Abstract

The effects of speckle on the performance of adaptive optical (COAT) systems is examined, with particular emphasis on multidither COAT systems. Experimental, analytical, and computer simulation data are presented that are in mutual agreement and that define the performance of multidither systems in the presence of speckle effects. In general, the performance of coherent-light adaptive systems can be degraded by speckle-induced effects. The severity of the degradation depends on the target parameters (surface roughness, glint structure, geometry, motion) and the adaptive system parameters (wavelength, bandwidth, servo details).

© 1976 Optical Society of America

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  1. The term “COAT” is generally applied to self-adaptive, optical-phased arrays that derive their phasing information from energy reflected from the target.
  2. R. F. Ogrodnik and G. Gurski, “Target Return-Adaptive Aperture System Interaction Effects,” (unpublished).
  3. J. Feinleib, S. G. Lipson, and P. F. Cone, “Monolithic piezoelectric mirror for wavefront correction,” Appl. Phys. Lett. 25, 311 (1974).
    [Crossref]
  4. P. F. Cone and J. Feinleib, “High-Speed Deformable Mirrors for Wavefront Correction,” J. Opt. Soc. Am,  65, 1212A (1975).
  5. A. W. Angelbeck, R. H. Freeman, and H. C. Reynolds, “Development of a High-Power Cooled Mirror with Active Figure Control,” (unpublished).
  6. R. A. Muller and A. Buffington, “Real-time correction of atmospherically degraded telescope images through image sharpening,” J. Opt. Soc. Am. 64, 1200 (1974).
    [Crossref]
  7. J. W. Hardy, J. Feinleib, and J. C. Wyant, “Real Time Phase Correction of Optical Imaging Systems,” Proceedings of the OSA Topical meeting on Optical Propagation Through Turbulence, July 1974, paper ThB1.
  8. L. Miller, W. P. Brown, J. A. Jenney, and T. R. O’Meara, “Imaging Through Turbulence with Coherent Optical Adaptive Techniques,” Proceedings of the OSA Topical Meeting on Optical Propagation Through Turbulence, July 1974, paper ThB2.
  9. J. E. Pearson, W. P. Brown, S. A. Kokorowski, T. R. O’Meara, and M. E. Pedinoff, “COAT Compensation for Turbulence and Thermal Blooming with Realistic, Complex Targets,” J. Opt. Soc. Am. 65, 1212A (1975).
  10. An “out-going wave” system senses phase changes on the laser beam as it propagates to the target. A “return-wave” system senses phase changes impressed on the energy reflected from the target. T. R. O’Meara in the “Multidither principle in adaptive optics” (submitted to J. Opt. Soc. Am.) has discussed these systems in detail.
  11. W. B. Bridges, P. T. Brunner, S. P. Lazzara, T. A. Nussmeier, T. R. O’Meara, J. A. Sanguinet, and W. P. Brown, “Coherent Optical Adaptive Techniques,” Appl. Opt. 13, 291 (1974).
    [Crossref] [PubMed]
  12. J. E. Pearson, W. B. Bridges, S. Hansen, T. A. Nussmeier, and M. E. Pedinoff, “Coherent Optical Adaptive Techniques: Design and Performance of an 18-Element, Visible, Multidither COAT System,” Appl. Opt. 15, 611 (1976).
    [Crossref] [PubMed]
  13. James E. Pearson, “Atmospheric Turbulence Compensation Using Coherent Optical Adaptive Techniques,” Appl. Opt. 15, 622 (1976).
    [Crossref] [PubMed]
  14. W. B. Bridges and J. E. Pearson, “Thermal Blooming Compensation Using Coherent Optical Adaptive Techniques (COAT),” Appl. Phys. Lett. 26, 539 (1975).
    [Crossref]
  15. L. I. Goldfisher, “Autocorrelation Function and Power Spectral Density of Laser-Produced Speckle Patterns,” J. Opt. Soc. Am. 55, 247 (1965).
    [Crossref]
  16. N. George (unpublished).
  17. S. A. Kokorowski, M. E. Pedinoff, and J. E. Pearson, “Analytical, Experimental, and Computer Simulation Results on the Interactive Effects of Speckle with Multidither Adaptive Optics Systems,” J. Opt. Soc. Am. (to be published).
  18. R. F. Ogradnik, “Adaptive Control Theory Applied to Active Optics,” J. Opt. Soc. Am. 65, 1213A (1975).

