Lecture 1: Introduction on Adaptive Optics
Transcript of Lecture 1: Introduction on Adaptive Optics
Lecture 1: Introduction on Adaptive Optics
Rufus [email protected]
TU Delft — Delft Center for Systems and Control
Apr. 18, 2011
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Outline
1 Course overview
2 History
3 Principles of light propagation
4 Adaptive Optics system components
5 Applications for AO
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Course overview — Teaching staffRufus FraanjeTU Delft, DCSC, 3ME, room 8c2-19,Email: [email protected]: efficient control for large scale adaptive optics systems,adaptive control algorithms, distributed system identification
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Course overview — Teaching staffRufus FraanjeTU Delft, DCSC, 3ME, room 8c2-19,Email: [email protected]: efficient control for large scale adaptive optics systems,adaptive control algorithms, distributed system identification
Silvania PereiraTU Delft, Optics Research Group, TNW, room E018,Email: [email protected]: high resolution optical recording, microscopy and opticalaperture synthesis
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Course overview — Teaching staffRufus FraanjeTU Delft, DCSC, 3ME, room 8c2-19,Email: [email protected]: efficient control for large scale adaptive optics systems,adaptive control algorithms, distributed system identification
Silvania PereiraTU Delft, Optics Research Group, TNW, room E018,Email: [email protected]: high resolution optical recording, microscopy and opticalaperture synthesis
Matthew KenworthyLeiden Univ., Leiden Observatory,Email: [email protected]: searches for extrasolar planets and techniques to findthem, e.g., coronagraphy and point spread function reconstruction
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Course overview — MotivationSmart Optics Systems , STW Perspectief programme, 20 PhD/PostdocsProgram leader: Prof. dr. ir. Michel Verhaegen (TU Delft)Goal: Integration of optical, mechanical, electronic, and control systems forincreasing image resolution taking cost and complexity of the design intoaccount.Application fields: Astronomy, Lithography, Microscope, Camera systems,LASER, . . .
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Course overview — Motivation
Center for Adaptive Optics (CfAO) , large group of researchers in CaliforniaYearly AO Summerschoolhttp://cfao.ucolick.org
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Course overview — Motivation
Center for Adaptive Optics (CfAO) , large group of researchers in CaliforniaYearly AO Summerschoolhttp://cfao.ucolick.org
AO enabling technology for European Extremely Large Telesc ope ,Dutch consortium for E-ELT instrumentationhttp://esfri.strw.leidenuniv.nl
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Course overview — Motivation
Center for Adaptive Optics (CfAO) , large group of researchers in CaliforniaYearly AO Summerschoolhttp://cfao.ucolick.org
AO enabling technology for European Extremely Large Telesc ope ,Dutch consortium for E-ELT instrumentationhttp://esfri.strw.leidenuniv.nl
Conferences: SPIE, OSA, AO4ELT (Paris, 2009), (Victoria, 2011), . . .
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Course overview — Motivation
Center for Adaptive Optics (CfAO) , large group of researchers in CaliforniaYearly AO Summerschoolhttp://cfao.ucolick.org
AO enabling technology for European Extremely Large Telesc ope ,Dutch consortium for E-ELT instrumentationhttp://esfri.strw.leidenuniv.nl
Conferences: SPIE, OSA, AO4ELT (Paris, 2009), (Victoria, 2011), . . .
Special issues in journals:Journal Optical Soc. of America, vol. 27, no. 11, 2010, 25 papers.Int. J. Optomechatronics, vol. 4, no. 3, 2010.European Journal of Control, appearing
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Course overview — Motivation
Center for Adaptive Optics (CfAO) , large group of researchers in CaliforniaYearly AO Summerschoolhttp://cfao.ucolick.org
AO enabling technology for European Extremely Large Telesc ope ,Dutch consortium for E-ELT instrumentationhttp://esfri.strw.leidenuniv.nl
Conferences: SPIE, OSA, AO4ELT (Paris, 2009), (Victoria, 2011), . . .
Special issues in journals:Journal Optical Soc. of America, vol. 27, no. 11, 2010, 25 papers.Int. J. Optomechatronics, vol. 4, no. 3, 2010.European Journal of Control, appearing
In the news: BBC Feb. 18, 2011, ’Adaptive optics’ come into focus’http://www.bbc.co.uk/news/science-environment-12500626
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Course overview — Teaching objectivesAfter succesfull completion of the course you will be able to:
Design simple adaptive optics systems;
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Course overview — Teaching objectivesAfter succesfull completion of the course you will be able to:
Design simple adaptive optics systems;Understand the working and main specifications of individual components:
Imaging system (e.g., telescope, microscope, . . . )Deformable mirror;Wavefront sensor;Controller.
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Course overview — Teaching objectivesAfter succesfull completion of the course you will be able to:
Design simple adaptive optics systems;Understand the working and main specifications of individual components:
Imaging system (e.g., telescope, microscope, . . . )Deformable mirror;Wavefront sensor;Controller.
