching in (coherent) nonlinear optics
zLc
If Δkne0 (dispersion) I2ω(z) prop sin2Δkz2coherent signal buildup is limited to Lc
If Δk=0 (phase-matching case) I2ω(z) prop z2
Δk = k2ω - 2kω = wave vector mismatch
laquoClassicalraquo example SHG by plane wave propagating in a nonlinear medium
Note if Δkne0 phase-matching
can be forced in a birefringent crystal eg
where ne(2ω)ltno(ω)
keθ(2ω)=2ko(ω)neθ(2ω)=2no(ω)
The same applies for other NL processes
such as THG
Lc = coherence length
But what happens in a tightly focused geometry
bull Presence of transverse componentsbull Many possible k
kω = 2π nω λ
I Field near focus from arbitrary pupil profile (Cf Richards amp Wolf 1959 Born amp Wolf 1980)
III Far-field signal (Cf Novotny amp Hecht 2006)
II Induced polarization density near focus
For a homogeneous isotropic medium
expressed using Greenrsquos function
Signal generation in coherent NL microscopy
Example for THG
Solve wave equation taking into account NL polarizations created at various locations in the focal volume + coherent superposition in the detector plane
( )int int ΘΦΘpropmax
0
2
0
22(det) sinα π
RREFFddPDetected power
Field near focus phase distribution
Phase anomaly of focused beams (Gouy phase)LG Gouy CR Acad Sciences Paris 1890
Intensity near focus
minusπ (Gouy shift)
0Phase near focus
Cal
culN
Oliv
ier (
LOB
)
Approximation of tightly focused field for modeling nonlinear interactions GaussianGaussian amplitude and reduced axial wave vector
( ) xexp 2
2
2
22
⎟⎟⎠
⎞⎜⎜⎝
⎛minusminus
+minusminusasymp zki
wz
wyxiEzyxE
zrωωω ξ
wr wz 1e radii of the focal ellipse
2221 rwkωξ minusasymp
CfM
orea
ux S
andr
e M
ertz
(200
0) J
OSA
B 1
7 1
685
For a linearly x-polarized beam near focus
z (nm)
z
ωξ k
2 Iξ
ωω πω nk 2=
880nm NA=09
ω 2ω
0
-πPha
se a
nom
aly
Axial direction
)(cos 1 ξθ minus=slope prop (ξminus1)
Normalized intensitysquared
SHG from a labeled membrane Gouy shift deflects emission off-axis
θ
k2ω
ξ kω ξ kω
(ξlt1)
Mertz Moreaux et al (2001) Biophys J
Sample and field structure govern emission diagrams
emax asymp 06w0
Exemple of coherence effectobservation of SHG laquo hot spots raquo whenlabeled vesicules are in close proximity
Possible application sub-microm distance
measurement
Mertz Moreaux et al (2001) Biophys J
⎟⎟⎠
⎞⎜⎜⎝
⎛Θasymp
PEF
mHG
PEF
mHG NPP
22 σσ
N number of radiating molecules
Θ parameter describing signal reduction due to the sub-micrometer arrangement of the emitters within the focal volume (typ 10-2 for SHG)
222 INP PEFPEF σprop
Signal level in 2PEFmHG imaging
mmHGmHG INP σ2 Θprop
~ 10-4
(pour SHG)
rarr mHG signal strongly depends on the density of emitters
(SHG THG)
Intrinsic 2PEFSHG signals in cells and tissues
SHG = coherent second-ordernonlinear signal
no centrosymmetrySHG prop (density)2
rArr Dense and orderedmacromolecular structures
Zipfel et al (2003) PNAS 100 7075 (2003)
ldquoLive tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and SHGrdquo
- collagen fibrils
- sarcomeres
- astroglial fibers
- polarized microT bundles
cellulose starch hellip
Myofilaments = endogenous SHG source
Myocytes(Frog heart)
Boulesteix et al (2004) Opt Lett
Plot
niko
vet
al (
2006
) Bio
phys
J
SHG imaging of muscle structures
23 s acquisition
Applications sarcomere contraction measurements study of myogenesis
4 6 80
20
40
60
SHG
sig
nal (
phot
ons)
Length (microm)
sarcomere
constant variable
Saxitoxin (8 nM) 214 plusmn 002 microm
Control 231 plusmn 002 microm
rArr contracture at rest 7
N = C
R -O
H R
Possible molecularorigin the dense (crystalline) packingof peptide bonds such as amide group
Collagen triple-helix
Fibrils
Fibers
Macromolecular Organization
SHG is obtained from fibrillar collagen
SHGis observed
No SHG
Collagen I II III V XI hellip form fibrils
Collagen IV VIII X hellip form networks
rarr SHG = probe of macromolecular structuration
50 nm
Combined 2PEFSHG imaging of intact tissue
2PEFelastin
lamellae
SHGcollagenfibrils
Unstained carotid artery (Rat)λexc= 860nm
Boulesteix et al (2006) Cytometry A 69
yz
x
yz
x
yz
x
yz
x
yz
x
yz
x
yz
x
x
y
x
y
Lumen
Media
Intima
Adventitia
Endothelial cellsInternal elasticlamella
External elasticlamella
Fibroblast
Smoothmuscle cell
TiSapph
Reg Amp
z rarr
z rarr
T τ ~ 1times105
T τ ~ 4times107
fmax rTS
fmax rRA
Δz asymp ln(rTSrRA)2 asymp 2-3 scattering lengths Δz
rTS = 80 MHz
rRA = 200 kHz
log F
log FTemporal redistribution of the
same excitation power
At large depths contrast (amp resolution)
loss
hellip in vivoexperiment
( )2balscat II +
Theer amp Denk (2006) JOSA A 23 3139
2PEF imaging depth fundamental limit
Note Zmax increases with staining heterogeneity Zmax is increased by ~Ls when stained fraction is reduced 6times
Zmax reached when
