High-resolution optical wave-front sensing and control

Harvard - Boston University - University of Maryland

High-resolution optical wave-front sensing and control

Eric W. Justh, P. S. Krishnaprasad

Institute for Systems ResearchUniversity of Maryland, College Park

Mikhail Vorontsov, Gary Carhart, Leonid BeresnevIntelligent Optics Laboratory

U.S. Army Research Laboratory, Adelphi, MD-----------------------

Other Collaborators: Ralph Etienne-Cummings, Viktor Gruev The Johns Hopkins University, Baltimore, MD

Presentation by PSK to Dr. Randy Zachery, ARO Harvard University, May 25, 2004 -------------


Outline

• Background- Adaptive optics: imaging through atmospheric turbulence- Spatial Light Modulator (SLM) technology- Phase-contrast technique for wave-front sensing

• Applications for high-resolution wave-front control

• Phase-contrast wave-front sensing using modern SLM technology- Simple mathematical modeling- Experimental results

• High-resolution wave-front control system- Block diagram- Careful mathematical modeling- Advantages over conventional approaches

• Overview of experimental and simulation work at ARL

• Analytical results


Imaging through turbulence

T.E. Bell, “Electronics and the stars,” IEEE Spectrum, pp. 16-24, Aug. 1995.


Astronomical telescope mirror array

T.E. Bell, “Electronics and the stars,” IEEE Spectrum, pp. 16-24, Aug. 1995.


Correction of vibrations and turbulence

• Structural vibrations compensated primarily by large segmented mirror

- Tens to hundreds of large mirror segments (order of a meter across)

- Low frequency motion and correction (order of Hz)

- Large displacements needed (>>)

- High positioning accuracy (</2)

• Atmospheric turbulence compensated by small deformable mirror

- Tens to hundreds of piezoelectric actuators

(mm to cm spacing)

- Higher frequency correction (hundreds of Hz)

- Modest displacements possible (several )

- Higher positioning accuracy (<< )


Texas Instruments Micromirror Array

L.J. Hornbeck, “From cathode rays to digital micromirrors: A history of electronic projection display technology,” TI Technical Journal, pp. 7-46, July-Sept. 1998.

• 106 mirrors on a 25mm 21mm chip (17m pitch)• +/- 10 degree tilts (digital on/off)• Time response of mirrors about 10s• Developed for displays rather than adaptive optics

ant leg

(Figures from TI web site)


High-resolution SLMs for adaptive optics

(Pixelized LC SLM figures from University of Edinburgh website)

Pixelized devices:

Continuous device:

Boston University micromirror array(Developed by Tom Bifano’s group.)

Pixelized liquid-crystal SLMArmy Research Lab liquid crystal light valve(Leonid Beresnev of Mikhail Vorontsov’s group)


Pioneers

Frits Zernike 1888-1966

Horace W. Babcock 1912-2003

Vladimir P. Linnik 1889-1984


References• H. W. Babcock (1953). “The possibility of compensating

astronomical seeing”, Publications of the Astronomical Society of the Pacific, 65(386):229-236.

• F. Zernike (1955). “How I discovered phase contrast”, Science, 121: 345-349. (Discusses his original 1935 discovery in the context of developments in microscopy for which he received the 1953 Nobel Prize in Physics. This is the paper based on his acceptance speech.)

• H. W. Babcock (1990). “Adaptive optics revisited”, Science, 249(4996):253-257.


Executive Summary

• Work at University of Maryland

• Ties to work at Boston University

• Ties to work at Harvard University


Accomplishments• Adaptive Optics

- Proof-of-concept experimental demonstration of the liquid crystal light valve (LCLV)-based high resolution wave-front control system (nonlinear Zernike filter realization)

- Simulation results show effectiveness against atmospheric turbulence

- Global nonlinear stability analysis for the continuous system model of the wave-front control system

- Patent disclosure (PS-2001-078) jointly to University of Maryland and Army Research Laboratory: Wave-front phase sensors based on optically or electrically controlled phase spatial light modulators for wave-front sensing and control (M.A. Vorontsov, E. W. Justh, L. Beresnev, P. S. Krishnaprasad, J. Ricklin)


From nonlinear Zernike filters to high-resolution adaptive optics


Micromachined deformable mirrors for adaptive opticsApplication: Optical systems used for communication, tracking, and imagingProblem: Aberrations in the beam path degrade performance substantially, particularly in horizontal beam paths. Higher resolution and better beam control are possible through active control using advanced wavefront compensation Solution: In a continuing collaboration, CDCSS researchers at Boston University and ARL researchers (M. Vorontsov) combined their respective technologies for Micromachined deformable mirrors (DMs) and advanced adaptive control to explore ultra-high resolution wavefront control.