Model dynamic wavefront distortions due to turbulence;
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Course overview — Teaching objectivesAfter succesfull completion of the course you will be able to:
Design simple adaptive optics systems;Understand the working and main specifications of individual components:
Imaging system (e.g., telescope, microscope, . . . )Deformable mirror;Wavefront sensor;Controller.
Model dynamic wavefront distortions due to turbulence;Evaluate various algorithms for wavefront reconstruction;
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Course overview — Teaching objectivesAfter succesfull completion of the course you will be able to:
Design simple adaptive optics systems;Understand the working and main specifications of individual components:
Imaging system (e.g., telescope, microscope, . . . )Deformable mirror;Wavefront sensor;Controller.
Model dynamic wavefront distortions due to turbulence;Evaluate various algorithms for wavefront reconstruction;Design controllers for adaptive optics systems;
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Course overview — Teaching objectivesAfter succesfull completion of the course you will be able to:
Design simple adaptive optics systems;Understand the working and main specifications of individual components:
Imaging system (e.g., telescope, microscope, . . . )Deformable mirror;Wavefront sensor;Controller.
Model dynamic wavefront distortions due to turbulence;Evaluate various algorithms for wavefront reconstruction;Design controllers for adaptive optics systems;Understand the role of AO in various applications, especially in astronomicalobservation.
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Course overview — Teaching objectivesAfter succesfull completion of the course you will be able to:
Design simple adaptive optics systems;Understand the working and main specifications of individual components:
Imaging system (e.g., telescope, microscope, . . . )Deformable mirror;Wavefront sensor;Controller.
Model dynamic wavefront distortions due to turbulence;Evaluate various algorithms for wavefront reconstruction;Design controllers for adaptive optics systems;Understand the role of AO in various applications, especially in astronomicalobservation.Understand current and future research in AO.
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Course overview — Teaching objectivesAfter succesfull completion of the course you will be able to:
Design simple adaptive optics systems;Understand the working and main specifications of individual components:
Imaging system (e.g., telescope, microscope, . . . )Deformable mirror;Wavefront sensor;Controller.
Model dynamic wavefront distortions due to turbulence;Evaluate various algorithms for wavefront reconstruction;Design controllers for adaptive optics systems;Understand the role of AO in various applications, especially in astronomicalobservation.Understand current and future research in AO.
Examination:Short paper (4 to 6 pages) on one topic (50%);Oral exam on paper and all topics (50%).
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Course overview — System designIntegrated systems design course:
ProcessingImage
Mechanics
Electronics
Control
Photonics
Optics
SmartOpticsSystems
Multidisciplinary approach, focus on interrelations;Details so far relevant for understanding system;Follow other courses for understanding disciplines, e.g.:
Geometrical optics (AP3391, TU Delft, TNW)Imaging Systems (AP3121, TU Delft, TNW)Systems and Control Engineering (WB2207, TU Delft, DCSC)Filtering and Identification (SC4040, TU Delft, DCSC)Detection of Light (Leiden);Mechanical design in mechatronics (WB2428-03, TU Delft, PME);. . .
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Course overview — Study material
Main study material:J.W. Hardy, Adaptive Optics for Astronomical Telescopes, Oxford, 1998.Lecture slides
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Course overview — Study material
Main study material:J.W. Hardy, Adaptive Optics for Astronomical Telescopes, Oxford, 1998.Lecture slides
Helpful study material on optics:Goodman, Introduction to Fourier Optics, McGraw-Hill, 1996Born & Wolf, Principles of optics, Cambridge, 2009Chartier, Introduction to Optics, Springer, 2005Hecht, Optics, Addison Wesley, 2002
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Course overview — Study material
Main study material:J.W. Hardy, Adaptive Optics for Astronomical Telescopes, Oxford, 1998.Lecture slides
Helpful study material on optics:Goodman, Introduction to Fourier Optics, McGraw-Hill, 1996Born & Wolf, Principles of optics, Cambridge, 2009Chartier, Introduction to Optics, Springer, 2005Hecht, Optics, Addison Wesley, 2002
Helpful study material on adaptive optics:Tyson, Field Guide to Adaptive Optics, SPIE, 2004.Roddier, Adaptive optics in astronomy, Cambridge, 1999Tyson, Adaptive optics engineering handbook, Dekker, 2000Porter, Adaptive optics for vision science, Wiley, 2006
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Course overview — Study material (Cont.)Helpful study material on control and identification:
Astrom & Murray, Feedback systems — An Introduction for Scientists andEngineers, Princeton, 2008Franklin et al., Feedback Control of Dynamic Systems, Pearson, 2008Verhaegen & Verdult, Filtering and System Identification — A Least SquaresApproach, Cambridge, 2007
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Course overview — Study material (Cont.)Helpful study material on control and identification:
Astrom & Murray, Feedback systems — An Introduction for Scientists andEngineers, Princeton, 2008Franklin et al., Feedback Control of Dynamic Systems, Pearson, 2008Verhaegen & Verdult, Filtering and System Identification — A Least SquaresApproach, Cambridge, 2007
Online texts:Tokovins Adaptive optics tutorial at CTIO:http://www.ctio.noao.edu/~atokovin/tutorial/intro.html
Adaptive optics at ESO:http://www.eso.org/sci/facilities/develop/ao/tecno/index.html
Claire Max’s Introduction to Adaptive Optics and its History:http://www.ucolick.org/~max/max-web/History_AO_Max.htm
also see her AO course http://www.ucolick.org/~max/289C/
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Course overview — Study material (Cont.)Helpful study material on control and identification:
Astrom & Murray, Feedback systems — An Introduction for Scientists andEngineers, Princeton, 2008Franklin et al., Feedback Control of Dynamic Systems, Pearson, 2008Verhaegen & Verdult, Filtering and System Identification — A Least SquaresApproach, Cambridge, 2007
Online texts:Tokovins Adaptive optics tutorial at CTIO:http://www.ctio.noao.edu/~atokovin/tutorial/intro.html
Adaptive optics at ESO:http://www.eso.org/sci/facilities/develop/ao/tecno/index.html
Claire Max’s Introduction to Adaptive Optics and its History:http://www.ucolick.org/~max/max-web/History_AO_Max.htm
also see her AO course http://www.ucolick.org/~max/289C/
References given at lectures.