( ) intint ge+focusat
balfocusofout
balscat III 22
Contribution of the different planes Model accounting for the temporal distribution of scattered light and assuming that scattering is mostly forward-directed
Influence of pulse duration rarr Using pulse duration of 20fs instead of 200fs should increase the SB ratio by 25times resulting in an increase of 05 scattering MFP to the depth limit
( )τα )(ln max)(
max TzPLz exs Φ=
How to increase imaging depth
zmax
bull Regenerative amplification multiplies Tτ by 400rarr Equivalent to multiplying P by 20
bull Implement wavefront correction to correct for specimen-induced aberrations (adaptive optics)
bull Design background rejection schemes to remove light generated out-of-focus when doing large depth imaging
B Improving excitation
bull Low mag objective multiplies Φ by 10(Only equivalent to multiplying P by 3)
bull And always non-descanned detection
A Improving collection Φ
Theer amp Denk OL2003
2PEF from a thin fluorescent slab as a function of slab defocus Ratio betweensignal detected with an unaberrated and an aberrated phase
2PEF images of a labeled glomerulus (from mouse olfactory bulb)
Wavefront correction in microscopy
Φ-Φ
Φ
Possible strategiesMeasure aberrated wavefront with wavefront sensor rarr implementation eg Denk PNAS 2006
Iterative sensorless approach with merit functioneg Wright et al OE 2007 (applied to CARS)
Model-based sensorless approach eg Deacutebarre Botcherby Booth Wilson OE 2008 (applied to structured illumination microscopy)
reference
astronomy ophtalmology microscopy
For small aberrations
( ) ( )2221 ΔΦminusasymp λπrefaber II
mean-square deformationof the wave front
( )2ΔΦ
rarr rapid impact on NL signal
LOB
-X
low-coherence interferometry+ wave-front sensing
4 images (I1hellipI4) recorded with reference path length shifts of 0 λ4 λ4 and 3λ4 For each pixel a complex amplitude A is calculated by
Reference
Sample
Low-coherence sourceTiS 915nm 100fs
CCD
( ) ( ) ⎟⎠⎞⎜
⎝⎛ ΔΔminus++=
22ln2expcos τνπδϕsrsrD iiiiI
z-resolution ~ 20 micromνΔ FWHM of source power spectral density
νΔprop 1
δϕ applied phase shift
τΔ delay due to path difference
+ ldquocompatiblerdquo with 2PEF microscopy
obj
(conjug with objective back focal plane)
Feieraband et al (2004) Opt Lett 29 2255Ruumlckel et al (2006) PNAS 103 17137Ruumlckel et al (2007) JOSA A 25 3517
δϕ
τΔ
6times 2PEF signal improvement
(2006) PNAS 103 17137
1P excitation 2P excitation
2PEF SHG prop I2
2PEF SHG
3PEF THG prop I3
excitation(IR)
F prop I
Fluoexcitation(visible) ωP ωS
3P excitation
3PEF
CARS prop IP2 IS
THG CARS
Different contrast mechanisms rarr different information
In particular SHG second harmonic generation ndash sensitive to symmetry at the sub-microm scaleTHG third harmonic generation ndash detects interfaces and microm-size inclusionsCARS laquononlinear Ramanraquo ndash chemical specificity
SHG THG specifically obtained from certain structures(little spectroscopic information)
Alternative contrast modes SHG THG CARS
E(ω) P(ω)
E(ω)
P(ω)
P(3ω)
SHG
THG
P(2ω)
Harmonic signal depends on the nature of the emitting medium
P(2ω)=frac12χ(2)(minus2ωωω) E(ω)E(ω)P(3ω)=frac14χ(3)(minus3ωωωω) E(ω)E(ω)E(ω)
Nonlinear microscopy harmonic generation
P = P(ω) + P(2)(2ω) + middot middot middot + P(n)(nω)= PL + PNL
avec P(n)(nω) =
Polarisable medium excited by an intense field components of order ngt1 in the induced polarization
rarr Emission at harmonic frequencies (nonlinear scattering)
non zero χ(2) =gt non centrosymmetric mediumχ(3) non zero everywhere (but weak)
Multiphoton microscope rarr combined contrast modes
2PEFsignal
SHGsignal
Osc
illato
r
THGsignal
Example of push-pull laquo harmonophore raquo molecule for SHG
(SHG)
Example stylbene derivative
hellip and amphiphilic version (for lipid membrane labeling)
M Blanchard-Desce (Univ Rennes)
SHG = coherent process (ne 2PEF)rarr possibility of constructive and destructive interferences
Example (labeled vesicle) parallel molecules rarr SHG
antiparallel molecules rarr no SHG (centrosymmetric medium)
Mertz amp Moreaux OL 2001
Constructive interference rarr enhanced signal Destructive interfeacuterence rarr null signal
Molecules emitting in phase Molecules emitting with opposite phases
ϕ1 = 0
ϕ2 = 0
ϕ1 = 0
ϕ2 = π
SHG
SHG
Excitation2PEF
Note in contrast 2PEF emission does not
depend on symmetry
SHG microscopy adapted for
membrane imaging
hellipand some endogenousstructures (see later)
Mor
eaux
Mer
tz e
t al
Bio
phys
J 8
0 1
568
(200
1)
SHG 2PEF
Wavelength (nm)400 450 500 550 600 650
Pow
er (a
u)
00
05
10
430 435 440 445 450
SH
G P
ower
(au
)
00
05
10
fluorescence
SHG
Spectrum radiated from a GUV labeledwith the styryl dye Di-6-ASPBS
