Abstract

A critical component of an active optical-compensation system is the formable mirror or other phase corrector. Because the corrector will have a finite number of controllable elements, it cannot perfectly correct a distorted wave front and the resulting error must be evaluated to model and design the system properly. This paper presents the full theory of the phase corrector in two common situations: one, where a particular known type of distortion such as focus or coma is to be corrected, and two, where the distortion is a random function of position, such as might arise from atmospheric turbulence. Results for a typical corrector are presented for both situations.

© 1977 Optical Society of America

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  1. R. A. Muller and A. Buffington, "Real-time correction of atmospherically degraded telescope images through image sharpening," J. Opt. Soc. Am. 64, 1200–1210 (1974).
  2. W. D. 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," J. Appl. Opt. 13, 291–300 (1974).
  3. J. W. Hard, J. Feinleib, and J. C. Wyant, in "Real-Time Phase Correction of Optical Imaging Systems," Digest of Technical Papers, Topical Meeting on Optical Propagation through Turbulence, sponsored by the OSA, ThB1-1 through ThB1-4.
  4. L. Miller, W. P. Brown, Jr., J. A. Jenney, and T. H. O'Meara, "Imaging Through Turbulence with Coherent Optical Adaptive Techniques," Ref. 3, ThB2-1 through ThB2-4.
  5. R. F. Ogrodnik, "Adaptive Aperture Wavefront Turbulence Compensation Techniques," Ref. 3, ThB4-4.
  6. J. E. Pearson, W. B. Bridges, L. S. Horwitz, T. J. Walsh, and R. F. Ogrodnik, "Atmospheric Turbulence Compensation Using Coherent Optical Adaptive Techniques," Ref. 3, ThB5-1 through ThB-3.
  7. R. M. Scott, "New Technique for Controlling Optical Mirror Shapes," Opt. Eng. 14, 112–115 (1975).
  8. R. Hudgin and S. Lipson, "Analysis of a Monolithic Piezoelectric Mirror," J. Appl. Phys. 46, 510–512 (1975).
  9. J. Feinleib, S. Lipson, and P. Cone, "Monolithic Piezoelectric Mirror for Wavefront Correction," Appl. Phys. Lett. 25, 311–313 (1974).

1975

R. Hudgin and S. Lipson, "Analysis of a Monolithic Piezoelectric Mirror," J. Appl. Phys. 46, 510–512 (1975).

1974

J. Feinleib, S. Lipson, and P. Cone, "Monolithic Piezoelectric Mirror for Wavefront Correction," Appl. Phys. Lett. 25, 311–313 (1974).

R. A. Muller and A. Buffington, "Real-time correction of atmospherically degraded telescope images through image sharpening," J. Opt. Soc. Am. 64, 1200–1210 (1974).

W. D. 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," J. Appl. Opt. 13, 291–300 (1974).

Bridges, W. B.

J. E. Pearson, W. B. Bridges, L. S. Horwitz, T. J. Walsh, and R. F. Ogrodnik, "Atmospheric Turbulence Compensation Using Coherent Optical Adaptive Techniques," Ref. 3, ThB5-1 through ThB-3.

Bridges, W. D.

W. D. 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," J. Appl. Opt. 13, 291–300 (1974).

Brown, W. P.

W. D. 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," J. Appl. Opt. 13, 291–300 (1974).

Brown, Jr., W. P.

L. Miller, W. P. Brown, Jr., J. A. Jenney, and T. H. O'Meara, "Imaging Through Turbulence with Coherent Optical Adaptive Techniques," Ref. 3, ThB2-1 through ThB2-4.

Brunner, P. T.

W. D. 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," J. Appl. Opt. 13, 291–300 (1974).

Buffington, A.

Cone, P.

J. Feinleib, S. Lipson, and P. Cone, "Monolithic Piezoelectric Mirror for Wavefront Correction," Appl. Phys. Lett. 25, 311–313 (1974).

Feinleib, J.

J. Feinleib, S. Lipson, and P. Cone, "Monolithic Piezoelectric Mirror for Wavefront Correction," Appl. Phys. Lett. 25, 311–313 (1974).

J. W. Hard, J. Feinleib, and J. C. Wyant, in "Real-Time Phase Correction of Optical Imaging Systems," Digest of Technical Papers, Topical Meeting on Optical Propagation through Turbulence, sponsored by the OSA, ThB1-1 through ThB1-4.

Hard, J. W.

J. W. Hard, J. Feinleib, and J. C. Wyant, in "Real-Time Phase Correction of Optical Imaging Systems," Digest of Technical Papers, Topical Meeting on Optical Propagation through Turbulence, sponsored by the OSA, ThB1-1 through ThB1-4.

Horwitz, L. S.

J. E. Pearson, W. B. Bridges, L. S. Horwitz, T. J. Walsh, and R. F. Ogrodnik, "Atmospheric Turbulence Compensation Using Coherent Optical Adaptive Techniques," Ref. 3, ThB5-1 through ThB-3.