Recent Highlights: A point-to-point laser communication test bed at ARL, incorporating a BU 140 actuator DM and controlled through a stochastic gradient descent algorithm, allowed unprecedented control over a 2.5 km horizontal path.


Electrostatic Control of Interfaces • Initial motivation from Adaptive Optics for telescopes• High speed electrostatic control of fluid-fluid interfaces• Issues include

• speed of response,• controllability of the interface,• stability of the fluid-fluid interface,• optimal dimensions and scale,• reflectivity

• Demonstrate the practicality of optical switching under 1ms• Develop theory for determining performance limitations• This ideas are the subject of a patent issued in 2002.


Design of Switching ElementTop ViewSide View

•Self assembly of liquid-gas interface


Close Up of Fluid Switch

Two switches


End of Executive Summary


Babcock’s System

H.W. Babcock, “The possibility of compensating atmospheric seeing,” Publ. Astron. Soc. Pacific., 65(386):229-236, 1953.

(Image from Olivier Lai’s view graphs on adaptive optics)

• First paper on adaptive optics

• The Eidophor was an early SLM based on charging an oil film with an electron gun.

• The Eidophor technology had been developed during the late 1930s and 1940s as a projection display technology.

oil

mirror

deposited charge


Zernike’s phase-contrast technique

F. Zernike, “How I Discovered Phase Contrast,” Science, 121: 345-349, 1955.

• Coherent optical waves have an intensity distribution (what is measured by a camera) and a phase distribution (which cannot be directly measured).

• In 1935 Frits Zernike, a professor at the University of Groningen in the Netherlands, realized that the phenomenon of optical diffraction makes it possible to produce an intensity image which is related to the phase distribution of the wave.

• For small phase deviations, a linear phase image is produced.

• Zernike invented the phase-contrast microscope, based on his phase-imaging technique.

- Advantage: can image living transparent biological specimens.- Before WWII, Zernike tried, but failed, to convince microscopists of the value of his ideas.- It was discovered after WWII that the Germans had actively developed Zernike’s invention

• Nobel Prize in Physics awarded to Zernike in 1953.


Phase-contrast sensing and astronomy

• Papers by Dicke and Hardy examined Zernike’s phase-contrast technique in the context of wave-front sensing for astronomy:

[1] R.H. Dicke, “Phase-contrast detection of telescope seeing errors and their correction,” The Astrophysical Journal, 198: 605-615, 1975.

[2] J.W. Hardy, “Active Optics: A New Technology for the Control of Light,” Proceedings of the IEEE, 66(6): 651-697, 1978.

• Linear analysis techniques are used, which are only applicable for small phase deviations.

• Practical difficulties with phase-contrast sensing have precluded its use to date in adaptive optics for astronomy.


Laser guide star techniques• Idea: use back-scattering of pulsed laser light by molecules or atoms in the atmosphere (e.g., sodium atoms at an altitude of 90km) to measure the wave-front distortion due to atmospheric turbulence.

- For bright objects, a laser guide star is unnecessary.

- For dim objects near bright objects, the bright object serves as a natural guide star (hence the terminology “guide star”).

- At visible wavelengths, natural guide stars are only available for a very small percentage of the sky (<1% at =2.2µm).

• From its invention in 1981 until 1992, laser guide star techniques were classified by the U.S. Government.

• Freeman Dyson on the wall of secrecy surrounding SDI: “This action set back progress in the field of adaptive optics by ten years. The programs inside the wall of secrecy achieved little, and programs outside were discouraged. As often happens when secrecy is imposed on a government program, secrecy hides failures and exaggerates successes.”


Applications for high-resolution wave-front control

• Atmospheric turbulence compensation- Laser communications- Laser polling of remote sensors- Laser radar- Directed laser energy applications (Airborne Laser)- Astronomy

• Atmospheric turbulence monitoring (potential application)- Study fluid-flow around aircraft surfaces- Sensor for active control of aircraft surfaces

• Imaging transparent specimens (phase-contrast microscope)- Biology- Medicine

• Correcting for phase distortion in optical system components


Airborne Laser Concept


• The Zernike phase-plate phase-shifts the zero-order Fourier component (ideally by /2) relative to the rest of the spectrum, producing an image analogous to that of an interferometer:

Iout(r) = I0(r) + (2F)2IF(0) - 4F I0(r) IF(0) [cos((r) - ) - sin ((r) - ) ].