Phase matching in (coherent) nonlinear optics
zLc
If Δkne0 (dispersion) I2ω(z) prop sin2Δkz2coherent signal buildup is limited to Lc
If Δk=0 (phase-matching case) I2ω(z) prop z2
Δk = k2ω - 2kω = wave vector mismatch
laquoClassicalraquo example SHG by plane wave propagating in a nonlinear medium
Note if Δkne0 phase-matching
can be forced in a birefringent crystal eg
where ne(2ω)ltno(ω)
keθ(2ω)=2ko(ω)neθ(2ω)=2no(ω)
The same applies for other NL processes
such as THG
Lc = coherence length
But what happens in a tightly focused geometry
bull Presence of transverse componentsbull Many possible k
kω = 2π nω λ
I Field near focus from arbitrary pupil profile (Cf Richards amp Wolf 1959 Born amp Wolf 1980)
III Far-field signal (Cf Novotny amp Hecht 2006)
II Induced polarization density near focus
For a homogeneous isotropic medium
expressed using Greenrsquos function
Signal generation in coherent NL microscopy
Example for THG
Solve wave equation taking into account NL polarizations created at various locations in the focal volume + coherent superposition in the detector plane
( )int int ΘΦΘpropmax
0
2
0
22(det) sinα π
RREFFddPDetected power
Field near focus phase distribution
Phase anomaly of focused beams (Gouy phase)LG Gouy CR Acad Sciences Paris 1890
Intensity near focus
minusπ (Gouy shift)
0Phase near focus
Cal
culN
Oliv
ier (
LOB
)
Approximation of tightly focused field for modeling nonlinear interactions GaussianGaussian amplitude and reduced axial wave vector
( ) xexp 2
2
2
22
⎟⎟⎠
⎞⎜⎜⎝
⎛minusminus
+minusminusasymp zki
wz
wyxiEzyxE
zrωωω ξ
wr wz 1e radii of the focal ellipse
2221 rwkωξ minusasymp
CfM
orea
ux S
andr
e M
ertz
(200
0) J
OSA
B 1
7 1
685
For a linearly x-polarized beam near focus
z (nm)
z
ωξ k
2 Iξ
ωω πω nk 2=
880nm NA=09
ω 2ω
0
-πPha
se a
nom
aly
Axial direction
)(cos 1 ξθ minus=slope prop (ξminus1)
Normalized intensitysquared
SHG from a labeled membrane Gouy shift deflects emission off-axis
θ
k2ω
ξ kω ξ kω
(ξlt1)
Mertz Moreaux et al (2001) Biophys J
Sample and field structure govern emission diagrams
emax asymp 06w0
Exemple of coherence effectobservation of SHG laquo hot spots raquo whenlabeled vesicules are in close proximity
Possible application sub-microm distance
measurement
Mertz Moreaux et al (2001) Biophys J
⎟⎟⎠
⎞⎜⎜⎝
⎛Θasymp
PEF
mHG
PEF
mHG NPP
22 σσ
N number of radiating molecules
Θ parameter describing signal reduction due to the sub-micrometer arrangement of the emitters within the focal volume (typ 10-2 for SHG)
222 INP PEFPEF σprop
Signal level in 2PEFmHG imaging
mmHGmHG INP σ2 Θprop
~ 10-4
(pour SHG)
rarr mHG signal strongly depends on the density of emitters
(SHG THG)
Intrinsic 2PEFSHG signals in cells and tissues
SHG = coherent second-ordernonlinear signal
no centrosymmetrySHG prop (density)2
rArr Dense and orderedmacromolecular structures
Zipfel et al (2003) PNAS 100 7075 (2003)
ldquoLive tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and SHGrdquo
- collagen fibrils
- sarcomeres
- astroglial fibers
- polarized microT bundles
cellulose starch hellip
Myofilaments = endogenous SHG source
Myocytes(Frog heart)
Boulesteix et al (2004) Opt Lett
Plot
niko
vet
al (
2006
) Bio
phys
J
SHG imaging of muscle structures
23 s acquisition
Applications sarcomere contraction measurements study of myogenesis
4 6 80
20
40
60
SHG
sig
nal (
phot
ons)
Length (microm)
sarcomere
constant variable
Saxitoxin (8 nM) 214 plusmn 002 microm
Control 231 plusmn 002 microm
rArr contracture at rest 7
N = C
R -O
H R
Possible molecularorigin the dense (crystalline) packingof peptide bonds such as amide group
Collagen triple-helix
Fibrils
Fibers
Macromolecular Organization
SHG is obtained from fibrillar collagen
SHGis observed
No SHG
Collagen I II III V XI hellip form fibrils
Collagen IV VIII X hellip form networks
rarr SHG = probe of macromolecular structuration
50 nm
Combined 2PEFSHG imaging of intact tissue
2PEFelastin
lamellae
SHGcollagenfibrils
Unstained carotid artery (Rat)λexc= 860nm
Boulesteix et al (2006) Cytometry A 69
yz
x
yz
x
yz
x
yz
x
yz
x
yz
x
yz
x
x
y
x
y
Lumen
Media
Intima
Adventitia
Endothelial cellsInternal elasticlamella
External elasticlamella
Fibroblast
Smoothmuscle cell
2PEF from a thin fluorescent slab as a function of slab defocus Ratio betweensignal detected with an unaberrated and an aberrated phase
2PEF images of a labeled glomerulus (from mouse olfactory bulb)
Wavefront correction in microscopy
Φ-Φ
Φ
Possible strategiesMeasure aberrated wavefront with wavefront sensor rarr implementation eg Denk PNAS 2006
Iterative sensorless approach with merit functioneg Wright et al OE 2007 (applied to CARS)
Model-based sensorless approach eg Deacutebarre Botcherby Booth Wilson OE 2008 (applied to structured illumination microscopy)