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Course overview — Schedule
Schedule:
DATE TOPIC LECTURER
18 Apr Introduction to AO systems Fraanje
2 May Optical image formation Pereira
9 May Optical wavefront sensors Pereira
16 May Turbulence modeling Fraanje
30 May Reconstruction and prediction Fraanje
6 Jun Astronomical observation Kenworthy
13 Jun Deformable mirror control Fraanje
Time: 10.45 - 12.30h
Location: TU Delft, API-CZ Rudolf Diesel (building 46)
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HistoryNewton:
If the Theory of making Telescopes could at length be fully brought into Practice,yet there would be certain Bounds beyond which Telescopes could not perform.For the Air through which we look upon the Stars, is in a perpetual Tremor.
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HistoryNewton:
If the Theory of making Telescopes could at length be fully brought into Practice,yet there would be certain Bounds beyond which Telescopes could not perform.For the Air through which we look upon the Stars, is in a perpetual Tremor.
Until Babcock (1953):
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History — Babcock’s compensator
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History — Adaptive Optics
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History — AO @ Keck10m Keck telescope @ Mauna Kea, Hawai
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History — AO @ KeckFeb. 5, 1999: First AO observation, V=5.6 A0 star
Without With Adaptive Optics
http://www2.keck.hawaii.edu/ao/aolight.html
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History — AO @ KeckMay 26, 1999: Mauna Kea, Hawai10mø Keck 2 pointed at galactic center with and without AO
http://cfao.ucolick.org/pgallery/gc.php
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History — AO @ Keck2005: Laser Guide Star vs. Natural Guide Star AO
Ghez et al, ApJ, 2005, vol. 635http://arxiv.org/pdf/astro-ph/0508664v1
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HistoryHistory of largest optical telescopes
1600 1700 1800 1900 200010
−2
10−1
100
101
102
Year
Dia
met
er [m
]
Galileo
Huygens
Newton
Herschel
Hale
Keck
VLT
E−ELT
TMT
after: Racine, Astr.Soc.Pac., 116:77−83,2004.
LensesMirrorsAchromatsShortcomingsSegmented mirrors
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History — Future E-ELTThe European Extremely Large Telescope Nasmyth configuration
Aperture: 38m �
Optical design: 5 mirrors, M1&M3 for AOM1: 984(?) segments, 38m �
M3: 8000 actuators, 2.5m �
Field of view: 10 arcminuteLocation: Cerro Armazones, ChileFirst light: 2020
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History — Future E-ELTThe European Extremely Large Telescope (E-ELT)
Diffraction limit (Rayleigh criterion):
sin(θ) = 1.22λ
D
θ < 10mas in near-infrared(1mas ≈ 4.8 · 10−9rad)
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History — Future E-ELTThe European Extremely Large Telescope (E-ELT)
Diffraction limit (Rayleigh criterion):
sin(θ) = 1.22λ
D
θ < 10mas in near-infrared(1mas ≈ 4.8 · 10−9rad)
Seeing conditions:
Coherence length (Fried parameter): r0 = 20cmEffective resolution without AO: 1.22λ/r0 ≈ 1800mas
Adaptive Optics:
→ (D/r0 = 200)2 = 40.000 actuators/sensors
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History — Future E-ELTDevelopment of computing power
1970 1980 1990 2000 2010 2020 203010
4
106
108
1010
1012
1014
Inst
ruct
ions
/flop
s pe
r se
cond
Year
source: Wikipedia
104
106
108
1010
1012
1014
Clo
ck F
requ
ency
[Hz]
GPU
Intel 8080
Motorola 68000
Intel 286Intel 386DX
Intel 486DX
DEC AlphaIntel Pentium Pro
AMD AthlonXbox360 (3 cores)
Intel i7(6 cores)AMD Phenom
(6 cores)
E−ELT AO
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Principles of light propagation
Literature: G. Chartier, Introduction to Optics, Springer, 2005 [online at TULibrary], Sec. 1.2, 1.3, parts Ch. 2, and Sec. 3.1, 3.2
Light acts as a particle and a wavePhotons characterized by:
individual energy W ;
momentum p.