1976 (2)

1975 (4)

J. E. Pearson, W. P. Brown, S. A. Kokorowski, T. R. O’Meara, and M. E. Pedinoff, “COAT Compensation for Turbulence and Thermal Blooming with Realistic, Complex Targets,” J. Opt. Soc. Am. 65, 1212A (1975).

P. F. Cone and J. Feinleib, “High-Speed Deformable Mirrors for Wavefront Correction,” J. Opt. Soc. Am,  65, 1212A (1975).

W. B. Bridges and J. E. Pearson, “Thermal Blooming Compensation Using Coherent Optical Adaptive Techniques (COAT),” Appl. Phys. Lett. 26, 539 (1975).
[Crossref]

R. F. Ogradnik, “Adaptive Control Theory Applied to Active Optics,” J. Opt. Soc. Am. 65, 1213A (1975).

1974 (3)

1965 (1)

Angelbeck, A. W.

A. W. Angelbeck, R. H. Freeman, and H. C. Reynolds, “Development of a High-Power Cooled Mirror with Active Figure Control,” (unpublished).

Bridges, W. B.

Brown, W. P.

J. E. Pearson, W. P. Brown, S. A. Kokorowski, T. R. O’Meara, and M. E. Pedinoff, “COAT Compensation for Turbulence and Thermal Blooming with Realistic, Complex Targets,” J. Opt. Soc. Am. 65, 1212A (1975).

W. B. Bridges, P. T. Brunner, S. P. Lazzara, T. A. Nussmeier, T. R. O’Meara, J. A. Sanguinet, and W. P. Brown, “Coherent Optical Adaptive Techniques,” Appl. Opt. 13, 291 (1974).
[Crossref] [PubMed]

L. Miller, W. P. Brown, J. A. Jenney, and T. R. O’Meara, “Imaging Through Turbulence with Coherent Optical Adaptive Techniques,” Proceedings of the OSA Topical Meeting on Optical Propagation Through Turbulence, July 1974, paper ThB2.

Brunner, P. T.

Buffington, A.

Cone, P. F.

P. F. Cone and J. Feinleib, “High-Speed Deformable Mirrors for Wavefront Correction,” J. Opt. Soc. Am,  65, 1212A (1975).

J. Feinleib, S. G. Lipson, and P. F. Cone, “Monolithic piezoelectric mirror for wavefront correction,” Appl. Phys. Lett. 25, 311 (1974).
[Crossref]

Feinleib, J.

P. F. Cone and J. Feinleib, “High-Speed Deformable Mirrors for Wavefront Correction,” J. Opt. Soc. Am,  65, 1212A (1975).

J. Feinleib, S. G. Lipson, and P. F. Cone, “Monolithic piezoelectric mirror for wavefront correction,” Appl. Phys. Lett. 25, 311 (1974).
[Crossref]

J. W. Hardy, J. Feinleib, and J. C. Wyant, “Real Time Phase Correction of Optical Imaging Systems,” Proceedings of the OSA Topical meeting on Optical Propagation Through Turbulence, July 1974, paper ThB1.

Freeman, R. H.

A. W. Angelbeck, R. H. Freeman, and H. C. Reynolds, “Development of a High-Power Cooled Mirror with Active Figure Control,” (unpublished).

George, N.

N. George (unpublished).

Goldfisher, L. I.

Gurski, G.

R. F. Ogrodnik and G. Gurski, “Target Return-Adaptive Aperture System Interaction Effects,” (unpublished).

Hansen, S.

Hardy, J. W.

J. W. Hardy, J. Feinleib, and J. C. Wyant, “Real Time Phase Correction of Optical Imaging Systems,” Proceedings of the OSA Topical meeting on Optical Propagation Through Turbulence, July 1974, paper ThB1.

Jenney, J. A.