reference
astronomy ophtalmology microscopy
For small aberrations
( ) ( )2221 ΔΦminusasymp λπrefaber II
mean-square deformationof the wave front
( )2ΔΦ
rarr rapid impact on NL signal
LOB
-X
low-coherence interferometry+ wave-front sensing
4 images (I1hellipI4) recorded with reference path length shifts of 0 λ4 λ4 and 3λ4 For each pixel a complex amplitude A is calculated by
Reference
Sample
Low-coherence sourceTiS 915nm 100fs
CCD
( ) ( ) ⎟⎠⎞⎜
⎝⎛ ΔΔminus++=
22ln2expcos τνπδϕsrsrD iiiiI
z-resolution ~ 20 micromνΔ FWHM of source power spectral density
νΔprop 1
δϕ applied phase shift
τΔ delay due to path difference
+ ldquocompatiblerdquo with 2PEF microscopy
obj
(conjug with objective back focal plane)
Feieraband et al (2004) Opt Lett 29 2255Ruumlckel et al (2006) PNAS 103 17137Ruumlckel et al (2007) JOSA A 25 3517
δϕ
τΔ
6times 2PEF signal improvement
(2006) PNAS 103 17137
1P excitation 2P excitation
2PEF SHG prop I2
2PEF SHG
3PEF THG prop I3
excitation(IR)
F prop I
Fluoexcitation(visible) ωP ωS
3P excitation
3PEF
CARS prop IP2 IS
THG CARS
Different contrast mechanisms rarr different information
In particular SHG second harmonic generation ndash sensitive to symmetry at the sub-microm scaleTHG third harmonic generation ndash detects interfaces and microm-size inclusionsCARS laquononlinear Ramanraquo ndash chemical specificity
SHG THG specifically obtained from certain structures(little spectroscopic information)
Alternative contrast modes SHG THG CARS
E(ω) P(ω)
E(ω)
P(ω)
P(3ω)
SHG
THG
P(2ω)
Harmonic signal depends on the nature of the emitting medium
P(2ω)=frac12χ(2)(minus2ωωω) E(ω)E(ω)P(3ω)=frac14χ(3)(minus3ωωωω) E(ω)E(ω)E(ω)
Nonlinear microscopy harmonic generation
P = P(ω) + P(2)(2ω) + middot middot middot + P(n)(nω)= PL + PNL
avec P(n)(nω) =
Polarisable medium excited by an intense field components of order ngt1 in the induced polarization
rarr Emission at harmonic frequencies (nonlinear scattering)
non zero χ(2) =gt non centrosymmetric mediumχ(3) non zero everywhere (but weak)
Multiphoton microscope rarr combined contrast modes
2PEFsignal
SHGsignal
Osc
illato
r
THGsignal
Example of push-pull laquo harmonophore raquo molecule for SHG
(SHG)
Example stylbene derivative
hellip and amphiphilic version (for lipid membrane labeling)
M Blanchard-Desce (Univ Rennes)
SHG = coherent process (ne 2PEF)rarr possibility of constructive and destructive interferences
Example (labeled vesicle) parallel molecules rarr SHG
antiparallel molecules rarr no SHG (centrosymmetric medium)
Mertz amp Moreaux OL 2001
Constructive interference rarr enhanced signal Destructive interfeacuterence rarr null signal
Molecules emitting in phase Molecules emitting with opposite phases
ϕ1 = 0
ϕ2 = 0
ϕ1 = 0
ϕ2 = π
SHG
SHG
Excitation2PEF
Note in contrast 2PEF emission does not
depend on symmetry
SHG microscopy adapted for
membrane imaging
hellipand some endogenousstructures (see later)
Mor
eaux
Mer
tz e
t al
Bio
phys
J 8
0 1
568
(200
1)
SHG 2PEF
Wavelength (nm)400 450 500 550 600 650
Pow
er (a
u)
00
05
10
430 435 440 445 450
SH
G P
ower
(au
)
00
05
10
fluorescence
SHG
Spectrum radiated from a GUV labeledwith the styryl dye Di-6-ASPBS
Phase matching in (coherent) nonlinear optics
zLc
If Δkne0 (dispersion) I2ω(z) prop sin2Δkz2coherent signal buildup is limited to Lc
If Δk=0 (phase-matching case) I2ω(z) prop z2
Δk = k2ω - 2kω = wave vector mismatch
laquoClassicalraquo example SHG by plane wave propagating in a nonlinear medium
Note if Δkne0 phase-matching
can be forced in a birefringent crystal eg
where ne(2ω)ltno(ω)
keθ(2ω)=2ko(ω)neθ(2ω)=2no(ω)
The same applies for other NL processes
such as THG
Lc = coherence length
But what happens in a tightly focused geometry
bull Presence of transverse componentsbull Many possible k
kω = 2π nω λ
I Field near focus from arbitrary pupil profile (Cf Richards amp Wolf 1959 Born amp Wolf 1980)
III Far-field signal (Cf Novotny amp Hecht 2006)
II Induced polarization density near focus
For a homogeneous isotropic medium
expressed using Greenrsquos function
Signal generation in coherent NL microscopy
Example for THG
Solve wave equation taking into account NL polarizations created at various locations in the focal volume + coherent superposition in the detector plane
( )int int ΘΦΘpropmax
0
2
0
22(det) sinα π
RREFFddPDetected power
Field near focus phase distribution
Phase anomaly of focused beams (Gouy phase)LG Gouy CR Acad Sciences Paris 1890
Intensity near focus
minusπ (Gouy shift)
0Phase near focus
Cal
culN
Oliv
ier (
LOB
)
Approximation of tightly focused field for modeling nonlinear interactions GaussianGaussian amplitude and reduced axial wave vector
( ) xexp 2
