Abstract

The theory of short-term average modulation transfer function developed by Fried is extended by considering the correlation between the turbulence-induced phase distortion and the residual phase aberrations after adaptive phase compensations. Calculation of the optical resolution shows that the original approximation is valid for the normalized lens diameter <i>D</i>/<i>r</i><sub>0</sub> less than 4.0; conversely, for <i>D</i>/<i>r</i><sub>0</sub> greater than 4.0 the optical resolution becomes arbitrarily large because the MTF is unrealistically overcorrected at high spatial frequencies. The extended formulation is then applied to the cases with higher-order phase compensations such as focus and astigmatism. The peak optical resolution occurs at larger values of <i>D</i>/<i>r</i><sub>0</sub> when the higher-order corrections are included.

© 1977 Optical Society of America

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  1. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).
  2. A. D. Varvatsis and M. I. Sancer, Can. J. Phys. 49, 1233 (1971).
  3. W. P. Brown, Jr., J. Opt. Soc. Am. 61, 1051 (1971).
  4. H. T. Yura, Appl. Opt. 10, 2771 (1971).
  5. D. A. deWolf, "Effects of Turbulence Instabilities on Laser Propagation," RADC-TR-72-119 (April 1972) (unpublished).
  6. D. L. Fried, J. Opt. Soc. Am. 56, 1372 (1966).
  7. D. L. Fried, Proc. IEEE 55, 57 (1967).
  8. R. F. Lutomirski and H. T. Yura, Appl. Opt. 10, 1652 (1971).
  9. G. R. Heidbreder, IEEE Trans. Antennas Propag. AP-15, 90 (1967).
  10. H. T. Yura, J. Opt. Soc. Am. 63, 567 (1973).
  11. T. Chiba, Appl. Opt. 10, 2456 (1971).
  12. J. A. Dowling and P. M. Livingston, J. Opt. Soc. Am. 63, 846 (1973).
  13. J. R. Dunphy and J. R. Kerr, J. Opt. Soc. Am. 64, 1015 (1974).
  14. W. T. Cathey, C. L. Hayes, W. C. Davis, and V. F. Pizzurro, Appl. Opt. 9, 701 (1970).
  15. J. E. Pearson, W. B. Bridges, S. Hansen, T. A. Nussmeier, and M. E. Pedinoff, Appl. Opt. 15, 611 (1976).
  16. A. Buffington, F. S. Crawford, R. A. Muller, A. J. Schwemiu, and R. G. Smith, "Active Image Restoration with a Flexible Mirror," in Proceedings of the SPIE, Imaging through the Atmosphere, Vol. 75, March 1976, p. 90.
  17. R. V. Wick and R. W. Goranson, "Infrared Position Sensing Detector: A Photopot for CO2 Lasers," in Laser Digest, AFWL-TR-75-229 (October 1975) (unpublished).
  18. J. C. Wyant, Appl. Opt. 14, 2622 (1975).
  19. J. Feinleib and J. W. Hardy, "Wideband Adaptive Optics for Imaging," in Proceedings of the SPIE, Imaging through the Atmosphere, Vol. 75, March 1976, p. 103.
  20. D. L. Fried, J. Opt. Soc. Am. 55, 1427 (1965).
  21. J. Herrmann, "Properties of Phase-Conjugate COAT," in Proceedings of the Optical Society of America Annual Meeting, Boston, October 1975, see J. Opt. Soc. Am. 65, 1212A (1975).
  22. D. R. Dean and L. T. James, "Adaptive Laser Optics Techniques (ALOT)," in Proceedings of the High Energy Laser Conference, San Diego, Calif., October 1975 (unpublished).
  23. M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 465.
  24. C. B. Hogge and R. R. Butts, IEEE Trans. Antennas Propag. AP-24, 144 (1976).
  25. R. J. Noll, J. Opt. Soc. Am. 66, 207 (1976).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 465.

Bridges, W. B.

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

Brown, Jr., W. P.

W. P. Brown, Jr., J. Opt. Soc. Am. 61, 1051 (1971).

Buffington, A.

A. Buffington, F. S. Crawford, R. A. Muller, A. J. Schwemiu, and R. G. Smith, "Active Image Restoration with a Flexible Mirror," in Proceedings of the SPIE, Imaging through the Atmosphere, Vol. 75, March 1976, p. 90.

Butts, R. R.

C. B. Hogge and R. R. Butts, IEEE Trans. Antennas Propag. AP-24, 144 (1976).

Cathey, W. T.

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

Chiba, T.

T. Chiba, Appl. Opt. 10, 2456 (1971).

Crawford, F. S.

A. Buffington, F. S. Crawford, R. A. Muller, A. J. Schwemiu, and R. G. Smith, "Active Image Restoration with a Flexible Mirror," in Proceedings of the SPIE, Imaging through the Atmosphere, Vol. 75, March 1976, p. 90.

Davis, W. C.

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

Dean, D. R.

D. R. Dean and L. T. James, "Adaptive Laser Optics Techniques (ALOT)," in Proceedings of the High Energy Laser Conference, San Diego, Calif., October 1975 (unpublished).

deWolf, D. A.

D. A. deWolf, "Effects of Turbulence Instabilities on Laser Propagation," RADC-TR-72-119 (April 1972) (unpublished).

Dowling, J. A.