Planck relationship: W = hν
Waves characterized by:
frequency ν;
wave vector k.
De Broglie relationship: p =h
2πk
(h = 6.626 · 10−34Js, Planck’s constant)
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Principles of light propagation← Increasing Energy (W)
4.1G 41M 0.41M 4.1K 41 0.41 4.1m 41u 0.41u 4.1n 41p 0.41p 4.1f W (eV)
3.1eV 1.8eV Energy
7‧10¹⁴Hz 4‧10¹⁴Hz Frequency
400nm 700nm Wavelength (in vacuum)
(source: Wikipedia)
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Principles of light propagationWaves propagate, mathematical formuation:
g(t , x) = f (t ± x/V )
V is velocity of wave
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Principles of light propagationWaves propagate, mathematical formuation:
g(t , x) = f (t ± x/V )
V is velocity of wave
Planar wave:
g(t , x) = f (t − u · x/V ), u, direction of wave
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Principles of light propagationWaves propagate, mathematical formuation:
g(t , x) = f (t ± x/V )
V is velocity of wave
Planar wave:
g(t , x) = f (t − u · x/V ), u, direction of wave
Amplitude variation due to absorption:
g(t , x) = e−αu·x f (t − u · x/V )
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Principles of light propagationWaves propagate, mathematical formuation:
g(t , x) = f (t ± x/V )
V is velocity of wave
Planar wave:
g(t , x) = f (t − u · x/V ), u, direction of wave
Amplitude variation due to absorption:
g(t , x) = e−αu·x f (t − u · x/V )
Spherical waves:
g(t , x) =e−αr
rf (t ± r/V ), r =
√xT x
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Principles of light propagationHarmonic planar waves:
g(t , x) = A cos(ωt − k · x)
Frequency: ν.
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Principles of light propagationHarmonic planar waves:
g(t , x) = A cos(ωt − k · x)
Frequency: ν.
Pulsation: ω (also angular frequency), ω = 2πν.
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Principles of light propagationHarmonic planar waves:
g(t , x) = A cos(ωt − k · x)
Frequency: ν.
Pulsation: ω (also angular frequency), ω = 2πν.
Period: T =1ν=
2πω
.
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Principles of light propagationHarmonic planar waves:
g(t , x) = A cos(ωt − k · x)
Frequency: ν.
Pulsation: ω (also angular frequency), ω = 2πν.
Period: T =1ν=
2πω
.
Speed of propagation: V = (Vx ,Vy ,Vz), V = ||V||2 =√
V 2x + V 2
y + V 2z .
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Principles of light propagationHarmonic planar waves:
g(t , x) = A cos(ωt − k · x)
Frequency: ν.
Pulsation: ω (also angular frequency), ω = 2πν.
Period: T =1ν=
2πω
.
Speed of propagation: V = (Vx ,Vy ,Vz), V = ||V||2 =√
V 2x + V 2
y + V 2z .
Wavelength: (space period), λ = VT =Vν
=2πk
.
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Principles of light propagationHarmonic planar waves:
g(t , x) = A cos(ωt − k · x)
Frequency: ν.
Pulsation: ω (also angular frequency), ω = 2πν.
Period: T =1ν=
2πω
.
Speed of propagation: V = (Vx ,Vy ,Vz), V = ||V||2 =√
V 2x + V 2
y + V 2z .
Wavelength: (space period), λ = VT =Vν
=2πk
.
Wave vector: (spatial frequency) k = (kx , ky , kz), k = ||k||2 =2πλ
=ω
V
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Principles of light propagationHarmonic planar waves:
g(t , x) = A cos(ωt − k · x)
Frequency: ν.
Pulsation: ω (also angular frequency), ω = 2πν.
Period: T =1ν=
2πω
.
Speed of propagation: V = (Vx ,Vy ,Vz), V = ||V||2 =√
V 2x + V 2
y + V 2z .
Wavelength: (space period), λ = VT =Vν
=2πk
.