Phase-contrast technique of Zernike

• Conventional Zernike filter phase-contrast sensor (Frits Zernike, 1935):

Ain(r,t)=A0exp[i(r)]

Lens

Zernike phase plate

Output intensity

Distorted wave front

Lens Iout(r)


Conventional Zernike Filter Principle of Operation

• The complex envelope of the input wave is A exp(iu(x,y)), where A is a uniform intensity (over the beam cross-section), and u(x,y) is the phase distribution.

• The left lens performs a spatial Fourier transform of the input wave.

• The perfectly centered phase-shifting dot on the glass slide phase-shifts the zero-order spectral component relative to the rest of the spectrum.

• The right lens performs the inverse Fourier transform.

• The camera records the intensity distribution of the resulting optical signal

O O2

f f f f

x

yz

cameraGlass slide with phase-

shifting dotA exp(iu(x,y)) O


Conventional Zernike Filter Response Function

• The intensity at the camera is

• The linearization of f around u (x,y)0 (and with the assumption that u(x,y) has zero mean, which involves no loss of generality) is

• The conventional Zernike filter thus produces an output signal that is a direct measure of the wavefront of the input beam.

f (u) = 2A (cos - 1)[P cos u + Q sin u - (P + Q )]

+ 2A sin (P sin u - Q cos u) + A

P = cos u dx dy, Q = sin u dx dy,

f (u) = (2A sin ) u.

O2

O2 2 2

O2

O

O2

where is the phase shift of the zero-order spectral component.


Conventional Zernike Filter Strengths and Weaknesses

• The conventional Zernike filter is highly sensitive to wavefront tilts and misalignment of optical components.

• When wavefront variation is large, not much of the optical power is phase-shifted by the phase-shifting dot, and image contrast suffers.

• Strengths

• Weaknesses

• Unlike an interferometer, no reference beam is required

• Directly measures wavefront, instead of wavefront slope (as in a Shack-Hartmann sensor or a shearing interferometer)


Advanced phase-contrast sensor references

V.Yu. Ivanov, V.P. Sivokon, and M.A. Vorontsov, “Phase retrieval from a set of intensity measurements: theory and experiment,” J. Opt. Soc. Am. A, Vol. 9, No. 9, pp. 1515-1524, 1992.

J. Glückstad and P.C. Mogensen, “Analysis of wavefront sensing using a common path interferometer architecture,” Proc. 2nd International Workshop on Adaptive Optics for Industry and Medicine , pp. 241-246, 1999.

J. Glückstad and P.C. Mogensen, “Reconfigurable ternary-phase array illuminator based on the generalized phase contrast method,” Optics Communications, Vol. 173, pp. 169-175, 2000.

P.C. Mogensen and J. Glückstad, “Phase-only optical encryption,” Optics Letters, Vol. 25, No. 8, pp. 566-568, 2000.

J. Glückstad, L. Lading, H. Toyoda, and T. Hara, “Lossless light projection,” Optics Letters, Vol. 22, No. 18, pp. 1373-1375, 1997.

J. Glückstad, “Adaptive array illumination and structured light generated by spatial zero-order self-phase modulation in a Kerr medium,” Optics Communications, Vol. 120, pp. 194-203, 1995.

A. Seward, F. Lacombe, and M. K. Giles, “Focal plane masks in adaptive optics systems,” SPIE Proceedings, Vol. 3762, pp. 283-293, July 1999.


LCLV-based nonlinear Zernike filter

• LCLV fabricated in-house at ARL

• LCLV acts as a high-resolution optically-controlled phase SLM

• Intensity-to-phase-shift gain controlled electronically

• Phase-shifts Fourier components in proportion to their power: robust to tilts

Liquid crystal light valve

M.A. Vorontsov, E.W. Justh, and L.A. Beresnev, JOSA A, 2001


Nonlinear Zernike filter experimental results

127-element liquid-crystal phase SLM

(Meadowlark Optics HEX127)

4 displacement of central electrode of a (Xintics) deformable

mirror

Snapshot of atmospheric turbulence from a space

heater with fan

M.A. Vorontsov, E.W. Justh, and L.A. Beresnev, JOSA A, 2001


Generic high-resolution adaptive optic system

Wave-front sensor

Performance metric


Corrected wave front

Computes the next wave-front corrector image based on the image from the wave-front sensor

High-resolution SLM (wave-front corrector)

Lens Pinhole

Camera

Ain(r,t)

Acor(r,t)

Iout(r,t)

IF(q=0,t)Beam splitter

Beam splitter


• Monochromatic light beam is an oscillatory field on space: use a complex envelope to describe a single component of electric or magnetic field.

