Abstract

Coherent optical adaptive techniques (COAT) offer promise for overcoming the deleterious effects of phase distortions experienced by optical beams propagating through distorting optics or via a turbulent and absorbing atmosphere. The theory of four classes of such systems, which employ similar multidither principles, is explored. Many modes of operating these systems are briefly reviewed and a detailed analysis of the most widely employed—a glint referencing system with sinusoidal dithers—is developed. A servo signal-to-noise analysis indicates how the optimum choice of dither magnitude depends on the system noise.

© 1977 Optical Society of America

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  1. W. T. Cathey, C. L. Hayes and W. C. Davis, Appl. Opt. 9, 701 (1970).
  2. T. R. O'Meara, W. P. Brown, W. B. Bridges, T. A. Nussmeier, A. D. Jacobson, J. F. Lotspeich, G. M. Janney, and J. Y. Wada, "Coherent Optical Adaptive Techniques," Hughes Research Laboratories Tech. Rep. RADC-TR (Dec. 1970) (unpublished).
  3. R. P. Futrelle, G. E. Meyers, and C. L. Hayes, "Coherent Optical Adaptive Techniques," Contract F30602-70-C-0298 (April 1971) (unpublished).
  4. T. R. O'Meara, U.S. Patent 3,727,223, "Adaptive Power Redistribution Systems" (April 10, 1973) (U. S. Patent Office, Washington, D. C.).
  5. T. R. O'Meara, U.S. Patent 3,731,103, "Adaptive Arrays" (May 1, 1973) (unpublished).
  6. T. R. O'Meara, U.S. Patent 3,764,213, "Return-Wave, Phase Controlled Adaptive Array" (October 9, 1973) (U. S. Patent Office, Washington, D. C.).
  7. W. B. Bridges, P. T. Brunner, S. P. Lazzara, T. A. Nussmeier, T. R. O'Meara, J. A. Sanguinet, and W. P. Brown, Jr., Appl. Opt. 13, 291 (1974).
  8. W. B. Bridges, S. Hansen, L. A. Horwitz, S. P. Lazzara, T. R. O'Meara, J. E. Pearson, and T. J. Walsh, J. Opt. Soc. Am. 64, 541 (1975).
  9. J. E. Pearson, W. B. Bridges, L. S. Horwitz, T. J. Walsh, and R. F. Ogrodnik, Paper ThB5, Proceedings of the OSA Topical Meeting on Optical Propagation through Turbulence, Boulder, Colo., July 1974.
  10. W. B. Bridges and J. E. Pearson, Appl. Phys. Lett. 26, 539 (1975).
  11. J. E. Pearson, W. B. Bridges, S. Hansen, T. A. Nussmeier, and M. E. Pedinoff, Appl. Opt. 15, 611 (1976).
  12. T. R. O'Meara, "Applications of Laser Radars as Assistors to High-Power Optical Systems (U)," Proceedings of the Sixth DoD Conference on Laser Technology, U. S. Air Force Academy, March 26, 1974, Vol. 1, p. 233.
  13. H. W. Babcock, J. Opt. Soc. Am. 48, 500 (1958).
  14. R. A. Muller and A. Buffington, J. Opt. Soc. Am. 64, 1200 (1974).
  15. J. Hardy, J. Feinleib, and J. C. Wyant, Paper ThB1, Proceedings of the OSA Topical Meeting on Optical Propagation through Turbulence, Boulder, Colo., July 1974.
  16. L. Miller, W. P. Brown, Jr., J. A. Jenney, and T. R. O'Meara, Paper ThB2, Proceedings of the OSA Topical Meeting on Optical Propagation through Turbulence, Boulder, Colo., July 1974.
  17. J. C. Wyant, Appl. Opt. 13, 200 (1974).
  18. J. F. Ebersole and J. C. Wyant, Appl. Opt. 13, 1004 (1974).
  19. Contracts F30602-73-C-0248 and F30602-75-C-0001, monitored through Rome Air Development Center. See RADC reports RADC-TR-73-384, July 1973; RADC-TR-74-38, Oct. 1973; RADC-TR-74-108, Jan. 1974; RADC-TR-74-187, Apr. 1974; RADC-TR-75-46, Jan. 1975; RADC-TR-75-47, Feb. 1975; RADC-TR-75-101, May 1975. All available from Defense Documentation Center.
  20. M. J. Lavan, W. K. Cadwallender, and T. F. DeYoung, "A Visible Wavelength COAT Array," Opt. Eng. 15, 56 (1976).
  21. Insofar as can be determined by us, the first use of the acronym was in the context "coherent optical array techniques," and the original motivation was for the cophasing of multiple low-power laser oscillators. There has been a tendency in recent years to employ a one-to-one correspondence between specific proprietary adaptive optical systems and acronyms. However, we have always employed the term COAT in the larger or generic sense.
  22. For long-range operation, the phase of the detected signal will be delayed by the round-trip propagation time, and the reference signal must be similarly delayed.
  23. All correctly operating systems ideally introduce the phase conjugate of path distortions. We reserve the term (after microwave terminology) to refer to return-wave systems with heterodyne extraction of phase error information.
  24. T. R. O'Meara, "Stability of an N-loop ensemble-reference phase control system," J. Opt. Soc. Am. 67, 315–318 (1977) (following paper).
  25. The piston elements may be one-dimensional or two-dimensional, commonly square, circular, or hexagonal.
  26. Any tilt component of øen which is common to all elements is assumed to be absorbed in a translation of x′.