Wave vector: (spatial frequency) k = (kx , ky , kz), k = ||k||2 =2πλ
=ω
V
Direction of propagation: u = V/V = k/k , k = ku = kV/V =ω
Vu
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Principles of light propagationPropagation of light through media described by Maxwell EquationsVector variables:
E(t , x) = (Ex ,Ey ,Ez)(t , x): electric field (V/m)H(t , x) = (Hx ,Hy ,Hz)(t , x): magnectic field (A/m)D(t , x) = (Dx ,Dy ,Dz)(t , x): electric displacement (C/m2)B(t , x) = (Bx ,By ,Bz)(t , x): magnetic induction (T)
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Principles of light propagationPropagation of light through media described by Maxwell EquationsVector variables:
E(t , x) = (Ex ,Ey ,Ez)(t , x): electric field (V/m)H(t , x) = (Hx ,Hy ,Hz)(t , x): magnectic field (A/m)D(t , x) = (Dx ,Dy ,Dz)(t , x): electric displacement (C/m2)B(t , x) = (Bx ,By ,Bz)(t , x): magnetic induction (T)
Transparent material usually no magnetic properties: B = µ0H, µ0 = 4π10−7H/m
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Principles of light propagationPropagation of light through media described by Maxwell EquationsVector variables:
E(t , x) = (Ex ,Ey ,Ez)(t , x): electric field (V/m)H(t , x) = (Hx ,Hy ,Hz)(t , x): magnectic field (A/m)D(t , x) = (Dx ,Dy ,Dz)(t , x): electric displacement (C/m2)B(t , x) = (Bx ,By ,Bz)(t , x): magnetic induction (T)
Transparent material usually no magnetic properties: B = µ0H, µ0 = 4π10−7H/m
Linear isotropic media: D = ǫE = ǫ0ǫr E, ǫ0 = 1/(36π109)F/m
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Principles of light propagationPropagation of light through media described by Maxwell EquationsVector variables:
E(t , x) = (Ex ,Ey ,Ez)(t , x): electric field (V/m)H(t , x) = (Hx ,Hy ,Hz)(t , x): magnectic field (A/m)D(t , x) = (Dx ,Dy ,Dz)(t , x): electric displacement (C/m2)B(t , x) = (Bx ,By ,Bz)(t , x): magnetic induction (T)
Transparent material usually no magnetic properties: B = µ0H, µ0 = 4π10−7H/m
Linear isotropic media: D = ǫE = ǫ0ǫr E, ǫ0 = 1/(36π109)F/m
Relative permittivity ǫr typically between 1 and 10,function of frequency (color) → dispersion.varies with space(/time) → (time-varying) refraction and reflection.
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Principles of light propagationPropagation of light through media described by Maxwell EquationsVector variables:
E(t , x) = (Ex ,Ey ,Ez)(t , x): electric field (V/m)H(t , x) = (Hx ,Hy ,Hz)(t , x): magnectic field (A/m)D(t , x) = (Dx ,Dy ,Dz)(t , x): electric displacement (C/m2)B(t , x) = (Bx ,By ,Bz)(t , x): magnetic induction (T)
Transparent material usually no magnetic properties: B = µ0H, µ0 = 4π10−7H/m
Linear isotropic media: D = ǫE = ǫ0ǫr E, ǫ0 = 1/(36π109)F/m
Relative permittivity ǫr typically between 1 and 10,function of frequency (color) → dispersion.varies with space(/time) → (time-varying) refraction and reflection.
EM-wave fully characterized by:
EM(t , x) = (E(t , x),H(t , x))26 / 47
Principles of light propagationFor harmonic waves Maxwell equations simplify to Helmholtz equation:
EM(t , x) = A(x) cos(
ωt − φ(x))
= Re{
U(x)ejωt}
whereU(x) = A(x)e−jφ(x)
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Principles of light propagationFor harmonic waves Maxwell equations simplify to Helmholtz equation:
EM(t , x) = A(x) cos(
ωt − φ(x))
= Re{
U(x)ejωt}
whereU(x) = A(x)e−jφ(x)
then the Helmholtz (wave) equation specifies:
∂2U∂x2
+∂2U∂y2
+∂2U∂z2
+ω2
V 2U = 0
where V the wave propagation speed
V =1√µ0ǫ
=1√µ0ǫ0ǫr
=cn
where c = 1/√µ0ǫ0 the speed of light in vacuum and n =
√ǫr the refraction index.
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Principles of light propagation
In general harmonic EM-waves with frequency ω need to satisfy:
∂2U∂x2
+∂2U∂y2
+∂2U∂z2
+ω2
V 2U = J(x, ω)
+ boundary conditions
where J(x, ω) an excitation function.
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Principles of light propagation
In general harmonic EM-waves with frequency ω need to satisfy:
∂2U∂x2
+∂2U∂y2
+∂2U∂z2
+ω2
V 2U = J(x, ω)
+ boundary conditions
where J(x, ω) an excitation function.
Special solutions of Helmholtz equation:
Planar waves: U(x) = A(x)e−jkT x .
Spherical waves: U(x) = A(x)e−jkr , r =√
xT x.
In finite volume at large distance from focus spherical waves with amplitudeproportional to 1/r can be considered as planar with constant amplitude.
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Principles of light propagationSpherical wave
U(x , y , z) =a
√
x2 + y2 + z2e±jk
√x2+y2+z2
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Principles of light propagationSpherical wave
U(x , y , z) =a
√
x2 + y2 + z2e±jk
√x2+y2+z2
for large |z| compared to√
x2 + y2 we have:
√
x2 + y2 + z2 ≈ |z|+ 12|z|
√
x2 + y2
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Principles of light propagationSpherical wave
U(x , y , z) =a
√
x2 + y2 + z2e±jk
√x2+y2+z2
for large |z| compared to√
x2 + y2 we have:
√
x2 + y2 + z2 ≈ |z|+ 12|z|
√
x2 + y2
such that U(x , y , z) is approximated by
U(x , y , z) ≈ a|z|e
±jk x2+y2
2|z| e−jk|z| ≈ a|z|e
±jk|z|
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Principles of light propagationSpherical wave
U(x , y , z) =a
√
x2 + y2 + z2e±jk
√x2+y2+z2
for large |z| compared to√
x2 + y2 we have:
√
x2 + y2 + z2 ≈ |z|+ 12|z|
√
x2 + y2
such that U(x , y , z) is approximated by
U(x , y , z) ≈ a|z|e
±jk x2+y2
2|z| e−jk|z| ≈ a|z|e
±jk|z|
and at z +∆z:
U(x , y , z +∆z) ≈ a|z +∆z|e
±jk|z+∆z| ≈ a|z|e
±jk|z+∆z|
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Principles — Fermat’s PrincipleFermat’s Principle:
The path followed by light going from point A to point B is such that thetransit time is stationary (minimum or maximum).