• Plane wave:

• Polar form:

• Drop z dependence (fix at z0)

• Care about how phase field evolves and is controlled at a point z0 on optical axis

• Time dependence in phase field introduced corresponding to quasi-static changes in complex envelope (e.g. turbulence, control action); not the time scale of electromagnetic field oscillations.

Complex envelope representation


Continuous system model

• Fourier series representation

• Wave-front sensor image

• Dynamics


• The dynamics are (formally) gradient with respect to the energy functional

i.e.,

• Power coalesces in the Fourier modes being phase-shifted by the Fourier filter.

• Changing the Fourier filter at discrete time instants yields a piecewise gradient flow.

• We would like to have a Fourier-domain intensity-to-phase-shift mapping, computable in a parallel, distributed fashion (i.e., in real time), that produces a piecewise gradient flow leading ultimately to all the energy being concentrated in the zero-order Fourier component.

Gradient dynamics property


• Phase-correcting SLM adds u(r,t) to the phase of the distorted input beam.

• Strehl ratio is a natural normalized measure of phase distortion.

• Ratio of the zero-order Fourier component intensity to the corresponding intensity in the absence of phase distortion.

• See also:

Strehl ratio

M.C. Roggemann, B.M. Welsh, and R.Q. Fugate, 1997, “Improving the resolution of ground-based telescopes,” Reviews of Modern Physics 69(2): 437-505.

M.C. Roggemann and B.M. Welsh, Imaging Through Turbulence, CRC Press, Boca Raton, 1996.


High-speed, high-resolution adaptive optic system

Wave-front sensor

Performance metric




Lens Pinhole

Camera

Ain(r,t)

Acor(r,t)

Iout(r,t)

IF(q=0,t)Beam splitter

Beam splitter

Parallel electronic interface


Wave-front control system block diagram


Opto-electronically controlled wave-front corrector


Opto-electronically controlled spatial Fourier filter

Implements Fourier filter operator


Mathematical modeling

• Nonlinearity plays an essential role.

• The key to successfully analyzing these feedback systems is to use models of the relevant optical physics which have sufficient fidelity, and yet are simple enough to yield qualitative insights.

• Because the beam has a finite cross-section, there is no loss of information in using a two-dimensional Fourier series representation, as long as the Fourier domain-resolution is sufficiently high (to avoid aliasing).

| |1/Spatial domain Fourier (spatial frequency) domain


Fourier filter model

• Fourier series representation

• Wave-front sensor image


Fourier filter operators

Alternating Fourier phase filters

Fourier-domain intensity image


Nonlinear Zernike Filter Feedback System

Zernike filter output intensityPhase-correcting SLM

is an identical 127-element liquid-crystal SLM

Distorted wave front produced by a 127-element liquid-crystal SLM (Meadowlark Optics HEX127)

Fourier spectrum of corrected wave

Feedback algorithm: integrate Iout with respect to time and feed back to SLM1

E.W. Justh, M.A. Vorontsov, G.W. Carhart, L.A. Beresnev, and P.S. Krishnaprasad, JOSA A, 2001


Feedback system experimental results

Interferometer measurement of initial phase distortion

Interferometer measurement of phase after correction (for 34 iterations)

Spectrum before correction

Spectrum after correction (Strehl ratio is improved by a factor of 8)



Simulation results for atmospheric turbulence

Phase distortion (sensor image)

Intensity distortion

Distortion suppression (N = number of iterations)

Phase profile =.23

=.41 =2.45

I=.35 I=.64



High-resolution wave-front control systemDistorted wave front



High-resolution SLM (Fourier filter)



Fourier-domain imager

Wave-front sensor imager

Wave-front sensor


(*)

Main result: gradient dynamics

E.W. Justh, P.S. Krishnaprasad, and M.A. Vorontsov, Proc. CDC, 2000

Diffusion ensures existence and uniqueness of weak solutions:

Proposition: For (*) with

• f corresponding to a common phase shift of an arbitrary (finite) collection I of Fourier components (0 < < )• sufficiently large; • u(r,0), Du(r,0), (r), D(r) L2();• periodic boundary conditions; • |a(r)|2dr is bounded;

if we let

then .


• With no diffusion, the energy functional becomes

and formally we have

• Power coalesces in the Fourier modes being phase-shifted by the Fourier filter.

• We try to understand the behavior of the system with a changing Fourier filter based on the analysis for fixed Fourier filters.

• We would like to have a Fourier filter operator which is computable in real time, and which leads ultimately to all the energy being concentrated in the zero-order Fourier component.

Gradient dynamics property


• Correcting for the distortion induced in an optical wave front due to propagation through a turbulent atmosphere can be formulated as a problem of automatic control.