L. Miller, W. P. Brown, J. A. Jenney, and T. R. O’Meara, “Imaging Through Turbulence with Coherent Optical Adaptive Techniques,” Proceedings of the OSA Topical Meeting on Optical Propagation Through Turbulence, July 1974, paper ThB2.

Kokorowski, S. A.

J. E. Pearson, W. P. Brown, S. A. Kokorowski, T. R. O’Meara, and M. E. Pedinoff, “COAT Compensation for Turbulence and Thermal Blooming with Realistic, Complex Targets,” J. Opt. Soc. Am. 65, 1212A (1975).

S. A. Kokorowski, M. E. Pedinoff, and J. E. Pearson, “Analytical, Experimental, and Computer Simulation Results on the Interactive Effects of Speckle with Multidither Adaptive Optics Systems,” J. Opt. Soc. Am. (to be published).

Lazzara, S. P.

Lipson, S. G.

J. Feinleib, S. G. Lipson, and P. F. Cone, “Monolithic piezoelectric mirror for wavefront correction,” Appl. Phys. Lett. 25, 311 (1974).
[Crossref]

Miller, L.

L. Miller, W. P. Brown, J. A. Jenney, and T. R. O’Meara, “Imaging Through Turbulence with Coherent Optical Adaptive Techniques,” Proceedings of the OSA Topical Meeting on Optical Propagation Through Turbulence, July 1974, paper ThB2.

Muller, R. A.

Nussmeier, T. A.

O’Meara, T. R.

J. E. Pearson, W. P. Brown, S. A. Kokorowski, T. R. O’Meara, and M. E. Pedinoff, “COAT Compensation for Turbulence and Thermal Blooming with Realistic, Complex Targets,” J. Opt. Soc. Am. 65, 1212A (1975).

W. B. Bridges, P. T. Brunner, S. P. Lazzara, T. A. Nussmeier, T. R. O’Meara, J. A. Sanguinet, and W. P. Brown, “Coherent Optical Adaptive Techniques,” Appl. Opt. 13, 291 (1974).
[Crossref] [PubMed]

An “out-going wave” system senses phase changes on the laser beam as it propagates to the target. A “return-wave” system senses phase changes impressed on the energy reflected from the target. T. R. O’Meara in the “Multidither principle in adaptive optics” (submitted to J. Opt. Soc. Am.) has discussed these systems in detail.

L. Miller, W. P. Brown, J. A. Jenney, and T. R. O’Meara, “Imaging Through Turbulence with Coherent Optical Adaptive Techniques,” Proceedings of the OSA Topical Meeting on Optical Propagation Through Turbulence, July 1974, paper ThB2.

Ogradnik, R. F.

R. F. Ogradnik, “Adaptive Control Theory Applied to Active Optics,” J. Opt. Soc. Am. 65, 1213A (1975).

Ogrodnik, R. F.

R. F. Ogrodnik and G. Gurski, “Target Return-Adaptive Aperture System Interaction Effects,” (unpublished).

Pearson, J. E.

J. E. Pearson, W. B. Bridges, S. Hansen, T. A. Nussmeier, and M. E. Pedinoff, “Coherent Optical Adaptive Techniques: Design and Performance of an 18-Element, Visible, Multidither COAT System,” Appl. Opt. 15, 611 (1976).
[Crossref] [PubMed]

J. E. Pearson, W. P. Brown, S. A. Kokorowski, T. R. O’Meara, and M. E. Pedinoff, “COAT Compensation for Turbulence and Thermal Blooming with Realistic, Complex Targets,” J. Opt. Soc. Am. 65, 1212A (1975).

W. B. Bridges and J. E. Pearson, “Thermal Blooming Compensation Using Coherent Optical Adaptive Techniques (COAT),” Appl. Phys. Lett. 26, 539 (1975).
[Crossref]

S. A. Kokorowski, M. E. Pedinoff, and J. E. Pearson, “Analytical, Experimental, and Computer Simulation Results on the Interactive Effects of Speckle with Multidither Adaptive Optics Systems,” J. Opt. Soc. Am. (to be published).

Pearson, James E.

Pedinoff, M. E.