1977 (1)

Babcock, H. W.

H. W. Babcock, J. Opt. Soc. Am. 48, 500 (1958).

Bridges, W. B.

J. E. Pearson, W. B. Bridges, S. Hansen, T. A. Nussmeier, and M. E. Pedinoff, Appl. Opt. 15, 611 (1976).

T. R. O'Meara, W. P. Brown, W. B. Bridges, T. A. Nussmeier, A. D. Jacobson, J. F. Lotspeich, G. M. Janney, and J. Y. Wada, "Coherent Optical Adaptive Techniques," Hughes Research Laboratories Tech. Rep. RADC-TR (Dec. 1970) (unpublished).

W. B. Bridges, P. T. Brunner, S. P. Lazzara, T. A. Nussmeier, T. R. O'Meara, J. A. Sanguinet, and W. P. Brown, Jr., Appl. Opt. 13, 291 (1974).

W. B. Bridges, S. Hansen, L. A. Horwitz, S. P. Lazzara, T. R. O'Meara, J. E. Pearson, and T. J. Walsh, J. Opt. Soc. Am. 64, 541 (1975).

J. E. Pearson, W. B. Bridges, L. S. Horwitz, T. J. Walsh, and R. F. Ogrodnik, Paper ThB5, Proceedings of the OSA Topical Meeting on Optical Propagation through Turbulence, Boulder, Colo., July 1974.

W. B. Bridges and J. E. Pearson, Appl. Phys. Lett. 26, 539 (1975).

Brown, W. P.

T. R. O'Meara, W. P. Brown, W. B. Bridges, T. A. Nussmeier, A. D. Jacobson, J. F. Lotspeich, G. M. Janney, and J. Y. Wada, "Coherent Optical Adaptive Techniques," Hughes Research Laboratories Tech. Rep. RADC-TR (Dec. 1970) (unpublished).

Brown, Jr., W. P.

W. B. Bridges, P. T. Brunner, S. P. Lazzara, T. A. Nussmeier, T. R. O'Meara, J. A. Sanguinet, and W. P. Brown, Jr., Appl. Opt. 13, 291 (1974).

L. Miller, W. P. Brown, Jr., J. A. Jenney, and T. R. O'Meara, Paper ThB2, Proceedings of the OSA Topical Meeting on Optical Propagation through Turbulence, Boulder, Colo., July 1974.

Brunner, P. T.

W. B. Bridges, P. T. Brunner, S. P. Lazzara, T. A. Nussmeier, T. R. O'Meara, J. A. Sanguinet, and W. P. Brown, Jr., Appl. Opt. 13, 291 (1974).

Buffington, A.

R. A. Muller and A. Buffington, J. Opt. Soc. Am. 64, 1200 (1974).

Cadwallender, W. K.

M. J. Lavan, W. K. Cadwallender, and T. F. DeYoung, "A Visible Wavelength COAT Array," Opt. Eng. 15, 56 (1976).

Cathey, W. T.

W. T. Cathey, C. L. Hayes and W. C. Davis, Appl. Opt. 9, 701 (1970).

Davis, W. C.

W. T. Cathey, C. L. Hayes and W. C. Davis, Appl. Opt. 9, 701 (1970).

DeYoung, T. F.

M. J. Lavan, W. K. Cadwallender, and T. F. DeYoung, "A Visible Wavelength COAT Array," Opt. Eng. 15, 56 (1976).

Ebersole, J. F.

J. F. Ebersole and J. C. Wyant, Appl. Opt. 13, 1004 (1974).

Feinleib, J.

J. Hardy, J. Feinleib, and J. C. Wyant, Paper ThB1, Proceedings of the OSA Topical Meeting on Optical Propagation through Turbulence, Boulder, Colo., July 1974.

Futrelle, R. P.

R. P. Futrelle, G. E. Meyers, and C. L. Hayes, "Coherent Optical Adaptive Techniques," Contract F30602-70-C-0298 (April 1971) (unpublished).

Hansen, S.

W. B. Bridges, S. Hansen, L. A. Horwitz, S. P. Lazzara, T. R. O'Meara, J. E. Pearson, and T. J. Walsh, J. Opt. Soc. Am. 64, 541 (1975).

J. E. Pearson, W. B. Bridges, S. Hansen, T. A. Nussmeier, and M. E. Pedinoff, Appl. Opt. 15, 611 (1976).

Hardy, J.

J. Hardy, J. Feinleib, and J. C. Wyant, Paper ThB1, Proceedings of the OSA Topical Meeting on Optical Propagation through Turbulence, Boulder, Colo., July 1974.

Hayes, C. L.

R. P. Futrelle, G. E. Meyers, and C. L. Hayes, "Coherent Optical Adaptive Techniques," Contract F30602-70-C-0298 (April 1971) (unpublished).

W. T. Cathey, C. L. Hayes and W. C. Davis, Appl. Opt. 9, 701 (1970).

Horwitz, L. A.

W. B. Bridges, S. Hansen, L. A. Horwitz, S. P. Lazzara, T. R. O'Meara, J. E. Pearson, and T. J. Walsh, J. Opt. Soc. Am. 64, 541 (1975).

Horwitz, L. S.

J. E. Pearson, W. B. Bridges, L. S. Horwitz, T. J. Walsh, and R. F. Ogrodnik, Paper ThB5, Proceedings of the OSA Topical Meeting on Optical Propagation through Turbulence, Boulder, Colo., July 1974.

Jacobson, A. D.

T. R. O'Meara, W. P. Brown, W. B. Bridges, T. A. Nussmeier, A. D. Jacobson, J. F. Lotspeich, G. M. Janney, and J. Y. Wada, "Coherent Optical Adaptive Techniques," Hughes Research Laboratories Tech. Rep. RADC-TR (Dec. 1970) (unpublished).

Janney, G. M.

T. R. O'Meara, W. P. Brown, W. B. Bridges, T. A. Nussmeier, A. D. Jacobson, J. F. Lotspeich, G. M. Janney, and J. Y. Wada, "Coherent Optical Adaptive Techniques," Hughes Research Laboratories Tech. Rep. RADC-TR (Dec. 1970) (unpublished).

Jenney, J. A.

L. Miller, W. P. Brown, Jr., J. A. Jenney, and T. R. O'Meara, Paper ThB2, Proceedings of the OSA Topical Meeting on Optical Propagation through Turbulence, Boulder, Colo., July 1974.