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Principles — Fermat’s PrincipleFermat’s Principle:
The path followed by light going from point A to point B is such that thetransit time is stationary (minimum or maximum).
A
B
I J
K
LM
N
I′ J ′
K ′ L′
M ′
N ′
n0 n1 n2 n3
t = (n0AI + n1IJ + n0JK + n2KL + n0LM + n3MN + n0NB)/c
t ′ = (n0AI′ + n1I′J ′ + n0J ′K ′ + n2K ′L′ + n0L′M ′ + n3M ′N ′ + n0N ′B)/c
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Principles — Fermat’s PrincipleFermat’s Principle:
The path followed by light going from point A to point B is such that thetransit time is stationary (minimum or maximum).
A
B
I J
K
LM
N
I′ J ′
K ′ L′
M ′
N ′
n0 n1 n2 n3
t = (n0AI + n1IJ + n0JK + n2KL + n0LM + n3MN + n0NB)/c
t ′ = (n0AI′ + n1I′J ′ + n0J ′K ′ + n2K ′L′ + n0L′M ′ + n3M ′N ′ + n0N ′B)/c
t =1c
∫ B
An(x , y , z)ds
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Principles — Fermat’s PrincipleLaw of Reflection:
angle of reflection equals angle of incidence
A B
A′
θθ′
I′ I I′′
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Principles — Fermat’s PrincipleLaw of Refraction (Snell’s law)1 :
The law of refraction states that the incident ray, the refracted ray, andthe normal to the interface, all lie in the same plane. Furthermore,
n1 sin(θ1) = n2 sin(θ2)
A
B
On1
n2
y1
−y2
x x2
θ1
θ2
1http://farside.ph.utexas.edu/teaching/302l/lectures/node128.html
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Principles — Fermat’s PrincipleLaw of Refraction (Snell’s law)1 :
The law of refraction states that the incident ray, the refracted ray, andthe normal to the interface, all lie in the same plane. Furthermore,
n1 sin(θ1) = n2 sin(θ2)
A
B
On1
n2
y1
−y2
x x2
θ1
θ2
t(x) =
(
n1
√
y21 + x2 + n2
√
y22 + (x2 − x)2
)
/c,
dtdx
=
(
n1x√
y21 + x2
− n2(x2 − x)√
y22 + (x2 − x)2
)
/c,
dtdx
= 0 ⇔ n1x√
y21 + x2
=n2(x2 − x)
√
y22 + (x2 − x)2
1http://farside.ph.utexas.edu/teaching/302l/lectures/node128.html
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Principles of light propagationplane with constantphase
n1 n2
n0
n2 > n1
h
d =(n2 − n1)h
n0
(optical path difference!)
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Principles of light propagationplane with constantphase
n1 n2
n0
n2 > n1
h
d =(n2 − n1)h
n0
(optical path difference!)
Phase difference (n0 = 1):
∆φ(x) = − kh(n(x)− 1) = − 2πh(n(x)− 1)λ
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Principles of light propagation
Concluding so far:
In transparent nonmagnetic media n =√ǫr ;
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Principles of light propagation
Concluding so far:
In transparent nonmagnetic media n =√ǫr ;
Fermat’s principle: time from A to B is minimum or maximum;
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Principles of light propagation
Concluding so far:
In transparent nonmagnetic media n =√ǫr ;
Fermat’s principle: time from A to B is minimum or maximum;
Variations in n result in optical pathlength differences:
∆φ(x , y) = −2πh(n(x)− 1)λ
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Principles of light propagation
Concluding so far:
In transparent nonmagnetic media n =√ǫr ;
Fermat’s principle: time from A to B is minimum or maximum;
Variations in n result in optical pathlength differences:
∆φ(x , y) = −2πh(n(x)− 1)λ
Dependency of phase on index of refraction decreases for increasing λ(sub-millimeter waves only suffer from pointing error);
34 / 47
Principles of light propagation
Concluding so far:
In transparent nonmagnetic media n =√ǫr ;
Fermat’s principle: time from A to B is minimum or maximum;
Variations in n result in optical pathlength differences:
∆φ(x , y) = −2πh(n(x)− 1)λ
Dependency of phase on index of refraction decreases for increasing λ(sub-millimeter waves only suffer from pointing error);
Compensation can be accomplished by changing optical pathlength ifrefraction index is independent of wavelength (no dispersion).