J. E. Pearson, W. B. Bridges, S. Hansen, T. A. Nussmeier, and M. E. Pedinoff, “Coherent Optical Adaptive Techniques: Design and Performance of an 18-Element, Visible, Multidither COAT System,” Appl. Opt. 15, 611 (1976).
[Crossref] [PubMed]

J. E. Pearson, W. P. Brown, S. A. Kokorowski, T. R. O’Meara, and M. E. Pedinoff, “COAT Compensation for Turbulence and Thermal Blooming with Realistic, Complex Targets,” J. Opt. Soc. Am. 65, 1212A (1975).

S. A. Kokorowski, M. E. Pedinoff, and J. E. Pearson, “Analytical, Experimental, and Computer Simulation Results on the Interactive Effects of Speckle with Multidither Adaptive Optics Systems,” J. Opt. Soc. Am. (to be published).

Reynolds, H. C.

A. W. Angelbeck, R. H. Freeman, and H. C. Reynolds, “Development of a High-Power Cooled Mirror with Active Figure Control,” (unpublished).

Sanguinet, J. A.

Wyant, J. C.

J. W. Hardy, J. Feinleib, and J. C. Wyant, “Real Time Phase Correction of Optical Imaging Systems,” Proceedings of the OSA Topical meeting on Optical Propagation Through Turbulence, July 1974, paper ThB1.

Appl. Opt. (3)

Appl. Phys. Lett. (2)

W. B. Bridges and J. E. Pearson, “Thermal Blooming Compensation Using Coherent Optical Adaptive Techniques (COAT),” Appl. Phys. Lett. 26, 539 (1975).
[Crossref]

J. Feinleib, S. G. Lipson, and P. F. Cone, “Monolithic piezoelectric mirror for wavefront correction,” Appl. Phys. Lett. 25, 311 (1974).
[Crossref]

J. Opt. Soc. Am (1)

P. F. Cone and J. Feinleib, “High-Speed Deformable Mirrors for Wavefront Correction,” J. Opt. Soc. Am,  65, 1212A (1975).

J. Opt. Soc. Am. (4)

J. E. Pearson, W. P. Brown, S. A. Kokorowski, T. R. O’Meara, and M. E. Pedinoff, “COAT Compensation for Turbulence and Thermal Blooming with Realistic, Complex Targets,” J. Opt. Soc. Am. 65, 1212A (1975).

R. F. Ogradnik, “Adaptive Control Theory Applied to Active Optics,” J. Opt. Soc. Am. 65, 1213A (1975).

L. I. Goldfisher, “Autocorrelation Function and Power Spectral Density of Laser-Produced Speckle Patterns,” J. Opt. Soc. Am. 55, 247 (1965).
[Crossref]

R. A. Muller and A. Buffington, “Real-time correction of atmospherically degraded telescope images through image sharpening,” J. Opt. Soc. Am. 64, 1200 (1974).
[Crossref]

Other (8)

N. George (unpublished).

S. A. Kokorowski, M. E. Pedinoff, and J. E. Pearson, “Analytical, Experimental, and Computer Simulation Results on the Interactive Effects of Speckle with Multidither Adaptive Optics Systems,” J. Opt. Soc. Am. (to be published).

An “out-going wave” system senses phase changes on the laser beam as it propagates to the target. A “return-wave” system senses phase changes impressed on the energy reflected from the target. T. R. O’Meara in the “Multidither principle in adaptive optics” (submitted to J. Opt. Soc. Am.) has discussed these systems in detail.

The term “COAT” is generally applied to self-adaptive, optical-phased arrays that derive their phasing information from energy reflected from the target.

R. F. Ogrodnik and G. Gurski, “Target Return-Adaptive Aperture System Interaction Effects,” (unpublished).

A. W. Angelbeck, R. H. Freeman, and H. C. Reynolds, “Development of a High-Power Cooled Mirror with Active Figure Control,” (unpublished).

J. W. Hardy, J. Feinleib, and J. C. Wyant, “Real Time Phase Correction of Optical Imaging Systems,” Proceedings of the OSA Topical meeting on Optical Propagation Through Turbulence, July 1974, paper ThB1.

L. Miller, W. P. Brown, J. A. Jenney, and T. R. O’Meara, “Imaging Through Turbulence with Coherent Optical Adaptive Techniques,” Proceedings of the OSA Topical Meeting on Optical Propagation Through Turbulence, July 1974, paper ThB2.

