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Reference: Bio l. Bul l. 1 9 5: 1 4 .Aug ust , 1 9 98 )
Concepts in Imaging and M icroscopy
C hoosing O bjective L enses:
The Im portance of Num erical Aperture
and Magnifica tion
in D igital O ptical M icroscopy
DA VID W . PISTON
Dep artm en t o f Mo le cu la r Phy sio lo gy a nd B io ph ysic s V an de rb ilt Un iv er sity
Nashvi ll e Tennes se e 37232 -0615
A bstract. M icroscopic images are characterized by a
n um be r o f m ic ro sc op e-sp ec ific p ara me te rs n um eric al a p
erture (NA ), magnification (M ), and resolution (R)and
b y p ara meters th at a lso d ep en d o n th e sp ecim en for ex
am ple, co ntrast, sig na l-to -n oise ratio , d ynam ic rang e, an d
integration tim e. In this article, issues associated w ith the
m ic ro sc op e- sp ec if ic p ar am e te rs N A , M , a nd R a re d is cu ss ed
w ith respect to both w idefield and laser scanning confocal
m ic ro sc op ie s. A lth ou gh m o st o f th e d isc uss io n p oin ts a pp ly
to o ptic al m ic ro sc op y in g en er al, th e m ain a pp lic atio n c on
sidered is fluorescence m icroscopy.
Introduction
T he o bjectiv e len s is a rg ua bly th e m ost im po rtan t co rn
ponent of any light m icroscope (K eller, 1995). A dvances
in d igital im agin g have com pletely ch an ged the w ay th at
o ptical m icro sco py is p erfo rm ed , an d h av e also ch an ged
th e r ele va nt s pe cific atio ns fo r o bje ctiv e le ns es . A lth ou gh
len s d esign , constru ction, and qu ality have im proved to
keep up with the requirem ents of m odern light micros
copy, the markings on the lenses remain as they have
been for decades. O n the objective lens shown in Figure
Received13 February1998;accepted28 May 1998.
E-mail:[email protected]
T h is i s t he s ec on d i n a s er ie s o fa rt ic le s e nt it le d Conceptsn Imag ing
and Microscopy.This series is supported by the Opto-Precis ion Instru
ments Associa tion(OPIA)and was in troducedwith an editori al in the
A pr il 1 99 8 i ss ue o f th is jo ur na l (B io l. B ull . 1 94 : 9 9) . T he f irs t a rt ic le
in the seriesw as wr it tenby Dr . KennethR. Cas tl emanand appearedin
the same issue (Biol .Bull .194: 100107).
1, the w ord FLUARescrib es th e ty pe of len s d esig n;
although all m anufacturers use sim ilar types of designs,
the nom enclature varies from com pany to com pan y. T he
next most notable feature on the objective lens is the
m agnification (M ), w hich in the illustration is lO Ox. It
is w ritten in th e largest font of all the specification s, yet
as is discussed here, it is not the m ost im portant param e
ter. This distinction belongs to the num erical aperture
(N A), which is written next to the m agnification, but in
a smaller font, and in this case is 1.30. The imm ersion
m ed iu m for this objective is also given. B elow the m agn i
fica tion a nd n um erica l a pertu re, th e tu be len gth (00 ) a nd
th e co verslip th ick ness (0 .17 m m ) a re given . C urr en tly all
m anufacturers are offering infinity-corrected optics (de
noted by the oo sym bol), and m ost lenses are optim ally
corrected for a num ber 1.5 coverslip, nom inally 170-@ zm
thick. Both of these param eters are important, but the
objective lens w ill still function adequately for m any ap
plications w ith other tube lengths and coverslip thick
nesses. H owever, because the m anufacturers perform
ch ro ma tic co rrectio ns in d ifferen t w ay s, m ulti-c olor cx
p erim en ts fo r in sta nc e, c o-lo ca liz atio n o f tw o d iffe re nt
colored im munofluorescent probesshould be per
form ed using only sets of optics that were designed to
work together. This applies not only to m ixing lenses of
different m anufacturers, but also to m ixing older and
new er lines of optics. T he w orkin g d istan ce of the objec
tive (the depth into the sam ple to which the lens can focus
before it runs into the sam ple) is also a very im portant
param eter, especially for confocal m icroscopy in thick
b io lo gic al sam ples. D esp ite th e c ritical nature of th is sp ec
1
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D . W . P IST ON
ture are im portant for the im age-formation properties of
a n o ptic al m ic ro sc op e. M a gn ific atio n fo r a n o ptic al in str u
m en t is d efined as the relative enlargem ent of th e im age
over the object. Although at first glance it would seem
best to use the highest magnification possible, the maxi
m al useful m agnification is lim ited by the resolution of
the im aging instrum ent (as described in the next para
g ra ph ). T he d efin itio n o f n um er ic al a pe rtu re is m or e c or n
p lic ate d. N A is d efin ed b y th e h alf-a ng le o f th e o bje ctiv e s
collection cone (a) and the index of refraction of the
im m ersion m edium (n), and is expressed by N A =
n sin(a) (Inouand Spring, 1997, p. 32). The larger the
cone of collected light, the higher the NA, and the more
light that w ill be collected. Thus in practice, N A can be
thought of as the am ount of light that is collected by the
objective lens; a high-NA lens collects m ore light than a
low -NA lens. A n analogy is with telescopes: a larger
telescope collects m ore light just as a lens w ith a larger
N A collects more light. M ost optical m icroscopes also
offer the option of secondary m agn ification b etw een th e
ob jective len s and the detector. U se of such extra m agni
fication m ay som etim es be required (see Table I), but
should be avoided if possible since extra light loss is
introduced.
