Download Optical Wavefront Sensing and Control

High-resolution optical wave-front
sensing and control
Eric W. Justh, P. S. Krishnaprasad
Institute for Systems Research
University of Maryland, College Park
Mikhail Vorontsov, Gary Carhart, Leonid Beresnev
Intelligent Optics Laboratory
U.S. Army Research Laboratory, Adelphi, MD
-----------------------
Presentation by PSK to Dr. Randy Zachery, ARO
Harvard University, May 25, 2004
------------Other Collaborators: Ralph Etienne-Cummings, Viktor Gruev
The Johns Hopkins University, Baltimore, MD
Harvard - Boston University - University of Maryland
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
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Imaging through turbulence
T.E. Bell, “Electronics and the stars,” IEEE Spectrum, pp. 16-24, Aug. 1995.
Harvard - Boston University - University of Maryland
Astronomical telescope mirror array
T.E. Bell, “Electronics and the stars,” IEEE Spectrum, pp. 16-24, Aug. 1995.
Harvard - Boston University - University of Maryland
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 (<< )
Harvard - Boston University - University of Maryland
Texas Instruments Micromirror Array
• 106 mirrors on a 25mm  21mm chip (17m pitch)
• +/- 10 degree tilts (digital on/off)
• Time response of mirrors about 10s
• Developed for displays rather than adaptive optics
ant leg
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.
(Figures from TI web site)
Harvard - Boston University - University of Maryland
High-resolution SLMs for adaptive optics
Pixelized devices:
Boston University micromirror array
(Developed by Tom Bifano’s group.)
Continuous device:
Pixelized liquid-crystal SLM
Army Research Lab liquid crystal light valve
(Leonid Beresnev of Mikhail Vorontsov’s group)
(Pixelized LC SLM figures from
University of Edinburgh website)
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Pioneers
Horace W. Babcock
1912-2003
Vladimir P. Linnik
1889-1984
Frits Zernike
1888-1966
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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.
Harvard - Boston University - University of Maryland
Executive Summary
• Work at University of Maryland
• Ties to work at Boston University
• Ties to work at Harvard University
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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)
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From nonlinear Zernike filters to high-resolution adaptive optics
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Micromachined deformable mirrors for adaptive optics
Application: Optical systems used for communication, tracking, and imaging
Problem: 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.
Harvard - Boston University - University of Maryland
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.
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Design of Switching Element
Side View
Top View
•Self assembly of liquid-gas interface
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Close Up of Fluid Switch
Two switches
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End of Executive Summary
Harvard - Boston University - University of Maryland
Babcock’s System
• First paper on adaptive optics
• The Eidophor was an early SLM
based on charging an oil film with
an electron gun.
deposited charge
oil
mirror
• The Eidophor technology had
been developed during the late
1930s and 1940s as a projection
display technology.
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)
Harvard - Boston University - University of Maryland
Zernike’s phase-contrast technique
• 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.
F. Zernike, “How I Discovered Phase Contrast,” Science, 121: 345-349, 1955.
Harvard - Boston University - University of Maryland
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.
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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.”
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Applications for high-resolution wavefront 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
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Airborne Laser Concept
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Phase-contrast technique of Zernike
• Conventional Zernike filter phase-contrast sensor (Frits Zernike, 1935):
Ain(r,t)=A0exp[i(r)]
Lens
Distorted
wave front
Lens
Zernike
phase plate
Iout(r)
Output
intensity
• 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) + (2F)2IF(0) - 4F I0(r) IF(0) [cos((r) - ) - sin ((r) - ) ].
Harvard - Boston University - University of Maryland
Conventional Zernike Filter Principle of Operation
Glass slide with phaseshifting dot
A O exp(iu(x,y))
camera
x
y
f
f
f
z
f
• The complex envelope of the input wave is AO exp(iu(x,y)), where A 2O 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 zeroorder 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
Harvard - Boston University - University of Maryland
Conventional Zernike Filter Response Function
• The intensity at the camera is
f (u) = 2A 2O (cos  - 1)[P cos u + Q sin u - (P2 + Q 2 )]
+ 2A2O sin  (P sin u - Q cos u) + AO2
P =   cos u dx dy, Q =   sin u dx dy,
where  is the phase shift of the zero-order spectral component.
• The linearization of f around uO(x,y)0 (and with the assumption that
u(x,y) has zero mean, which involves no loss of generality) is
f (u) = (2A O2 sin ) u.
• The conventional Zernike filter thus produces an output signal that is a
direct measure of the wavefront of the input beam.
Harvard - Boston University - University of Maryland
Conventional Zernike Filter Strengths and Weaknesses
• Strengths
• 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)
• 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.
Harvard - Boston University - University of Maryland
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 selfphase 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.
Harvard - Boston University - University of Maryland
LCLV-based nonlinear Zernike filter
Liquid crystal light valve
• LCLV fabricated in-house at ARL
• LCLV acts as a high-resolution opticallycontrolled phase SLM
• Intensity-to-phase-shift gain controlled
electronically
• Phase-shifts Fourier components in
proportion to their power: robust to tilts
M.A. Vorontsov, E.W. Justh, and L.A. Beresnev, JOSA A, 2001
Harvard - Boston University - University of Maryland
Nonlinear Zernike filter experimental results
127-element liquidcrystal phase SLM
(Meadowlark Optics
HEX127)
4 displacement of
central electrode of a
(Xintics) 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
Harvard - Boston University - University of Maryland
Generic high-resolution adaptive optic system
Ain(r,t)
Distorted
wave front
Corrected
wave front
Lens
Beam
splitter
Pinhole
IF(q=0,t)
Acor(r,t)
Beam splitter
High-resolution
SLM (wavefront corrector)
Wave-front
sensor
Performance
metric
Camera
Iout(r,t)
Computes the next wave-front corrector image
based on the image from the wave-front sensor
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Complex envelope representation
• 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.
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Continuous system model
• Fourier series representation
• Wave-front sensor image
• Dynamics
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Gradient dynamics property
• 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.
Harvard - Boston University - University of Maryland
Strehl ratio
• 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: 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.
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High-speed, high-resolution adaptive optic system
Ain(r,t)
Distorted
wave front
Corrected
wave front
Lens
Beam
splitter
IF(q=0,t)
Acor(r,t)
High-resolution
SLM (wavefront corrector)
Parallel
electronic
interface
Pinhole
Beam splitter
Wave-front
sensor
Performance
metric
Camera
Iout(r,t)
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Wave-front control system block diagram
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Opto-electronically controlled wave-front corrector
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Opto-electronically controlled spatial Fourier filter
Implements Fourier
filter operator
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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).