2
2
22
⎟⎟⎠
⎞⎜⎜⎝
⎛minusminus
+minusminusasymp zki
wz
wyxiEzyxE
zrωωω ξ
wr wz 1e radii of the focal ellipse
2221 rwkωξ minusasymp
CfM
orea
ux S
andr
e M
ertz
(200
0) J
OSA
B 1
7 1
685
For a linearly x-polarized beam near focus
z (nm)
z
ωξ k
2 Iξ
ωω πω nk 2=
880nm NA=09
ω 2ω
0
-πPha
se a
nom
aly
Axial direction
)(cos 1 ξθ minus=slope prop (ξminus1)
Normalized intensitysquared
SHG from a labeled membrane Gouy shift deflects emission off-axis
θ
k2ω
ξ kω ξ kω
(ξlt1)
Mertz Moreaux et al (2001) Biophys J
Sample and field structure govern emission diagrams
emax asymp 06w0
Exemple of coherence effectobservation of SHG laquo hot spots raquo whenlabeled vesicules are in close proximity
Possible application sub-microm distance
measurement
Mertz Moreaux et al (2001) Biophys J
⎟⎟⎠
⎞⎜⎜⎝
⎛Θasymp
PEF
mHG
PEF
mHG NPP
22 σσ
N number of radiating molecules
Θ parameter describing signal reduction due to the sub-micrometer arrangement of the emitters within the focal volume (typ 10-2 for SHG)
222 INP PEFPEF σprop
Signal level in 2PEFmHG imaging
mmHGmHG INP σ2 Θprop
~ 10-4
(pour SHG)
rarr mHG signal strongly depends on the density of emitters
(SHG THG)
Intrinsic 2PEFSHG signals in cells and tissues
SHG = coherent second-ordernonlinear signal
no centrosymmetrySHG prop (density)2
rArr Dense and orderedmacromolecular structures
Zipfel et al (2003) PNAS 100 7075 (2003)
ldquoLive tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and SHGrdquo
- collagen fibrils
- sarcomeres
- astroglial fibers
- polarized microT bundles
cellulose starch hellip
Myofilaments = endogenous SHG source
Myocytes(Frog heart)
Boulesteix et al (2004) Opt Lett
Plot
niko
vet
al (
2006
) Bio
phys
J
SHG imaging of muscle structures
23 s acquisition
Applications sarcomere contraction measurements study of myogenesis
4 6 80
20
40
60
SHG
sig
nal (
phot
ons)
Length (microm)
sarcomere
constant variable
Saxitoxin (8 nM) 214 plusmn 002 microm
Control 231 plusmn 002 microm
rArr contracture at rest 7
N = C
R -O
H R
Possible molecularorigin the dense (crystalline) packingof peptide bonds such as amide group
Collagen triple-helix
Fibrils
Fibers
Macromolecular Organization
SHG is obtained from fibrillar collagen
SHGis observed
No SHG
Collagen I II III V XI hellip form fibrils
Collagen IV VIII X hellip form networks
rarr SHG = probe of macromolecular structuration
50 nm
Combined 2PEFSHG imaging of intact tissue
2PEFelastin
lamellae
SHGcollagenfibrils
Unstained carotid artery (Rat)λexc= 860nm
Boulesteix et al (2006) Cytometry A 69
yz
x
yz
x
yz
x
yz
x
yz
x
yz
x
yz
x
x
y
x
y
Lumen
Media
Intima
Adventitia
Endothelial cellsInternal elasticlamella
External elasticlamella
Fibroblast
Smoothmuscle cell
1P excitation 2P excitation
2PEF SHG prop I2
2PEF SHG
3PEF THG prop I3
excitation(IR)
F prop I
Fluoexcitation(visible) ωP ωS
3P excitation
3PEF
CARS prop IP2 IS
THG CARS
Different contrast mechanisms rarr different information
In particular SHG second harmonic generation ndash sensitive to symmetry at the sub-microm scaleTHG third harmonic generation ndash detects interfaces and microm-size inclusionsCARS laquononlinear Ramanraquo ndash chemical specificity
SHG THG specifically obtained from certain structures(little spectroscopic information)
Alternative contrast modes SHG THG CARS
E(ω) P(ω)
E(ω)
P(ω)
P(3ω)
SHG
THG
P(2ω)
Harmonic signal depends on the nature of the emitting medium
P(2ω)=frac12χ(2)(minus2ωωω) E(ω)E(ω)P(3ω)=frac14χ(3)(minus3ωωωω) E(ω)E(ω)E(ω)
Nonlinear microscopy harmonic generation
P = P(ω) + P(2)(2ω) + middot middot middot + P(n)(nω)= PL + PNL
avec P(n)(nω) =
Polarisable medium excited by an intense field components of order ngt1 in the induced polarization
rarr Emission at harmonic frequencies (nonlinear scattering)
non zero χ(2) =gt non centrosymmetric mediumχ(3) non zero everywhere (but weak)
Multiphoton microscope rarr combined contrast modes
2PEFsignal
SHGsignal
Osc
illato
r
THGsignal
Example of push-pull laquo harmonophore raquo molecule for SHG
(SHG)
Example stylbene derivative
hellip and amphiphilic version (for lipid membrane labeling)
M Blanchard-Desce (Univ Rennes)
SHG = coherent process (ne 2PEF)rarr possibility of constructive and destructive interferences
Example (labeled vesicle) parallel molecules rarr SHG
antiparallel molecules rarr no SHG (centrosymmetric medium)
Mertz amp Moreaux OL 2001
Constructive interference rarr enhanced signal Destructive interfeacuterence rarr null signal
Molecules emitting in phase Molecules emitting with opposite phases
ϕ1 = 0
ϕ2 = 0
ϕ1 = 0
ϕ2 = π
SHG
SHG
Excitation2PEF
Note in contrast 2PEF emission does not
depend on symmetry
SHG microscopy adapted for
membrane imaging
hellipand some endogenousstructures (see later)