Hudgin, R.

R. Hudgin and S. Lipson, "Analysis of a Monolithic Piezoelectric Mirror," J. Appl. Phys. 46, 510–512 (1975).

Jenney, J. A.

L. Miller, W. P. Brown, Jr., J. A. Jenney, and T. H. O'Meara, "Imaging Through Turbulence with Coherent Optical Adaptive Techniques," Ref. 3, ThB2-1 through ThB2-4.

Lazzara, S. P.

W. D. 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," J. Appl. Opt. 13, 291–300 (1974).

Lipson, S.

R. Hudgin and S. Lipson, "Analysis of a Monolithic Piezoelectric Mirror," J. Appl. Phys. 46, 510–512 (1975).

J. Feinleib, S. Lipson, and P. Cone, "Monolithic Piezoelectric Mirror for Wavefront Correction," Appl. Phys. Lett. 25, 311–313 (1974).

Miller, L.

L. Miller, W. P. Brown, Jr., J. A. Jenney, and T. H. O'Meara, "Imaging Through Turbulence with Coherent Optical Adaptive Techniques," Ref. 3, ThB2-1 through ThB2-4.

Muller, R. A.

Nussmeier, T. A.

W. D. 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," J. Appl. Opt. 13, 291–300 (1974).

Ogrodnik, R. F.

J. E. Pearson, W. B. Bridges, L. S. Horwitz, T. J. Walsh, and R. F. Ogrodnik, "Atmospheric Turbulence Compensation Using Coherent Optical Adaptive Techniques," Ref. 3, ThB5-1 through ThB-3.

R. F. Ogrodnik, "Adaptive Aperture Wavefront Turbulence Compensation Techniques," Ref. 3, ThB4-4.

O'Meara, T. H.

L. Miller, W. P. Brown, Jr., J. A. Jenney, and T. H. O'Meara, "Imaging Through Turbulence with Coherent Optical Adaptive Techniques," Ref. 3, ThB2-1 through ThB2-4.

O'Meara, T. R.

W. D. 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," J. Appl. Opt. 13, 291–300 (1974).

Pearson, J. E.

J. E. Pearson, W. B. Bridges, L. S. Horwitz, T. J. Walsh, and R. F. Ogrodnik, "Atmospheric Turbulence Compensation Using Coherent Optical Adaptive Techniques," Ref. 3, ThB5-1 through ThB-3.

Sanguinet, J. A.

W. D. 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," J. Appl. Opt. 13, 291–300 (1974).

Scott, R. M.

R. M. Scott, "New Technique for Controlling Optical Mirror Shapes," Opt. Eng. 14, 112–115 (1975).

Walsh, T. J.

J. E. Pearson, W. B. Bridges, L. S. Horwitz, T. J. Walsh, and R. F. Ogrodnik, "Atmospheric Turbulence Compensation Using Coherent Optical Adaptive Techniques," Ref. 3, ThB5-1 through ThB-3.

Wyant, J. C.

J. W. Hard, J. Feinleib, and J. C. Wyant, in "Real-Time Phase Correction of Optical Imaging Systems," Digest of Technical Papers, Topical Meeting on Optical Propagation through Turbulence, sponsored by the OSA, ThB1-1 through ThB1-4.

Appl. Phys. Lett.

J. Feinleib, S. Lipson, and P. Cone, "Monolithic Piezoelectric Mirror for Wavefront Correction," Appl. Phys. Lett. 25, 311–313 (1974).

J. Appl. Opt.

W. D. 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," J. Appl. Opt. 13, 291–300 (1974).

J. Appl. Phys.

R. Hudgin and S. Lipson, "Analysis of a Monolithic Piezoelectric Mirror," J. Appl. Phys. 46, 510–512 (1975).

J. Opt. Soc. Am.

Other

J. W. Hard, J. Feinleib, and J. C. Wyant, in "Real-Time Phase Correction of Optical Imaging Systems," Digest of Technical Papers, Topical Meeting on Optical Propagation through Turbulence, sponsored by the OSA, ThB1-1 through ThB1-4.

L. Miller, W. P. Brown, Jr., J. A. Jenney, and T. H. O'Meara, "Imaging Through Turbulence with Coherent Optical Adaptive Techniques," Ref. 3, ThB2-1 through ThB2-4.

R. F. Ogrodnik, "Adaptive Aperture Wavefront Turbulence Compensation Techniques," Ref. 3, ThB4-4.

J. E. Pearson, W. B. Bridges, L. S. Horwitz, T. J. Walsh, and R. F. Ogrodnik, "Atmospheric Turbulence Compensation Using Coherent Optical Adaptive Techniques," Ref. 3, ThB5-1 through ThB-3.

R. M. Scott, "New Technique for Controlling Optical Mirror Shapes," Opt. Eng. 14, 112–115 (1975).

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