Lavan, M. J.

M. J. Lavan, W. K. Cadwallender, and T. F. DeYoung, "A Visible Wavelength COAT Array," Opt. Eng. 15, 56 (1976).

Lazzara, S. P.

W. B. Bridges, S. Hansen, L. A. Horwitz, S. P. Lazzara, T. R. O'Meara, J. E. Pearson, and T. J. Walsh, J. Opt. Soc. Am. 64, 541 (1975).

W. B. Bridges, P. T. Brunner, S. P. Lazzara, T. A. Nussmeier, T. R. O'Meara, J. A. Sanguinet, and W. P. Brown, Jr., Appl. Opt. 13, 291 (1974).

Lotspeich, J. F.

T. R. O'Meara, W. P. Brown, W. B. Bridges, T. A. Nussmeier, A. D. Jacobson, J. F. Lotspeich, G. M. Janney, and J. Y. Wada, "Coherent Optical Adaptive Techniques," Hughes Research Laboratories Tech. Rep. RADC-TR (Dec. 1970) (unpublished).

Meyers, G. E.

R. P. Futrelle, G. E. Meyers, and C. L. Hayes, "Coherent Optical Adaptive Techniques," Contract F30602-70-C-0298 (April 1971) (unpublished).

Miller, L.

L. Miller, W. P. Brown, Jr., J. A. Jenney, and T. R. O'Meara, Paper ThB2, Proceedings of the OSA Topical Meeting on Optical Propagation through Turbulence, Boulder, Colo., July 1974.

Muller, R. A.

R. A. Muller and A. Buffington, J. Opt. Soc. Am. 64, 1200 (1974).

Nussmeier, T. A.

J. E. Pearson, W. B. Bridges, S. Hansen, T. A. Nussmeier, and M. E. Pedinoff, Appl. Opt. 15, 611 (1976).

T. R. O'Meara, W. P. Brown, W. B. Bridges, T. A. Nussmeier, A. D. Jacobson, J. F. Lotspeich, G. M. Janney, and J. Y. Wada, "Coherent Optical Adaptive Techniques," Hughes Research Laboratories Tech. Rep. RADC-TR (Dec. 1970) (unpublished).

W. B. Bridges, P. T. Brunner, S. P. Lazzara, T. A. Nussmeier, T. R. O'Meara, J. A. Sanguinet, and W. P. Brown, Jr., Appl. Opt. 13, 291 (1974).

Ogrodnik, R. F.

J. E. Pearson, W. B. Bridges, L. S. Horwitz, T. J. Walsh, and R. F. Ogrodnik, Paper ThB5, Proceedings of the OSA Topical Meeting on Optical Propagation through Turbulence, Boulder, Colo., July 1974.

O'Meara, T. R.

T. R. O'Meara, "Stability of an N-loop ensemble-reference phase control system," J. Opt. Soc. Am. 67, 315–318 (1977) (following paper).

T. R. O'Meara, "Applications of Laser Radars as Assistors to High-Power Optical Systems (U)," Proceedings of the Sixth DoD Conference on Laser Technology, U. S. Air Force Academy, March 26, 1974, Vol. 1, p. 233.

L. Miller, W. P. Brown, Jr., J. A. Jenney, and T. R. O'Meara, Paper ThB2, Proceedings of the OSA Topical Meeting on Optical Propagation through Turbulence, Boulder, Colo., July 1974.

W. B. Bridges, P. T. Brunner, S. P. Lazzara, T. A. Nussmeier, T. R. O'Meara, J. A. Sanguinet, and W. P. Brown, Jr., Appl. Opt. 13, 291 (1974).

W. B. Bridges, S. Hansen, L. A. Horwitz, S. P. Lazzara, T. R. O'Meara, J. E. Pearson, and T. J. Walsh, J. Opt. Soc. Am. 64, 541 (1975).