J. A. Dowling and P. M. Livingston, J. Opt. Soc. Am. 63, 846 (1973).

Dunphy, J. R.

J. R. Dunphy and J. R. Kerr, J. Opt. Soc. Am. 64, 1015 (1974).

Feinleib, J.

J. Feinleib and J. W. Hardy, "Wideband Adaptive Optics for Imaging," in Proceedings of the SPIE, Imaging through the Atmosphere, Vol. 75, March 1976, p. 103.

Fried, D. L.

D. L. Fried, J. Opt. Soc. Am. 56, 1372 (1966).

D. L. Fried, J. Opt. Soc. Am. 55, 1427 (1965).

D. L. Fried, Proc. IEEE 55, 57 (1967).

Goranson, R. W.

R. V. Wick and R. W. Goranson, "Infrared Position Sensing Detector: A Photopot for CO2 Lasers," in Laser Digest, AFWL-TR-75-229 (October 1975) (unpublished).

Hansen, S.

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

Hardy, J. W.

J. Feinleib and J. W. Hardy, "Wideband Adaptive Optics for Imaging," in Proceedings of the SPIE, Imaging through the Atmosphere, Vol. 75, March 1976, p. 103.

Hayes, C. L.

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

Heidbreder, G. R.

G. R. Heidbreder, IEEE Trans. Antennas Propag. AP-15, 90 (1967).

Herrmann, J.

J. Herrmann, "Properties of Phase-Conjugate COAT," in Proceedings of the Optical Society of America Annual Meeting, Boston, October 1975, see J. Opt. Soc. Am. 65, 1212A (1975).

Hogge, C. B.

C. B. Hogge and R. R. Butts, IEEE Trans. Antennas Propag. AP-24, 144 (1976).

James, L. T.

D. R. Dean and L. T. James, "Adaptive Laser Optics Techniques (ALOT)," in Proceedings of the High Energy Laser Conference, San Diego, Calif., October 1975 (unpublished).

Kerr, J. R.

J. R. Dunphy and J. R. Kerr, J. Opt. Soc. Am. 64, 1015 (1974).

Livingston, P. M.

J. A. Dowling and P. M. Livingston, J. Opt. Soc. Am. 63, 846 (1973).

Lutomirski, R. F.

R. F. Lutomirski and H. T. Yura, Appl. Opt. 10, 1652 (1971).

Muller, R. A.

A. Buffington, F. S. Crawford, R. A. Muller, A. J. Schwemiu, and R. G. Smith, "Active Image Restoration with a Flexible Mirror," in Proceedings of the SPIE, Imaging through the Atmosphere, Vol. 75, March 1976, p. 90.

Noll, R. J.

R. J. Noll, J. Opt. Soc. Am. 66, 207 (1976).

Nussmeier, T. A.

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

Pearson, J. E.

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).

Pizzurro, V. F.

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

Sancer, M. I.

A. D. Varvatsis and M. I. Sancer, Can. J. Phys. 49, 1233 (1971).

Schwemiu, A. J.

A. Buffington, F. S. Crawford, R. A. Muller, A. J. Schwemiu, and R. G. Smith, "Active Image Restoration with a Flexible Mirror," in Proceedings of the SPIE, Imaging through the Atmosphere, Vol. 75, March 1976, p. 90.

Smith, R. G.

A. Buffington, F. S. Crawford, R. A. Muller, A. J. Schwemiu, and R. G. Smith, "Active Image Restoration with a Flexible Mirror," in Proceedings of the SPIE, Imaging through the Atmosphere, Vol. 75, March 1976, p. 90.

Tatarski, V. I.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).

Varvatsis, A. D.

A. D. Varvatsis and M. I. Sancer, Can. J. Phys. 49, 1233 (1971).

Wick, R. V.

R. V. Wick and R. W. Goranson, "Infrared Position Sensing Detector: A Photopot for CO2 Lasers," in Laser Digest, AFWL-TR-75-229 (October 1975) (unpublished).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 465.

Wyant, C.

J. C. Wyant, Appl. Opt. 14, 2622 (1975).

Yura, H. T.

H. T. Yura, J. Opt. Soc. Am. 63, 567 (1973).

H. T. Yura, Appl. Opt. 10, 2771 (1971).

R. F. Lutomirski and H. T. Yura, Appl. Opt. 10, 1652 (1971).

in Proceedings of the SPIE

A. Buffington, F. S. Crawford, R. A. Muller, A. J. Schwemiu, and R. G. Smith, "Active Image Restoration with a Flexible Mirror," in Proceedings of the SPIE, Imaging through the Atmosphere, Vol. 75, March 1976, p. 90.

Other

R. V. Wick and R. W. Goranson, "Infrared Position Sensing Detector: A Photopot for CO2 Lasers," in Laser Digest, AFWL-TR-75-229 (October 1975) (unpublished).

J. C. Wyant, Appl. Opt. 14, 2622 (1975).

J. Feinleib and J. W. Hardy, "Wideband Adaptive Optics for Imaging," in Proceedings of the SPIE, Imaging through the Atmosphere, Vol. 75, March 1976, p. 103.

D. L. Fried, J. Opt. Soc. Am. 55, 1427 (1965).

J. Herrmann, "Properties of Phase-Conjugate COAT," in Proceedings of the Optical Society of America Annual Meeting, Boston, October 1975, see J. Opt. Soc. Am. 65, 1212A (1975).

D. R. