Abstract

Wave-front sensing and deformable mirror control algorithms in adaptive optics systems are designed on the premise that a continuous phase function exists in the telescope pupil that can be conjugated with a deformable mirror for the purpose of projecting a laser beam. However, recent studies of coherent wave propagation through turbulence have shown that under conditions where scintillation is not negligible, a truly continuous phase function does not in general exist as a result of the presence of branch points in the complex optical field. Because of branch points and the associated branch cuts, least-squares wave-front reconstruction paradigms can have large errors. We study the improvement that can be obtained by implementing wave-front reconstructors that can sense the presence of branch points and reconstruct a discontinuous phase function in the context of a laser beam projection system. This study was conducted by fitting a finite-degree-of-freedom deformable mirror to branch-point and least-squares reconstructions of the phase of the beacon field, propagating the corrected field to the beacon plane, and evaluating performance in the beacon plane. We find that the value of implementing branch-point reconstructors with a finite-degree-of-freedom deformable mirror is significant for optical paths that cause saturated log-amplitude fluctuations.

© 2000 Optical Society of America

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1998

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1977

1976

1969

R. W. Lee, J. C. Harp, “Weak scattering in random media, with applications to remote probing,” Proc. IEEE 57, 375–406 (1969).
[CrossRef]

1966

Beland, R. R.

R. R. Beland, “Propagation through atmospheric optical turbulence,” in IR/EO Handbook, F. G. Smith, ed. (SPIE Press, Bellingham, Wash., 1993), Vol. 2, pp. 157–232.

Boeke, B. R.

Carlson, L.

T. Goldring, L. Carlson, “Analysis and implementation of non-Kolmogorov phase screens appropriate to structured environments,” in Nonlinear Optical Beam Manipulation and High Energy Beam Propagation through the Atmosphere, R. A. Fisher, L. E. Wilson, eds., Proc. SPIE1060, 244–264 (1989).

Cleis, R. A.

Ellerbroek, B. L.

Flatte, S. M.

Fried, D. L.

Fugate, R. Q.

Gaskill, J. D.

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).

Ghiglia, D. C.

D. C. Ghiglia, M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley Interscience, New York, 1998).

Goldring, T.

T. Goldring, L. Carlson, “Analysis and implementation of non-Kolmogorov phase screens appropriate to structured environments,” in Nonlinear Optical Beam Manipulation and High Energy Beam Propagation through the Atmosphere, R. A. Fisher, L. E. Wilson, eds., Proc. SPIE1060, 244–264 (1989).

Gonzalez, R. C.

R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Wesley, Reading, Mass., 1993).

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Harp, J. C.

R. W. Lee, J. C. Harp, “Weak scattering in random media, with applications to remote probing,” Proc. IEEE 57, 375–406 (1969).
[CrossRef]

Higgins, C. H.

Jelonek, M. P.

Knox, K. T.

Lange, W. J.

Lee, D. J.

Lee, R. W.

R. W. Lee, J. C. Harp, “Weak scattering in random media, with applications to remote probing,” Proc. IEEE 57, 375–406 (1969).
[CrossRef]

Lukin, V. P.

V. P. Lukin, Atmospheric Adaptive Optics (SPIE Press, Bellingham, Wash., 1995).

Martin, J. M.

McGlamery, B. L.

Moroney, J. F.

Oliker, M. D.

Pritt, M. D.

D. C. Ghiglia, M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley Interscience, New York, 1998).

Roggemann, M. C.

Ruane, R. E.

Sindle, D. W.

Slavin, A. C.

Spinhirne, J. M.

Tatarskii, V. I.

V. I. Tatarskii, The Effects of the Turbulence Atmosphere on Wave Propagation, (National Technical Information Service, Springfield, Va., 1971).

Vaughn, J. L.

Wang, G. Y.

Welsh, B. M.

M. C. Roggemann, B. M. Welsh, Imaging through Turbulence (CRC Press, Boca Raton, Fla., 1996).

Wild, W. J.

Winker, D. M.

Woods, R. E.

R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Wesley, Reading, Mass., 1993).

Wynia, J. M.

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Proc. IEEE

R. W. Lee, J. C. Harp, “Weak scattering in random media, with applications to remote probing,” Proc. IEEE 57, 375–406 (1969).
[CrossRef]

Other

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

M. C. Roggemann, B. M. Welsh, Imaging through Turbulence (CRC Press, Boca Raton, Fla., 1996).

V. P. Lukin, Atmospheric Adaptive Optics (SPIE Press, Bellingham, Wash., 1995).

D. C. Ghiglia, M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley Interscience, New York, 1998).

V. I. Tatarskii, The Effects of the Turbulence Atmosphere on Wave Propagation, (National Technical Information Service, Springfield, Va., 1971).

R. R. Beland, “Propagation through atmospheric optical turbulence,” in IR/EO Handbook, F. G. Smith, ed. (SPIE Press, Bellingham, Wash., 1993), Vol. 2, pp. 157–232.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Wesley, Reading, Mass., 1993).

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).

T. Goldring, L. Carlson, “Analysis and implementation of non-Kolmogorov phase screens appropriate to structured environments,” in Nonlinear Optical Beam Manipulation and High Energy Beam Propagation through the Atmosphere, R. A. Fisher, L. E. Wilson, eds., Proc. SPIE1060, 244–264 (1989).

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