A s suggested above, resolution (as determ ined by the
b asic d iffr ac tio n p rin cip le s o flig ht) lim its th e u se fu l m ag
nification in an optical m icroscope. Resolution (R ) is de
fin ed a s th e sm allest d ista nce th at tw o o bjec ts ca n b e a pa rt
and still be discerned as two separate objects. There are
m an y m ath em atical d efin itio ns fo r resolutio n, b ut a sim ple
and reasonable approxim ation is R = X /(2 . N A), w here
x is thewav elengthfthelight(Inou ndSpring,1997,
p . 3 1). T his rela tio nsh ip in dica tes th at w hen u sin g a h ig h
N A lens and 500-nm (blue-green) light, the sm allest re
solva ble d ista nc e is @ 20 0rn, or 0.2 @ .tm ,w hic h a gr ee s
w ell w ith ex perim en ta l v alu es. O ne fr eq uen t p oin t o f co n
fusion for microscope users is the difference betw een
sp atia l reso lu tio n (th e a bility to d istin gu ish m ultip le o h
jects) and spatial precision (the ability to localize a single
object). M any im age-processing enhancem ents can be
used to increase the precision of localization. For exam
ple, the path of a single m icrotubule can be determ ined
to 10 nm precision by pixel-fitting (e.g., G hosh and
W ebb, 1994) or deconvolution methods (e.g., Agard et
al. 1989; Carrington et al. 1990; H olm es et al. 1995 .
H ow ev er, th is is n ot 1 0-n m reso lu tio n; 1 0-n m resolu tio n
m eans that two m icrotubules that are 10-nm apart can be
recogn ized as tw o sep arate tu bu les. If m ultiple objects
are sm all and close together (that is, close enough that
they cannot be resolved), then no am ount of image pro
cessing can differentiate betw een several individual oh
jects and a single object.
S in ce th ere is a m in im um reso lv ab le d ista nce fo r ev ery
m ic ro sc op e, c on tin uin g to in cr ea se th e m ag nific atio n p as t
a certain point will no longer increase the inform ation
O O @ @ 3o
1 j 0.17
@ -
fL-UAF@
Fig u re 1 . An o b je ct iv e l en s wi th t yp ic al m a rk in g s. Al th o ug h t hi s
i s a Zeiss lens ,m os tm anufac turersuse s imi la rmarkings .
ification, the w orking distance is not marked on m ost
lenses. Nikon has now started writing the working dis
tance on their CFI6O optics, and it is hoped that this trend
w ill be follow ed by th e other m an ufacturers.
This short article describes the relative im portance of
m ag nificatio n and n um erical ape rture fo r d ig ital op tical m i
croscop y. T rad ition ally, ob servation s m ad e w ith op tical m i
croscopes were detected by eye, and in this case, the size
o f th e d etecto r p ix els giv en b y p hy siolog ic al fa cto rs in
th e h um an e ye is n ot op tim al, so th e m ag nifica tio n w as
increased so the sam ple cou ld be seene tt er . I n d ig it al
im aging, how ever, the m agnification can be determ ined by
the com bin ation of resolu tion and detector p ixel size. To
u nd ersta nd th e rela tiv e im po rtan ce of N A a nd m ag nifica
tion, we m ust consider the basics of im age form ation and
th e e ffe ct o f le ns p ar am ete rs o n th e r es olu tio n a nd in fo rm a
tion content in optical m icroscopy. Because the resolving
pow er of an optical m icroscope is dependent only on the
num erical aperture, m agnification should be thought of as
a secon dary param eter w hose optim al value can be d eter
m ined by the N A, detector pixel size, and other instrum ent
independent im aging param eters. Thus, NA is a m ore im
portant parameter than m agnification in digital imaging.
T he p ra ctic al im p lic atio ns o f th is c on clu sio n a re d es cr ib ed
for two com monly used m odes of fluorescence im aging:
w id efie ld e pi-flu or esc en ce m ic ro sc op y w ith a C C D c am er a
as the d etector, and laser scann ing confocal m icroscopy
w i th photomult ip li er t ube de tect ors.