Mor
eaux
Mer
tz e
t al
Bio
phys
J 8
0 1
568
(200
1)
SHG 2PEF
Wavelength (nm)400 450 500 550 600 650
Pow
er (a
u)
00
05
10
430 435 440 445 450
SH
G P
ower
(au
)
00
05
10
fluorescence
SHG
Spectrum radiated from a GUV labeledwith the styryl dye Di-6-ASPBS
Phase matching in (coherent) nonlinear optics
zLc
If Δkne0 (dispersion) I2ω(z) prop sin2Δkz2coherent signal buildup is limited to Lc
If Δk=0 (phase-matching case) I2ω(z) prop z2
Δk = k2ω - 2kω = wave vector mismatch
laquoClassicalraquo example SHG by plane wave propagating in a nonlinear medium
Note if Δkne0 phase-matching
can be forced in a birefringent crystal eg
where ne(2ω)ltno(ω)
keθ(2ω)=2ko(ω)neθ(2ω)=2no(ω)
The same applies for other NL processes
such as THG
Lc = coherence length
But what happens in a tightly focused geometry
bull Presence of transverse componentsbull Many possible k
kω = 2π nω λ
I Field near focus from arbitrary pupil profile (Cf Richards amp Wolf 1959 Born amp Wolf 1980)
III Far-field signal (Cf Novotny amp Hecht 2006)
II Induced polarization density near focus
For a homogeneous isotropic medium
expressed using Greenrsquos function
Signal generation in coherent NL microscopy
Example for THG
Solve wave equation taking into account NL polarizations created at various locations in the focal volume + coherent superposition in the detector plane
( )int int ΘΦΘpropmax
0
2
0
22(det) sinα π
RREFFddPDetected power
Field near focus phase distribution
Phase anomaly of focused beams (Gouy phase)LG Gouy CR Acad Sciences Paris 1890
Intensity near focus
minusπ (Gouy shift)
0Phase near focus
Cal
culN
Oliv
ier (
LOB
)
Approximation of tightly focused field for modeling nonlinear interactions GaussianGaussian amplitude and reduced axial wave vector
( ) xexp 2
2
2
22
⎟⎟⎠
⎞⎜⎜⎝
⎛minusminus
+minusminusasymp zki
wz
wyxiEzyxE
zrωωω ξ
wr wz 1e radii of the focal ellipse
2221 rwkωξ minusasymp
CfM
orea
ux S
andr
e M
ertz
(200
0) J
OSA
B 1
7 1
685
For a linearly x-polarized beam near focus
z (nm)
z
ωξ k
2 Iξ
ωω πω nk 2=
880nm NA=09
ω 2ω
0
-πPha
se a
nom
aly
Axial direction
)(cos 1 ξθ minus=slope prop (ξminus1)
Normalized intensitysquared
SHG from a labeled membrane Gouy shift deflects emission off-axis
θ
k2ω
ξ kω ξ kω
(ξlt1)
Mertz Moreaux et al (2001) Biophys J
Sample and field structure govern emission diagrams
emax asymp 06w0
Exemple of coherence effectobservation of SHG laquo hot spots raquo whenlabeled vesicules are in close proximity
Possible application sub-microm distance
measurement
Mertz Moreaux et al (2001) Biophys J
⎟⎟⎠
⎞⎜⎜⎝
⎛Θasymp
PEF
mHG
PEF
mHG NPP
22 σσ
N number of radiating molecules
Θ parameter describing signal reduction due to the sub-micrometer arrangement of the emitters within the focal volume (typ 10-2 for SHG)
222 INP PEFPEF σprop
Signal level in 2PEFmHG imaging
mmHGmHG INP σ2 Θprop
~ 10-4
(pour SHG)
rarr mHG signal strongly depends on the density of emitters
(SHG THG)
Intrinsic 2PEFSHG signals in cells and tissues
SHG = coherent second-ordernonlinear signal
no centrosymmetrySHG prop (density)2
rArr Dense and orderedmacromolecular structures
Zipfel et al (2003) PNAS 100 7075 (2003)
ldquoLive tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and SHGrdquo
- collagen fibrils
- sarcomeres
- astroglial fibers
- polarized microT bundles
cellulose starch hellip
Myofilaments = endogenous SHG source
Myocytes(Frog heart)
Boulesteix et al (2004) Opt Lett
Plot
niko
vet
al (
2006
) Bio
phys
J
SHG imaging of muscle structures
23 s acquisition
Applications sarcomere contraction measurements study of myogenesis
4 6 80
20
40
60
SHG
sig
nal (
phot
ons)
Length (microm)
sarcomere
constant variable
Saxitoxin (8 nM) 214 plusmn 002 microm
Control 231 plusmn 002 microm
rArr contracture at rest 7
N = C
R -O
H R
Possible molecularorigin the dense (crystalline) packingof peptide bonds such as amide group
Collagen triple-helix
Fibrils
Fibers
Macromolecular Organization
SHG is obtained from fibrillar collagen
SHGis observed
No SHG
Collagen I II III V XI hellip form fibrils
Collagen IV VIII X hellip form networks
rarr SHG = probe of macromolecular structuration
50 nm
Combined 2PEFSHG imaging of intact tissue
2PEFelastin
lamellae
SHGcollagenfibrils
Unstained carotid artery (Rat)λexc= 860nm
Boulesteix et al (2006) Cytometry A 69
yz
x
yz
x
yz
x
yz
x
yz
x
yz
x
yz
x
x
y
x
y
Lumen
Media
Intima
Adventitia
Endothelial cellsInternal elasticlamella
External elasticlamella
Fibroblast
Smoothmuscle cell
SHG = coherent process (ne 2PEF)rarr possibility of constructive and destructive interferences
Example (labeled vesicle) parallel molecules rarr SHG
antiparallel molecules rarr no SHG (centrosymmetric medium)
Mertz amp Moreaux OL 2001