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Figures (9)

FIG. 1
FIG. 1

COAT compensation for propagation distortions. (a) In the absence of distortions a transmitting array can focus a diffraction-limited beam on a point. (b) Distortions such as turbulence spread, defocus, and distort the beam. (c) If a proper “predistortion” is applied to the transmitted phase front, a nearly diffraction-limited focused spot is again achieved.

FIG. 2
FIG. 2

Three principal types of adaptive optical systems used to correct transmitted beams. (a) Phase conjugate. This system interferes a portion of the transmitted beam with target-reflected radiation to measure the correction phase. (b) “TRIM-COAT.” An image-compensation system that works with broadband radiation (not reflected laser energy) from the target to correct the target to correct the transmitted laser beam. (c) Multidither, outgoing-wave. Phase modulations on the transmitted beam wave front are sensed as amplitude modulations in the target-reflected energy and used to correct the transmitted beam phase.

FIG. 3
FIG. 3

Two-element optical phased array example for understanding multidither COAT operation. The one phase-controlled element forms a closed-loop, hill-climbing servo mechanism that acts to maximize the irradiance at the target glint.

FIG. 4
FIG. 4

Speckle effects in a multidither COAT system. (a) Definition of various geometrical quantities such as DT and DR, the transmitter and receiver aperture diameters; λ3, the speckle coherence length; VT and ΩT, the target translational and rotational velocities; and vs, the translation velocity of the speckle pattern in the receiver plane. (b) Receiver signal in the absence of speckle effects (e.g., when a very large receiver is employed); the only modulations are the dither control modulations. (c) Receiver signal when the receiver aperture is comparable to the transmitter. Large amplitude fluctuations can occur.

FIG. 5
FIG. 5

Schematic of experimental apparatus used to study speckle effects on a multidither COAT system. Laser: 0.488 μm argon. Phasor matrix: optical elements where dither and correction phase changes are impressed on beam. L1, L2: recollimating telescope,: BS: beamsplitter. D: pinhole detector. PMT: photomultiplier tube.

FIG. 6
FIG. 6

Experimental speckle effects. The upper pictures are outputs of a spectrum analyzer looking at the COAT receiver signal. The lower pictures show the peak target irradiance seen by a pinhole detector (D in Fig. 5) as the servo loop is closed. (a) Target rotation rate ΩT = 0. Average power after convergence = P = 1.0 (b) ΩT = π rad/s, P = 0.70, (c) ΩT = 2π rad/s, P = 0.31.

FIG. 7
FIG. 7

Schematic of elements in detailed computer simulation of a multidither servo system. Speckle effects are introduced as a constant power, non-negative signal that multiplies the normal receiver signal.

FIG. 8
FIG. 8

Computer simulation results of speckle effects. With no speckle modulations, the 18-channel COAT system converges in about 2 ms. When strong speckle effects are present, the COAT system convergence is limited to an average level of about 40% of the “no speckle” maximum and the intensity fluctuates about this average level. Simulated Target: pyroceram sphere (10 cm diameter, 1 m radius) uniformly illuminated with 10.6 μm light at 2 km from transmitter/receiver. Target rotating at 2 rad/s. Receiver: 1.2 × 1.0 m annulus.

FIG. 9
FIG. 9

Summary of analytical results on 18-channel multidither COAT performance in the presence of spurious amplitude modulations. Peak dither amplitude = 20°, 8–32 kHz dithers. ——: Theory, with ρ = (ave. dither power)/(ave. speckle power). - - - - -: Empirical Gaussian fit to theory. Points are from computer simulation: ●, S/N (shot) = 1010; ▲, S/N = 40.

Equations (5)

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S ( f x ) B exp - [ ( 2 σ / N ) f x ] 2 ,
λ s = 2 ( 2 σ / N ) D T / N ,
v s / λ s ( v T + 2 Ω T Z ) / D T f d ,
f max - f min 3.2 ( N C - 1 ) f c ,
C s = ( ± ω i ω i - Δ ω ω i + Δ ω P s ( ω ) d ω ) 1 / 2 ,