Basics of Image Formation
As m ight be guessed by looking at the m arkings on
any objective lens, the m agnification and num erical aper
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HOOSI NGOBJ ECTI VELENSES
(usually a CCD cam era) that takes the place of the eye.
T hus, to optim ize the inform ation content of the resulting
digital im age, the pixels on the detector m ust be m atched
to the desired im age resolution. A s describ ed above, th e
radius of a diffraction-lim ited spot, R@ X /(2 NA), is
a good quantity to use for the definition of resolution.
In the im age plane, this spot will still give the sm allest
resolvable object, but the w idth of the spot will now be
M . R . Based on the Nyquist criterion, the desired sam
pling rate should be twice the resolution, so we w ant a
pixel size in the object of R@ 1, R@ J2. In practice, the
p ixel size in w id efield m icro sco py is fix ed b y th e im ag in g
cam era used, so the m agnification is the only variable that
can be adjusted. For the purposes of these calculations,
we can assum e X = 0.5 @ tm(a good approxim ation for
fluorescein (FITC ) im aging). W e can determ ine the opti
m al M to be used for a given pixel size by m atching the
sam pling resolution in the im age plane to the pixel size
(P) by P = M . . Table I show s the results of this
calculation for tw o typical pixel sizes: 24 @ tm(an older
SITe 512D CCD chip) and 6.8 @ m(the m ore m odern
K odak KAF1400 CCD chip). As can be seen from the
tab le, the o ld er ch ip s (w ith the ir larg er p ix el size s) requ ire
higher m agnification. For these larger pixels, an extra
interm ediate m agnification of 2.5 w ould be required to
m axim ize the in form ation content of an im age collected
w ith a lOOx/l .3 N A objective lens, and in fact cam eras
that use the older SITe chip usually have som e extra
m agnification built into them . A s m icro-fabrication tech
n ology contin ues to ad van ce, how ever, the need for h igh
m agnification lenses will decrease. Obviously, it is not
possible to purchase a 72x/l.30 NA lens (although given
the popularity of the KAF1400 CCD chip, perhaps it
should be), so these optim al m agnifications can only serve
as a guide for selection of the best objective lens. Further
calculations, such as those presented in the table, reveal
that a cam era with a pixel size of 5.4 @ .tmwould be ideal
for use w ith m any existing lenses, such as 60x/l.4 NA ,
40x/0.90 N A, and 25x/0.60 NA. It should be noted,
however, that as pixel sizes get sm aller, the dynam ic
range of the detector m ay be reduced. For instance, the
5 .4 -@ .tmp ix els w ou ld lik ely b e fille d b y fe we r th an 2 0,0 00
counts, w hich w ould lim it the detector to 14-bit dynam ic
range. This is in contrast to larger pixel sizes (i.e., the
24 @ tmn the SITe 512D CCD chip), which can easily
deliver > 16-bit dynam ic range. For applications that
require high precision, such as deconvolution m ethods,
sm aller pixels m ay be unw orkable.
N u m er ic al a pe rtu re m a gn ifi ca tio n a nd r es olu tio n i n
la se r sc an nin g m ic ro sc op y
M uch has been m ade of the im provem ent in resolution
provided by confocal m icroscopy. B ut this im provem ent
is at best m inim al, and is only attained for extrem ely
content of the im age. Further m agnification beyond this
point is som etim es referred to as emptyr meaningless
m agnification. This is analogous to any digital im age on
a com puter, w here pixelation is observed w hen an im age
is m agnified on the screen (this can be seen, for exam ple,
by repeatedly using the z oo mn c om m an d in A do be
P ho to sh op ). S o th e q uestion o bv io usly a rises, h ow sh ou ld
the correct m agnification be chosen? A good rule is to
use the N yquist criterion, which basically says that one
should collect tw o points per resolution size (Inou and
Spring, 1997, p. 513). Collecting im ages in this m anner
m axim izes the in form ation con ten t.
The use of XI(2 . NA ) for the resolution criterion, and
of R /2 for the sampling rate are both arbitrary. M any
m icroscopists select other resolution criteria, but all of
these choices are only m athem atical approxim ations of
the sam e physical properties. U se of any other resolution
criteria w ould not affect the argum ents presented here,
a lth ou gh th e n um bers (e.g ., th ose sh ow n in T ab le I) w ou ld
c ha ng e s lig ht ly .
