anisoplanatic wavefront error estimation using coherent imaging

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Anisoplanatic Wavefront Error Estimation using Coherent Imaging

Anisoplanatic Wavefront Error Estimation using Coherent Imaging

Rick Kendrick1, Joe Marron2, Bob Benson1

1Lockheed Martin Advanced Technology CenterPalo Alto, California

2Lockheed Martin Coherent TechnologiesLouisville, Colorado

Rick Kendrick1, Joe Marron2, Bob Benson1

1Lockheed Martin Advanced Technology CenterPalo Alto, California

2Lockheed Martin Coherent TechnologiesLouisville, Colorado

15th Coherent Laser Radar ConferenceJune 2009


Previous CLRC PapersPrevious Previous CLRCCLRC PapersPapers

Novel Multi-Aperture 3D Imaging SystemsJ.C. Marron, R. L. Kendrick*, T. A. Höft, and N. Seldomridge

Lockheed Martin Coherent Technologies135 South Taylor Ave.Louisville, CO 80027


AnisoplanatismAnisoplanatismAnisoplanatism

Local Oscillator


AgendaAgendaAgenda

• Bar Target Imaging Experiment• Data Analysis Process• Anisoplanatism• Point Source Array Experiment• Comparison to closed form calculation• Depth of focus demonstration• Summary

•• Bar Target Imaging ExperimentBar Target Imaging Experiment•• Data Analysis ProcessData Analysis Process•• AnisoplanatismAnisoplanatism•• Point Source Array ExperimentPoint Source Array Experiment•• Comparison to closed form calculationComparison to closed form calculation•• Depth of focus demonstrationDepth of focus demonstration•• SummarySummary


Table Mountain Test RangeTable Mountain Test RangeTable Mountain Test Range

Target StandTarget Stand Imaging SystemImaging System100 meters100 meters

1.2 meter beam height1.2 meter beam height


Sensor ArrangementSensor ArrangementSensor Arrangement

ScintecScintec ScintillometerScintillometer

Active ImagerActive Imager


Cn2 = 6.5e-13L=100 m

Typical Scintillometer ReadingTypical Typical ScintillometerScintillometer ReadingReading

Sunny, Cloudless day with Little windSunny, Cloudless day with Little wind


Data analysis stepsData analysis stepsData analysis steps

2004006008001000

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300400

500600

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9001000

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2004006008001000

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Image Plane: Sharpness = 1.2122

20406080100120

2040

6080

100120

16 pupil images16 pupil images

Fringes from LO Fringes from LO interferenceinterference

FFTFFT

FFTFFT

Complex Object Complex Object InformationInformation

Complex Pupil Complex Pupil Function Function ++

Maximize Sharpness by adding phase estimateMaximize Sharpness by adding phase estimate(48 (48 ZernikesZernikes))

FFTFFT

FFTFFT

Calculate SharpnessCalculate SharpnessΣΣ(Intensity(Intensity 22))

Final ImageFinal Image


Set: 1244

Cn2 = 5.11 e-13

r0 = 0.0083

Iso patch= 0.0046

Fixed Aberrations Fixed Aberrations RemovedRemoved

Atmospheric Atmospheric Aberrations Aberrations

RemovedRemoved

Set: 1451

Cn2 = 5.51 e-14

r0 = 0.0317

Iso patch= 0.0176

Set: 1544

Cn2 = 6.0 e-15

r0 = 0.120

Iso patch= 0.0666

D= 50 mmD= 50 mmWavelength = 532 nmWavelength = 532 nm16 speckle realizations16 speckle realizationsTarget moved for each Target moved for each realizationrealization


AnisoplanatismAnisoplanatismAnisoplanatism

Region over which the sharpness metric is maximizedRegion over which the sharpness metric is maximized

Set: 1244

Cn2 = 5.11 e-13

r0 = 0.0083

Iso patch= 0.0046

MTFMTF = 0.26= 0.26 MTFMTF = 0.43= 0.43 MTFMTF = 0.61= 0.61


Point Source ArrayPoint Source ArrayPoint Source Array

• Retro Array is on 20 mm centers– 12.7 mm diameter

•• Retro Array is on 20 mm centersRetro Array is on 20 mm centers–– 12.7 mm diameter12.7 mm diameter


Point Source Array Point Source Array Point Source Array

Raw DataRaw Data Sharpened for one Sharpened for one field pointfield point


Phase Versus SeeingPhase Versus SeeingPhase Versus Seeing

• Cosine of the (phase difference )^2•• Cosine of the (phase difference )^2Cosine of the (phase difference )^2