T. R. O'Meara, W. P. Brown, W. B. Bridges, T. A. Nussmeier, A. D. Jacobson, J. F. Lotspeich, G. M. Janney, and J. Y. Wada, "Coherent Optical Adaptive Techniques," Hughes Research Laboratories Tech. Rep. RADC-TR (Dec. 1970) (unpublished).

T. R. O'Meara, U.S. Patent 3,727,223, "Adaptive Power Redistribution Systems" (April 10, 1973) (U. S. Patent Office, Washington, D. C.).

T. R. O'Meara, U.S. Patent 3,731,103, "Adaptive Arrays" (May 1, 1973) (unpublished).

T. R. O'Meara, U.S. Patent 3,764,213, "Return-Wave, Phase Controlled Adaptive Array" (October 9, 1973) (U. S. Patent Office, Washington, D. C.).

Pearson, J. E.

W. B. Bridges, S. Hansen, L. A. Horwitz, S. P. Lazzara, T. R. O'Meara, J. E. Pearson, and T. J. Walsh, J. Opt. Soc. Am. 64, 541 (1975).

J. E. Pearson, W. B. Bridges, L. S. Horwitz, T. J. Walsh, and R. F. Ogrodnik, Paper ThB5, Proceedings of the OSA Topical Meeting on Optical Propagation through Turbulence, Boulder, Colo., July 1974.

W. B. Bridges and J. E. Pearson, Appl. Phys. Lett. 26, 539 (1975).

J. E. Pearson, W. B. Bridges, S. Hansen, T. A. Nussmeier, and M. E. Pedinoff, Appl. Opt. 15, 611 (1976).

Pedinoff, M. E.

J. E. Pearson, W. B. Bridges, S. Hansen, T. A. Nussmeier, and M. E. Pedinoff, Appl. Opt. 15, 611 (1976).

Sanguinet, J. A.

W. B. Bridges, P. T. Brunner, S. P. Lazzara, T. A. Nussmeier, T. R. O'Meara, J. A. Sanguinet, and W. P. Brown, Jr., Appl. Opt. 13, 291 (1974).

Wada, J. Y.

T. R. O'Meara, W. P. Brown, W. B. Bridges, T. A. Nussmeier, A. D. Jacobson, J. F. Lotspeich, G. M. Janney, and J. Y. Wada, "Coherent Optical Adaptive Techniques," Hughes Research Laboratories Tech. Rep. RADC-TR (Dec. 1970) (unpublished).

Walsh, T. J.

W. B. Bridges, S. Hansen, L. A. Horwitz, S. P. Lazzara, T. R. O'Meara, J. E. Pearson, and T. J. Walsh, J. Opt. Soc. Am. 64, 541 (1975).

J. E. Pearson, W. B. Bridges, L. S. Horwitz, T. J. Walsh, and R. F. Ogrodnik, Paper ThB5, Proceedings of the OSA Topical Meeting on Optical Propagation through Turbulence, Boulder, Colo., July 1974.

Wyant, J. C.

J. C. Wyant, Appl. Opt. 13, 200 (1974).

J. Hardy, J. Feinleib, and J. C. Wyant, Paper ThB1, Proceedings of the OSA Topical Meeting on Optical Propagation through Turbulence, Boulder, Colo., July 1974.

J. F. Ebersole and J. C. Wyant, Appl. Opt. 13, 1004 (1974).

J. Opt. Soc. Am. (1)

Other (25)

The piston elements may be one-dimensional or two-dimensional, commonly square, circular, or hexagonal.

Any tilt component of øen which is common to all elements is assumed to be absorbed in a translation of x′.

W. T. Cathey, C. L. Hayes and W. C. Davis, Appl. Opt. 9, 701 (1970).

T. R. O'Meara, W. P. Brown, W. B. Bridges, T. A. Nussmeier, A. D. Jacobson, J. F. Lotspeich, G. M. Janney, and J. Y. Wada, "Coherent Optical Adaptive Techniques," Hughes Research Laboratories Tech. Rep. RADC-TR (Dec. 1970) (unpublished).