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Adaptive Optics system components
(scientificinstrument)
exoplanet
atmosphericturbulence
spectrograph
ELT
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Adaptive Optics system components
(scientificinstrument)
exoplanet
atmosphericturbulence
spectrograph
ELT
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Adaptive Optics system components
(scientificinstrument)
exoplanet
atmosphericturbulence
WFSControl
DMspectrograph
ELT
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Adaptive Optics system components
alignment errors andtemperature variations
(scientificinstrument)
forcewind disturbance
exoplanet
atmosphericturbulence
vibrations(ground)
WFSControl
DMspectrograph
ELT
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Adaptive Optics system components
Generalized plant:d(k) φd (k)
S(z)
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Adaptive Optics system components
Generalized plant:
+
+
d(k)
u(k)
φd (k)
φu(k)
φr (k)S(z)
H(z)
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Adaptive Optics system components
Generalized plant:
+
+
d(k)
u(k)
φd (k)
φu(k)
φr (k)
s(k)
S(z)
H(z) G(z)
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Adaptive Optics system components
Generalized plant:
+
+
++
d(k)
u(k)
φd (k)
φu(k)
φr (k)
s(k)
S(z)
H(z) G(z)
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Adaptive Optics system components
Generalized plant:
+
+
++
d(k)
u(k)
φd (k)
φu(k)
φr (k)
s(k)
S(z)
H(z) G(z)
C(z)
36 / 47
Adaptive Optics system components
Generalized plant:
+
+
++
d(k)
u(k)
φd (k)
φu(k)
φr (k)
s(k)
S(z)
H(z) G(z)
Optimal control law (static DM with unit sample delay):
C(z) : u(k + 1) = −H†φd(k + 1|k)
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Adaptive Optics system components
Generalized plant:
+
+
++
d(k)
u(k)
φd (k)
φu(k)
φr (k)
s(k)
S(z)
H(z) G(z)
Optimal control law with control weighting:
C(z) : u(k + 1) = −(HT H + αI)−1HT φd(k + 1|k)
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Adaptive Optics system componentsKolmogorov distributed disturbance measured atWilliam Herschel Telescope, La Palma (Spain)
100
101
102
10−18
10−17
10−16
10−15
10−14
10−13
10−12
Frequency [Hz]
Pow
er s
pect
ral d
ensi
ty [r
ad2 /H
z]
Measured
f(−2)
f(−4)
f(−8/3) (Kolmogorov)
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Adaptive Optics system componentsKolmogorov distributed disturbance measured atWilliam Herschel Telescope, La Palma (Spain)
100
101
102
10−18
10−17
10−16
10−15
10−14
10−13
10−12
Frequency [Hz]
Pow
er s
pect
ral d
ensi
ty [r
ad2 /H
z]
Measured
f(−2)
f(−4)
f(−8/3) (Kolmogorov)
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Adaptive Optics system componentsQuality of imaging system: Strehl ratio (Sr ) (K.Strehl [1895]),
Sr :=Im (measured peak intensity)
Io (diffraction limited peak intensity)
≈ e−||φr ||22
c.f. Born and Wolf, Principles of Optics.Minimize cost function: J := ||φr ||22
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Adaptive Optics system components
Star
CCD camera view
Shack HartmannLenslet array
No turbulence(bright picture of star)
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Adaptive Optics system components
Atmosphericturbulence
Star
CCD camera view
Shack HartmannLenslet array
Measurement: sx = ∂φr
∂x and sy = ∂φr
∂y , s = [sTx , sT
y ]T
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Adaptive Optics system components
Wavefront sensors:
Shack Hartmann sensor (local wavefront slopes)
Shearing interferometer (local wavefront slopes)
Curvature Wavefront Sensor (local second order spatial derivative)
Pyramid sensor
Pinhole (light intensitiy at single spot)
c.f. Roddier[1994], Guyon[AO4ELT, 2009].
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Adaptive Optics system components
Lenslet array CCD Camera
++
G
ψr ▽x/y
∫ t+tet
T
s
v
‘Static’ model:s(k) = Gφr (k − 1) + v(k)
Dynamic model: Looze[Automatica,2005], c.f. Hinnen[JOSA,2007].
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Adaptive Optics system componentsDeformable mirrors:
Continuous membrane(Flexible Optical, TNO, ...)local influence function per actuator
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Adaptive Optics system componentsDeformable mirrors:
Continuous membrane(Flexible Optical, TNO, ...)local influence function per actuator
Segmented membrane(E-ELT primary mirror 1000 segments,Boston micromachines, ...)fully decoupled actuators
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Adaptive Optics system componentsDeformable mirrors:
Continuous membrane(Flexible Optical, TNO, ...)local influence function per actuator
Segmented membrane(E-ELT primary mirror 1000 segments,Boston micromachines, ...)fully decoupled actuators
Kilo-DM (Boston),1020 actuators,60kHz frame-rate
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Adaptive Optics system componentsDeformable mirrors:
Continuous membrane(Flexible Optical, TNO, ...)local influence function per actuator
Segmented membrane(E-ELT primary mirror 1000 segments,Boston micromachines, ...)fully decoupled actuators
Kilo-DM (Boston),1020 actuators,60kHz frame-rate
Piezoelectric DM(Flexible Optical, Delft),low cost
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Adaptive Optics system components
Performance limitations:
Limited spatial actuation (number/position/range actuators);
Limited spatial sensing (number/position/range sensors);
Non-minimum phase dynamics (e.g., delays);
Sensor noise;
(Anisoplanatism, e.g., in astronomy).
