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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[email protected]

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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Silvania PereiraTU Delft, Optics Research Group, TNW, room E018,Email: [email protected]: high resolution optical recording, microscopy and opticalaperture synthesis

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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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http://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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http://esfri.strw.leidenuniv.nl




Conferences: SPIE, OSA, AO4ELT (Paris, 2009), (Victoria, 2011), . . .

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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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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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http://www.bbc.co.uk/news/science-environment-12500626

Course overview — Teaching objectivesAfter succesfull completion of the course you will be able to:

Design simple adaptive optics systems;

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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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Model dynamic wavefront distortions due to turbulence;

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Model dynamic wavefront distortions due to turbulence;Evaluate various algorithms for wavefront reconstruction;

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Model dynamic wavefront distortions due to turbulence;Evaluate various algorithms for wavefront reconstruction;Design controllers for adaptive optics systems;

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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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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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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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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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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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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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http://www.ctio.noao.edu/~atokovin/tutorial/intro.html

http://www.eso.org/sci/facilities/develop/ao/tecno/index.html

http://www.ucolick.org/~max/max-web/History_AO_Max.htm

http://www.ucolick.org/~max/289C/



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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http://www.ctio.noao.edu/~atokovin/tutorial/intro.html

http://www.eso.org/sci/facilities/develop/ao/tecno/index.html

http://www.ucolick.org/~max/max-web/History_AO_Max.htm

http://www.ucolick.org/~max/289C/

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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http://www2.keck.hawaii.edu/ao/aolight.html

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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http://cfao.ucolick.org/pgallery/gc.php

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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http://arxiv.org/pdf/astro-ph/0508664v1

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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g(t , x) = f (t ± x/V )


Planar wave:

g(t , x) = f (t − u · x/V ), u, direction of wave

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g(t , x) = f (t ± x/V )


Planar wave:


Amplitude variation due to absorption:

g(t , x) = e−αu·x f (t − u · x/V )

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g(t , x) = f (t ± x/V )


Planar 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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g(t , x) = A cos(ωt − k · x)

Frequency: ν.

Pulsation: ω (also angular frequency), ω = 2πν.

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g(t , x) = A cos(ωt − k · x)

Frequency: ν.


Period: T =1ν=

2πω

.

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g(t , x) = A cos(ωt − k · x)

Frequency: ν.


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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g(t , x) = A cos(ωt − k · x)

Frequency: ν.


Period: T =1ν=

2πω

.


V 2x + V 2

y + V 2z .

Wavelength: (space period), λ = VT =Vν

=2πk

.

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g(t , x) = A cos(ωt − k · x)

Frequency: ν.


Period: T =1ν=

2πω

.


V 2x + V 2

y + V 2z .


=2πk

.

Wave vector: (spatial frequency) k = (kx , ky , kz), k = ||k||2 =2πλ

=ω

V

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g(t , x) = A cos(ωt − k · x)

Frequency: ν.


Period: T =1ν=

2πω

.


V 2x + V 2

y + V 2z .


=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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Transparent material usually no magnetic properties: B = µ0H, µ0 = 4π10−7H/m

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Linear isotropic media: D = ǫE = ǫ0ǫr E, ǫ0 = 1/(36π109)F/m

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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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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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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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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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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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U(x , y , z) =a

√

x2 + y2 + z2e±jk

√x2+y2+z2


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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U(x , y , z) =a

√

x2 + y2 + z2e±jk

√x2+y2+z2


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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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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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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http://farside.ph.utexas.edu/teaching/302l/lectures/node128.html

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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http://farside.ph.utexas.edu/teaching/302l/lectures/node128.html

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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Concluding so far:

In transparent nonmagnetic media n =√ǫr ;

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Concluding so far:


Fermat’s principle: time from A to B is minimum or maximum;

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Concluding so far:



Variations in n result in optical pathlength differences:

∆φ(x , y) = −2πh(n(x)− 1)λ

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Concluding so far:




∆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);

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Concluding so far:




∆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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exoplanet


WFSControl

DMspectrograph

ELT

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alignment errors andtemperature variations


forcewind disturbance

exoplanet


vibrations(ground)

WFSControl

DMspectrograph

ELT

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Generalized plant:d(k) φd (k)

S(z)

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Generalized plant:

+

+

d(k)

u(k)

φd (k)

φu(k)

φr (k)S(z)

H(z)

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Generalized plant:

+

+

d(k)

u(k)

φd (k)

φu(k)

φr (k)

s(k)

S(z)

H(z) G(z)

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Generalized plant:

+

+

++

d(k)

u(k)

φd (k)

φu(k)

φr (k)

s(k)

S(z)

H(z) G(z)

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Generalized plant:

+

+

++

d(k)

u(k)

φd (k)

φu(k)

φr (k)

s(k)

S(z)

H(z) G(z)

C(z)

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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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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 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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Star

CCD camera view

Shack HartmannLenslet array

No turbulence(bright picture of star)

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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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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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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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Segmented membrane(E-ELT primary mirror 1000 segments,Boston micromachines, ...)fully decoupled actuators

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Kilo-DM (Boston),1020 actuators,60kHz frame-rate

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Kilo-DM (Boston),1020 actuators,60kHz frame-rate

Piezoelectric DM(Flexible Optical, Delft),low cost

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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



Ophtalmology: inspection/compensation eye aberations;

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Applications




Lithography: compensation of (time varying) errors;

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Applications





Microscopy: compensation change diffraction index in living cells;

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Applications






Long range cameras: compensation of turbulence in air;

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Applications







LASERS: increase coherence length / power;

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Applications







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:

LA

SER

DETECTOR

LAS

ER

CONTROLLER

DEFORMABLEMIRROR

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ConclusionsBabcock (1953), Keck (1999), E-ELT, . . .

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Spherical and Planar wave propagation;

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Propagation of light, Fermat’s principle;

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Variations in refraction index lead to optical pathlength variations(∆d(x) = n(x)h);

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Pathlength variations lead to wavefront phase variations(∆φ(x) = −2π∆d(x)/λ);

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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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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

lecture 1: introduction on adaptive optics

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