Constructive interference rarr enhanced signal Destructive interfeacuterence rarr null signal
Molecules emitting in phase Molecules emitting with opposite phases
ϕ1 = 0
ϕ2 = 0
ϕ1 = 0
ϕ2 = π
SHG
SHG
Excitation2PEF
Note in contrast 2PEF emission does not
depend on symmetry
SHG microscopy adapted for
membrane imaging
hellipand some endogenousstructures (see later)
Mor
eaux
Mer
tz e
t al
Bio
phys
J 8
0 1
568
(200
1)
SHG 2PEF
Wavelength (nm)400 450 500 550 600 650
Pow
er (a
u)
00
05
10
430 435 440 445 450
SH
G P
ower
(au
)
00
05
10
fluorescence
SHG
Spectrum radiated from a GUV labeledwith the styryl dye Di-6-ASPBS
Phase matching in (coherent) nonlinear optics
zLc
If Δkne0 (dispersion) I2ω(z) prop sin2Δkz2coherent signal buildup is limited to Lc
If Δk=0 (phase-matching case) I2ω(z) prop z2
Δk = k2ω - 2kω = wave vector mismatch
laquoClassicalraquo example SHG by plane wave propagating in a nonlinear medium
Note if Δkne0 phase-matching
can be forced in a birefringent crystal eg
where ne(2ω)ltno(ω)
keθ(2ω)=2ko(ω)neθ(2ω)=2no(ω)
The same applies for other NL processes
such as THG
Lc = coherence length
But what happens in a tightly focused geometry
bull Presence of transverse componentsbull Many possible k
kω = 2π nω λ
I Field near focus from arbitrary pupil profile (Cf Richards amp Wolf 1959 Born amp Wolf 1980)
III Far-field signal (Cf Novotny amp Hecht 2006)
II Induced polarization density near focus
For a homogeneous isotropic medium
expressed using Greenrsquos function
Signal generation in coherent NL microscopy
Example for THG
Solve wave equation taking into account NL polarizations created at various locations in the focal volume + coherent superposition in the detector plane
( )int int ΘΦΘpropmax
0
2
0
22(det) sinα π
RREFFddPDetected power
Field near focus phase distribution
Phase anomaly of focused beams (Gouy phase)LG Gouy CR Acad Sciences Paris 1890
Intensity near focus
minusπ (Gouy shift)
0Phase near focus
Cal
culN
Oliv
ier (
LOB
)
Approximation of tightly focused field for modeling nonlinear interactions GaussianGaussian amplitude and reduced axial wave vector
( ) xexp 2
2
2
22
⎟⎟⎠
⎞⎜⎜⎝
⎛minusminus
+minusminusasymp zki
wz
wyxiEzyxE
zrωωω ξ
wr wz 1e radii of the focal ellipse
2221 rwkωξ minusasymp
CfM
orea
ux S
andr
e M
ertz
(200
0) J
OSA
B 1
7 1
685
For a linearly x-polarized beam near focus
z (nm)
z
ωξ k
2 Iξ
ωω πω nk 2=
880nm NA=09
ω 2ω
0
-πPha
se a
nom
aly
Axial direction
)(cos 1 ξθ minus=slope prop (ξminus1)
Normalized intensitysquared
SHG from a labeled membrane Gouy shift deflects emission off-axis
θ
k2ω
ξ kω ξ kω
(ξlt1)
Mertz Moreaux et al (2001) Biophys J
Sample and field structure govern emission diagrams
emax asymp 06w0
Exemple of coherence effectobservation of SHG laquo hot spots raquo whenlabeled vesicules are in close proximity
Possible application sub-microm distance
measurement
Mertz Moreaux et al (2001) Biophys J
⎟⎟⎠
⎞⎜⎜⎝
⎛Θasymp
PEF
mHG
PEF
mHG NPP
22 σσ
N number of radiating molecules
Θ parameter describing signal reduction due to the sub-micrometer arrangement of the emitters within the focal volume (typ 10-2 for SHG)
222 INP PEFPEF σprop
Signal level in 2PEFmHG imaging
mmHGmHG INP σ2 Θprop
~ 10-4
(pour SHG)
rarr mHG signal strongly depends on the density of emitters
(SHG THG)
Intrinsic 2PEFSHG signals in cells and tissues
SHG = coherent second-ordernonlinear signal
no centrosymmetrySHG prop (density)2
rArr Dense and orderedmacromolecular structures
Zipfel et al (2003) PNAS 100 7075 (2003)
ldquoLive tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and SHGrdquo
- collagen fibrils
- sarcomeres
- astroglial fibers
- polarized microT bundles
cellulose starch hellip
Myofilaments = endogenous SHG source
Myocytes(Frog heart)
Boulesteix et al (2004) Opt Lett
Plot
niko
vet
al (
2006
) Bio
phys
J
SHG imaging of muscle structures
23 s acquisition
Applications sarcomere contraction measurements study of myogenesis
4 6 80
20
40
60
SHG
sig
nal (
phot
ons)
Length (microm)
sarcomere
constant variable
Saxitoxin (8 nM) 214 plusmn 002 microm
Control 231 plusmn 002 microm
rArr contracture at rest 7
N = C
R -O
H R
Possible molecularorigin the dense (crystalline) packingof peptide bonds such as amide group
Collagen triple-helix
Fibrils
Fibers
Macromolecular Organization
SHG is obtained from fibrillar collagen
SHGis observed
No SHG
Collagen I II III V XI hellip form fibrils
Collagen IV VIII X hellip form networks
rarr SHG = probe of macromolecular structuration
50 nm
Combined 2PEFSHG imaging of intact tissue
2PEFelastin
lamellae
SHGcollagenfibrils
Unstained carotid artery (Rat)λexc= 860nm
Boulesteix et al (2006) Cytometry A 69
yz
x
yz
x
yz
x
yz
x
yz
x
yz
x
yz
x
x
y
x
y
Lumen
Media
Intima
Adventitia