Limited spatial actuation and sensing =⇒ fitting error.
Good design: often these errors are in same order of magnitude.
Trend: more actuators/sensors → fitting error ↓but time-error and sensor noise become more dominant!
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Applications
Applications of adaptive optics:
Astronomy: high resolution ground based telescopes;
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Applications
Applications of adaptive optics:
Astronomy: high resolution ground based telescopes;
Ophtalmology: inspection/compensation eye aberations;
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Applications
Applications of adaptive optics:
Astronomy: high resolution ground based telescopes;
Ophtalmology: inspection/compensation eye aberations;
Lithography: compensation of (time varying) errors;
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Applications
Applications of adaptive optics:
Astronomy: high resolution ground based telescopes;
Ophtalmology: inspection/compensation eye aberations;
Lithography: compensation of (time varying) errors;
Microscopy: compensation change diffraction index in living cells;
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Applications
Applications of adaptive optics:
Astronomy: high resolution ground based telescopes;
Ophtalmology: inspection/compensation eye aberations;
Lithography: compensation of (time varying) errors;
Microscopy: compensation change diffraction index in living cells;
Long range cameras: compensation of turbulence in air;
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Applications
Applications of adaptive optics:
Astronomy: high resolution ground based telescopes;
Ophtalmology: inspection/compensation eye aberations;
Lithography: compensation of (time varying) errors;
Microscopy: compensation change diffraction index in living cells;
Long range cameras: compensation of turbulence in air;
LASERS: increase coherence length / power;
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Applications
Applications of adaptive optics:
Astronomy: high resolution ground based telescopes;
Ophtalmology: inspection/compensation eye aberations;
Lithography: compensation of (time varying) errors;
Microscopy: compensation change diffraction index in living cells;
Long range cameras: compensation of turbulence in air;
LASERS: increase coherence length / power;
...
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Applications — Ophtalmology
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Applications — Microscopy
Confocal microscope/2-photon microscope:
LASER
DETECTOR
LASER
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Applications — Microscopy
Confocal microscope/2-photon microscope:
LASER
DETECTOR
LASER
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Applications — Microscopy
Confocal microscope/2-photon microscope:
LA
SER
DETECTOR
LAS
ER
CONTROLLER
DEFORMABLEMIRROR
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ConclusionsBabcock (1953), Keck (1999), E-ELT, . . .
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ConclusionsBabcock (1953), Keck (1999), E-ELT, . . .
Spherical and Planar wave propagation;
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ConclusionsBabcock (1953), Keck (1999), E-ELT, . . .
Spherical and Planar wave propagation;
Propagation of light, Fermat’s principle;
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ConclusionsBabcock (1953), Keck (1999), E-ELT, . . .
Spherical and Planar wave propagation;
Propagation of light, Fermat’s principle;
Variations in refraction index lead to optical pathlength variations(∆d(x) = n(x)h);
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ConclusionsBabcock (1953), Keck (1999), E-ELT, . . .
Spherical and Planar wave propagation;
Propagation of light, Fermat’s principle;
Variations in refraction index lead to optical pathlength variations(∆d(x) = n(x)h);
Pathlength variations lead to wavefront phase variations(∆φ(x) = −2π∆d(x)/λ);
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ConclusionsBabcock (1953), Keck (1999), E-ELT, . . .
Spherical and Planar wave propagation;
Propagation of light, Fermat’s principle;
Variations in refraction index lead to optical pathlength variations(∆d(x) = n(x)h);
Pathlength variations lead to wavefront phase variations(∆φ(x) = −2π∆d(x)/λ);
A generalized plant description of an AO system consists of:Disturbance model (wavefront phase variations);Performance criterion (e.g., Strehl or Contrast);Actuation to adjust optical pathlength (e.g., deformable mirror);Device to measure the variation in optical pathlength or wavefront phase (e.g., aShack Hartmann wavefront sensor).
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ConclusionsBabcock (1953), Keck (1999), E-ELT, . . .
Spherical and Planar wave propagation;
Propagation of light, Fermat’s principle;
Variations in refraction index lead to optical pathlength variations(∆d(x) = n(x)h);
Pathlength variations lead to wavefront phase variations(∆φ(x) = −2π∆d(x)/λ);
A generalized plant description of an AO system consists of:Disturbance model (wavefront phase variations);Performance criterion (e.g., Strehl or Contrast);Actuation to adjust optical pathlength (e.g., deformable mirror);Device to measure the variation in optical pathlength or wavefront phase (e.g., aShack Hartmann wavefront sensor).
Study: Chartier Sec. 1.2, 1.3, parts Ch. 2, and Sec. 3.1, 3.2, Hardy Ch. 1.47 / 47