Som e atten tion should also be given to special con sid
erations for fluorescence m icroscopy (R ost, 1992). Since
fluorescence is subject to fluorophore saturation and pho
tobleaching effects that do not affect other optical m eth
ods, the highest possible light collection efficiency is de
sirab le. T his co nside ratio n d ictates th at th e h ig hest po ssi
ble N A should be used. However, the highest NA lenses
(N A = 1.40) are usually of a plan-Apochrom at esign;
this type of lens consists of up to 14 elem ents and has a
lo we r tr an sm itta nc e th an a Fluoresign. A lso, if aq ue
ous sam ples are used, the actual N A is lim ited to @.2
because of total internal reflection for higher collection
a ng le s a t th e in te rfa ce b etw ee n w ate r a nd c ov er slip (I no u
a nd S pr in g, 1 99 7, p p. 5 3 55 ). Fo r th ese r ea so ns, flu or es
cence from an aqueous sam ple appears brighter through
a 100x/l.30 N A FLUA R (as shown in Fig. 1) than
through a lO Ox/1.40 plan-A pochrom at objective lens.
Finally, it should be noted that im provem ents in alm ost
every aspect of lens design and construction (e.g., corn
puter design of com plex lens com bination, autom ated
grinding of arbitrary lens shapes, new optical m aterials
fo r b oth len ses an d coa tin gs, and co mp uter-con tro lled th in
film d ep osition for p recise o ptical co atin gs) m ak e m odern
objective lenses superior to and m ore reliable than older
lenses. A lthough m any older lenses are superb, variables
during their construction m ad e find in g a good one som e
w hat challenging, and m any researchers just took what
cam e. Today s lenses are consistently of high quality,
and also offer higher transm ission efficiency and low er
autofluorescence than did older lenses.
N u me ric al a pe rtu re m a gn ifi ca tio n an d r es olu tio n i n
wide fi el d m i croscopy
In a digital w idefield (conventional fluorescence) m i
croscope, the im age is projected onto an im aging detector
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Numerical apertureNA)1.401.300.900.600.30Calculated
resolutionsam)Rdjff0.180.190.280.420.831L,,0.0900.0950.1400.2100.415Magnification
(x)24-jim
pixels*267253171114586.8-jim
pixelst7672493216
4 D. W . PISTO N
T abl e I
Optima l magni fica tionfor de tec to rs wi th d i ffe ren tp ixel s ize s ca lcu la ted for f ive numer ica l aper tures
Represents the SITe5 l2D CCD chip.
t Representshe KodakKAF1400CCDchip.
sm all p in holes. In p rac tical flu orescen ce m icro scop y, th e
pinhole m ust be opened som ewhat to increase the effi
ciency of fluorescence collection. In fact, the pinhole is
alm ost always opened enough to negate any resolution
enhancem ent (Sandison et al., 1995). In this practical
ca se, th ere is a n im prov em en t in rejectio n o f o ut-o f-fo cu s
background, but the resolution is still given by R@
(2 N A), so the ideal sam pling resolution rem ains as show n
in Table I.
A key point in laser scanning m icroscopy is that there
is no longer a fixed pixel size. Because the field over
which the laser is scanned can be varied (this variation
is usually called zoom,r m ore appropriately elec
t ron ic zoom, nd is analogous to using an optical zoom
len s), the sam plin g resolution can b e easily changed . F or
this reason, users often have a lot of trouble choosing
lenses w hen they switch to laser scanning confocal m i
croscopy. For instance, a 40x lens w ith a zoom factor of
2.5 is basically equivalent to a lO O x lens with no extra
zoom . Thus, a 40x/1 .3 NA lens should be chosen over
an equivalent lO Ox/1.3 N A lens, because it offers a poten
tially larger field of view w ith no fall-off in light collec
t io n o r r es olu tio n.
In laser scanning confocal m icroscopy, tw o other pa
ra meters m ust b e co nsid ered . F irst is th e size of th e d etec
tor pinhole, which depends on the m agnification. M ost
confocal m icroscopes have an adjustab le pinhole that is
easily set to m atch the m agnification (e.g., for equiva
lence, a 60x lens needs a pinhole 1.5-fold larger than a
4 0x len s). S eco nd ly , th e len s d esig n fo r co nfo cal m icro s
copy m ay, in som e cases, be m ore im portant than either
M or N A. T his is esp ecia lly tru e fo r co -lo caliza tio n ex per
im ents, in which the chrom atic corrections of a plan
Apochrom at make it preferable despite its lower light
co llectio n efficien cy (th e sam e tra de-o ff m ust b e co nsid
ered for any three-dimensional microscopies based on
w id efield an d decon volu tion m eth od s, as w ell). R egard
less of the lens design, how ever, a lower m agnification
lens (of equivalent N A) is alm ost always preferable, be
cause it offers a larger field-of-view , and delivers equiva
l ent resolut ion.
Acknowledgments
This work w as supported by an Arnold and M abel
Beckm an Foundation Y oung Investigator A ward, NIH
grant DK 53434, and the Vanderbilt Cell Im aging Re
source (underw ritten by C A68485 and D K20593).
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