R. P. Futrelle, G. E. Meyers, and C. L. Hayes, "Coherent Optical Adaptive Techniques," Contract F30602-70-C-0298 (April 1971) (unpublished).

T. R. O'Meara, U.S. Patent 3,727,223, "Adaptive Power Redistribution Systems" (April 10, 1973) (U. S. Patent Office, Washington, D. C.).

T. R. O'Meara, U.S. Patent 3,731,103, "Adaptive Arrays" (May 1, 1973) (unpublished).

T. R. O'Meara, U.S. Patent 3,764,213, "Return-Wave, Phase Controlled Adaptive Array" (October 9, 1973) (U. S. Patent Office, Washington, D. C.).

W. B. Bridges, P. T. Brunner, S. P. Lazzara, T. A. Nussmeier, T. R. O'Meara, J. A. Sanguinet, and W. P. Brown, Jr., Appl. Opt. 13, 291 (1974).

W. B. Bridges, S. Hansen, L. A. Horwitz, S. P. Lazzara, T. R. O'Meara, J. E. Pearson, and T. J. Walsh, J. Opt. Soc. Am. 64, 541 (1975).

J. E. Pearson, W. B. Bridges, L. S. Horwitz, T. J. Walsh, and R. F. Ogrodnik, Paper ThB5, Proceedings of the OSA Topical Meeting on Optical Propagation through Turbulence, Boulder, Colo., July 1974.

W. B. Bridges and J. E. Pearson, Appl. Phys. Lett. 26, 539 (1975).

J. E. Pearson, W. B. Bridges, S. Hansen, T. A. Nussmeier, and M. E. Pedinoff, Appl. Opt. 15, 611 (1976).

T. R. O'Meara, "Applications of Laser Radars as Assistors to High-Power Optical Systems (U)," Proceedings of the Sixth DoD Conference on Laser Technology, U. S. Air Force Academy, March 26, 1974, Vol. 1, p. 233.

H. W. Babcock, J. Opt. Soc. Am. 48, 500 (1958).

R. A. Muller and A. Buffington, J. Opt. Soc. Am. 64, 1200 (1974).

J. Hardy, J. Feinleib, and J. C. Wyant, Paper ThB1, Proceedings of the OSA Topical Meeting on Optical Propagation through Turbulence, Boulder, Colo., July 1974.

L. Miller, W. P. Brown, Jr., J. A. Jenney, and T. R. O'Meara, Paper ThB2, Proceedings of the OSA Topical Meeting on Optical Propagation through Turbulence, Boulder, Colo., July 1974.

J. C. Wyant, Appl. Opt. 13, 200 (1974).

J. F. Ebersole and J. C. Wyant, Appl. Opt. 13, 1004 (1974).

Contracts F30602-73-C-0248 and F30602-75-C-0001, monitored through Rome Air Development Center. See RADC reports RADC-TR-73-384, July 1973; RADC-TR-74-38, Oct. 1973; RADC-TR-74-108, Jan. 1974; RADC-TR-74-187, Apr. 1974; RADC-TR-75-46, Jan. 1975; RADC-TR-75-47, Feb. 1975; RADC-TR-75-101, May 1975. All available from Defense Documentation Center.

M. J. Lavan, W. K. Cadwallender, and T. F. DeYoung, "A Visible Wavelength COAT Array," Opt. Eng. 15, 56 (1976).

Insofar as can be determined by us, the first use of the acronym was in the context "coherent optical array techniques," and the original motivation was for the cophasing of multiple low-power laser oscillators. There has been a tendency in recent years to employ a one-to-one correspondence between specific proprietary adaptive optical systems and acronyms. However, we have always employed the term COAT in the larger or generic sense.

For long-range operation, the phase of the detected signal will be delayed by the round-trip propagation time, and the reference signal must be similarly delayed.

All correctly operating systems ideally introduce the phase conjugate of path distortions. We reserve the term (after microwave terminology) to refer to return-wave systems with heterodyne extraction of phase error information.

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