• General problem formulation: Subject to constraints of realizability, how can atmospheric turbulence compensation be performed optimally, given stochastic models for the wave-front distortion and photodetector noise?

• Weaker problem formulation: Subject to constraints of realizability, how can atmospheric turbulence compensation be performed nearly optimally when the residual distortion is small, and adequately when the residual distortion is large, given simplified stochastic models for the wave-front distortion and photodetector noise?

Design problem formulation


• Given our basic system architecture, the design problem consists of:

- Choosing the Fourier filter operator

- Choosing feedback gain distribution

• Design objectives:

- In the large-distortion (highly nonlinear) regime, the system remains nonlinearly stable and evolves toward the low-distortion (linear) regime.

- Requires judicious choice of Fourier filter operator

- Feedback gain limited by stability requirement

- In the low-distortion (linear) regime,

- Fourier filter operator has converged to a single-pixel Fourier filter

- Feedback gains depend on the turbulence, noise, and residual wave- front correction error statistics

Design problem


Fourier filter evolution in experimental system

Initial spectrum

Spectrum after 10 iterations



E.W. Justh, M.A. Vorontsov, G.W. Carhart, L.A. Beresnev, and P.S. Krishnaprasad, Proc. SPIE, 2001


Wave-front estimation problem

w(k)(k)

v(k)

(k|k-1)^

(k)St(k)

[f()](k)

^

+

_

+

+

f

St


• Zero-order Fourier component power:

• Taylor series expansion is

with

• Strehl ratio:

• The measured Strehl ratio may be useful as an estimate of the error covariance for determining the “optimal” feedback gain coefficients cs(k) on-line.

Strehl ratio and minimum variance estimation


Summary

• Long-term goal: small, inexpensive, high-resolution wave-front control systems for

- Adaptive optics

- Sensor applications based on optical phase

• Significant accomplishments of the high-resolution adaptive optics project (Army Research Lab, University of Maryland, The Johns Hopkins University):

- Proof-of-concept experimental work demonstrating operation of the LCLV-based wave-front control system

- Simulation results showing effectiveness against atmospheric turbulence

- Global nonlinear stability analysis for the continuous system model

- Development of VLSI components needed for improved performance (at The Johns Hopkins University)


ReferencesM.A. Vorontsov, E.W. Justh, and L.A. Beresnev, “Advanced phase-contrast techniques for wavefront sensing and adaptive optics,” SPIE Proc., 4124: 98-109, 2000.

E.W. Justh, M.A. Vorontsov, G.W. Carhart, L.A. Beresnev, and P.S. Krishnaprasad, “Adaptive wavefront control using a nonlinear Zernike filter,” SPIE Proc., 4124: 189-200, 2000.

G.W. Carhart, M.A. Vorontsov, and E.W. Justh, “Opto-electronic Zernike filter for high-resolution wavefront analysis using a phase-only liquid-crystal spatial light modulator,” SPIE Proc., 4124: 138-147, 2000.

E.W. Justh, P.S. Krishnaprasad, and M.A. Vorontsov, “Nonlinear Analysis of a High-Resolution Optical Wavefront Control System,” Proc. IEEE Conf. on Decision and Control, pp. 3301-3306, 2000.

E.W. Justh and P.S. Krishnaprasad, “Analysis of a High-Resolution Optical Wavefront Control System,” Proc. Conf. on Information Sciences and Systems, 2: 718-723, 2001.

M.A. Vorontsov, E.W. Justh, and L.A. Beresnev, “Adaptive Optics with Advanced Phase-Contrast Techniques: Part I. High-Resolution Wavefront Sensing,” J. Opt. Soc. Am. A, 18(6): 1289-1299, 2001.

E.W. Justh, M.A. Vorontsov, G.W. Carhart, L.A. Beresnev, and P.S. Krishnaprasad, “Adaptive Optics with Advanced Phase-Contrast Techniques: Part II. High-Resolution Wavefront Control,” J. Opt. Soc. Am. A, 18(6): 1300-1311, 2001.

E.W. Justh, P.S. Krishnaprasad, and M.A. Vorontsov, “Analysis of a high-resolution optical wave-front control system,” Automatica, 40 (7): 1129-1141, 2004.


Patent

M. A. Vorontsov, E. Justh, L. Bersenev, P. S. Krishnaprasad, and J. C. Ricklin, “Wavefront Phase Sensors Based on Optically or Electrically Controlled Phase Spatial Light Modulators for Wavefront Sensing and Control”, (2002). Joint disclosure to the University of Maryland and the Army Research Laboratory (PS-2001-078). Patent applied for through Army Research Laboratory.

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High-resolution optical wave-front sensing and control