(14:46)(14:46)rroo =5.6 mm=5.6 mm

(15:28)(15:28)rroo = 51 mm= 51 mm


Anisoplanatism Versus SeeingAnisoplanatismAnisoplanatism Versus SeeingVersus Seeing

1540 sharpened over entire image

• Time Cn2 ro

• 1446 9.85 E-13 5.6 mm• 1502 2.20 E-13 13.8 mm• 1528 2.49 E-14 51.0 mm• 1540 5.83 E-15 122.0 mm

•• Time Time CCnn22 rroo

•• 1446 1446 9.85 E9.85 E--13 13 5.6 mm5.6 mm•• 1502 1502 2.20 E2.20 E--13 13 13.8 mm13.8 mm•• 1528 1528 2.49 E2.49 E--14 14 51.0 mm51.0 mm•• 1540 1540 5.83 E5.83 E--15 15 122.0 mm122.0 mm

Frame = 1 Sharpness = 2.4904

50 100 150 200 250

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Pupil Phase Screen

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Frame = 1 Sharpness = 2.0134

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Pupil Phase Screen

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Phase Map1446 sharpened over entire image

Phase Map


Predicted phase error as a function of field angle

The phase difference structure function, The phase difference structure function, SS((rr,,θθ), derived by Fried,* is evaluated ), derived by Fried,* is evaluated in these calculations for a horizontal path (constant in these calculations for a horizontal path (constant CCnn

22). The separation of ). The separation of two points in the aperture is denoted by two points in the aperture is denoted by rr, and , and θθ is the angular separation is the angular separation between point sources. Denoting by between point sources. Denoting by ΔΔΦΦ the difference in phase between the difference in phase between the two sources after the mean value is removed, the aperturethe two sources after the mean value is removed, the aperture--average average square of the phase difference, ensemblesquare of the phase difference, ensemble--averaged, is given byaveraged, is given by

[1][1]

……where where x = r / D x = r / D and r is the radial position within the aperture and and r is the radial position within the aperture and DD is the is the aperture diameter. The aperture diameter. The MTFMTF for the circular aperture is given byfor the circular aperture is given by

[2][2]

In using In using eqeq. [1] we have neglected a weak dependence of . [1] we have neglected a weak dependence of SS on azimuth within on azimuth within the aperture. When the aperture. When DD/r/roo is not large, is not large, eq.[1eq.[1] predicts mean] predicts mean--square phase square phase differences that can be significantly smaller than the simple exdifferences that can be significantly smaller than the simple expression pression ((θθ//θθisoiso))55/3/3 which is appropriate for very large which is appropriate for very large DD/r/roo..

* David L. Fried. “Anisoplanatism in adaptive optics,” J. Opt. Soc. Am. A, 72, 52-61, (Jan 1982).

rr

θθLL

Aperture, DAperture, D


AnisoplanatismAnisoplanatism Experiment Experiment vs. Theoryvs. Theory

ApertureAperture--average of the phase difference at points in the aperture for vaaverage of the phase difference at points in the aperture for varying rying seeing conditions. seeing conditions.

The error bars indicate the one sigma variability in the data. Note that the variability is much larger for large values of Cn

2 as expected.

Lines = experimental data

Points = closed form calculation


-3 -2 -1 0

1

Image Plane: Sharpness = 1.0782

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Best Focus at ~700 meters

Corrected image

Waves of Focus

3 waves corresponds to about a 600 meter range shift

700 m

100 m

The Jeep is ~ 700 metersThe stand is ~ 100 metersThe beam went through the stand about where the bar target is shown

Depth of Focus DemonstrationDepth of Focus DemonstrationDepth of Focus Demonstration

32


SummarySummarySummary

• Reasonable agreement between experiment and theory.

• This work continues at longer ranges and with more severe atmospheric turbulence.

•• Reasonable agreement between Reasonable agreement between experiment and theory.experiment and theory.

•• This work continues at longer ranges This work continues at longer ranges and with more severe atmospheric and with more severe atmospheric turbulence.turbulence.

Atmospheric turbulence correction using digital holographic detection: experimental results

Joseph C. Marron, 1,* Richard L. Kendrick, 2 Nathan Seldomridge, 1

Taylor D. Grow1 and Thomas A. Höft1

1Lockheed Martin Coherent Technologies, 135 S. Taylor Ave.,Louisville, CO 80027, USA 2 Lockheed Martin Advanced Technology Center, 3251 Hanover Street, Palo Alto, CA 94304 USA

*Corresponding author: [email protected]

Out Soon in:OPTICS EXPRESS


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anisoplanatic wavefront error estimation using coherent imaging

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