Endothelial cellsInternal elasticlamella
External elasticlamella
Fibroblast
Smoothmuscle cell
Field near focus phase distribution
Phase anomaly of focused beams (Gouy phase)LG Gouy CR Acad Sciences Paris 1890
Intensity near focus
minusπ (Gouy shift)
0Phase near focus
Cal
culN
Oliv
ier (
LOB
)
Approximation of tightly focused field for modeling nonlinear interactions GaussianGaussian amplitude and reduced axial wave vector
( ) xexp 2
2
2
22
⎟⎟⎠
⎞⎜⎜⎝
⎛minusminus
+minusminusasymp zki
wz
wyxiEzyxE
zrωωω ξ
wr wz 1e radii of the focal ellipse
2221 rwkωξ minusasymp
CfM
orea
ux S
andr
e M
ertz
(200
0) J
OSA
B 1
7 1
685
For a linearly x-polarized beam near focus
z (nm)
z
ωξ k
2 Iξ
ωω πω nk 2=
880nm NA=09
ω 2ω
0
-πPha
se a
nom
aly
Axial direction
)(cos 1 ξθ minus=slope prop (ξminus1)
Normalized intensitysquared
SHG from a labeled membrane Gouy shift deflects emission off-axis
θ
k2ω
ξ kω ξ kω
(ξlt1)
Mertz Moreaux et al (2001) Biophys J
Sample and field structure govern emission diagrams
emax asymp 06w0
Exemple of coherence effectobservation of SHG laquo hot spots raquo whenlabeled vesicules are in close proximity
Possible application sub-microm distance
measurement
Mertz Moreaux et al (2001) Biophys J
⎟⎟⎠
⎞⎜⎜⎝
⎛Θasymp
PEF
mHG
PEF
mHG NPP
22 σσ
N number of radiating molecules
Θ parameter describing signal reduction due to the sub-micrometer arrangement of the emitters within the focal volume (typ 10-2 for SHG)
222 INP PEFPEF σprop
Signal level in 2PEFmHG imaging
mmHGmHG INP σ2 Θprop
~ 10-4
(pour SHG)
rarr mHG signal strongly depends on the density of emitters
(SHG THG)
Intrinsic 2PEFSHG signals in cells and tissues
SHG = coherent second-ordernonlinear signal
no centrosymmetrySHG prop (density)2
rArr Dense and orderedmacromolecular structures
Zipfel et al (2003) PNAS 100 7075 (2003)
ldquoLive tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and SHGrdquo
- collagen fibrils
- sarcomeres
- astroglial fibers
- polarized microT bundles
cellulose starch hellip
Myofilaments = endogenous SHG source
Myocytes(Frog heart)
Boulesteix et al (2004) Opt Lett
Plot
niko
vet
al (
2006
) Bio
phys
J
SHG imaging of muscle structures
23 s acquisition
Applications sarcomere contraction measurements study of myogenesis
4 6 80
20
40
60
SHG
sig
nal (
phot
ons)
Length (microm)
sarcomere
constant variable
Saxitoxin (8 nM) 214 plusmn 002 microm
Control 231 plusmn 002 microm
rArr contracture at rest 7
N = C
R -O
H R
Possible molecularorigin the dense (crystalline) packingof peptide bonds such as amide group
Collagen triple-helix
Fibrils
Fibers
Macromolecular Organization
SHG is obtained from fibrillar collagen
SHGis observed
No SHG
Collagen I II III V XI hellip form fibrils
Collagen IV VIII X hellip form networks
rarr SHG = probe of macromolecular structuration
50 nm
Combined 2PEFSHG imaging of intact tissue
2PEFelastin
lamellae
SHGcollagenfibrils
Unstained carotid artery (Rat)λexc= 860nm
Boulesteix et al (2006) Cytometry A 69
yz
x
yz
x
yz
x
yz
x
yz
x
yz
x
yz
x
x
y
x
y
Lumen
Media
Intima
Adventitia
Endothelial cellsInternal elasticlamella
External elasticlamella
Fibroblast
Smoothmuscle cell
Intrinsic 2PEFSHG signals in cells and tissues
SHG = coherent second-ordernonlinear signal
no centrosymmetrySHG prop (density)2
rArr Dense and orderedmacromolecular structures
Zipfel et al (2003) PNAS 100 7075 (2003)
ldquoLive tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and SHGrdquo
- collagen fibrils
- sarcomeres
- astroglial fibers
- polarized microT bundles
cellulose starch hellip
Myofilaments = endogenous SHG source
Myocytes(Frog heart)
Boulesteix et al (2004) Opt Lett
Plot
niko
vet
al (
2006
) Bio
phys
J
SHG imaging of muscle structures
23 s acquisition
Applications sarcomere contraction measurements study of myogenesis
4 6 80
20
40
60
SHG
sig
nal (
phot
ons)
Length (microm)
sarcomere
constant variable
Saxitoxin (8 nM) 214 plusmn 002 microm
Control 231 plusmn 002 microm
rArr contracture at rest 7
N = C
R -O
H R
Possible molecularorigin the dense (crystalline) packingof peptide bonds such as amide group
Collagen triple-helix
Fibrils
Fibers
Macromolecular Organization
SHG is obtained from fibrillar collagen
SHGis observed
No SHG
Collagen I II III V XI hellip form fibrils
Collagen IV VIII X hellip form networks
rarr SHG = probe of macromolecular structuration
50 nm
Combined 2PEFSHG imaging of intact tissue
2PEFelastin
lamellae
SHGcollagenfibrils
Unstained carotid artery (Rat)λexc= 860nm
Boulesteix et al (2006) Cytometry A 69
yz
x
yz
x
yz
x
yz
x
yz
x
yz
x
yz
x
x
y
x
y
Lumen
Media
Intima
Adventitia
Endothelial cellsInternal elasticlamella
External elasticlamella
Fibroblast
Smoothmuscle cell
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