Spatial domain
| |1/
Fourier (spatial frequency) domain
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Fourier filter model
• Fourier series representation
• Wave-front sensor image
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Fourier filter operators
Fourier-domain
intensity image
Alternating
Fourier
phase filters
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Nonlinear Zernike Filter Feedback System
Fourier spectrum of corrected wave
Distorted wave front
produced by a 127element liquid-crystal
SLM (Meadowlark
Optics HEX127)
Phase-correcting SLM
is an identical 127element liquid-crystal
SLM
Zernike filter
output intensity
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
Harvard - Boston University - University of Maryland
Feedback system experimental results
Interferometer
measurement of
initial phase
distortion
Spectrum before
correction
Interferometer
measurement of
phase after
correction (for
34 iterations)
Spectrum after
correction (Strehl
ratio is improved
by a factor of 8)
E.W. Justh, M.A. Vorontsov, G.W. Carhart, L.A. Beresnev, and P.S. Krishnaprasad, JOSA A, 2001
Harvard - Boston University - University of Maryland
Simulation results for atmospheric turbulence
Phase
profile
=.23
=.41
=2.45
Phase distortion (sensor image)
I=.35
I=.64
Intensity distortion
Distortion suppression
(N = number of iterations)
E.W. Justh, M.A. Vorontsov, G.W. Carhart, L.A. Beresnev, and P.S. Krishnaprasad, JOSA A, 2001
Harvard - Boston University - University of Maryland
High-resolution wave-front control system
Distorted
wave front
Corrected
wave front
Wave-front
sensor
High-resolution
SLM (Fourier filter)
High-resolution
SLM (wavefront corrector)
Wave-front
sensor imager
Parallel
electronic
interface
Fourier-domain
imager
Parallel electronic
interface
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Main result: gradient dynamics
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
.
E.W. Justh, P.S. Krishnaprasad, and M.A. Vorontsov, Proc. CDC, 2000
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Gradient dynamics property
• 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.
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Design problem formulation
• 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?
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Design problem
• 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 wavefront correction error statistics
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Fourier filter evolution in experimental system
Initial
spectrum
Spectrum
after 10
iterations
Spectrum
after 20
iterations
Spectrum
after 30
iterations
E.W. Justh, M.A. Vorontsov, G.W. Carhart, L.A. Beresnev, and P.S. Krishnaprasad, Proc. SPIE, 2001
Harvard - Boston University - University of Maryland
Wave-front estimation problem

w(k)
v(k)
^

+
(k) +
(k)
_
St
St(k)
^
(k|k-1)
+
f
[f()](k)
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Strehl ratio and minimum variance estimation
• 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.
Harvard - Boston University - University of Maryland
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)
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References
M.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: 138147, 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.
Harvard - Boston University - University of Maryland
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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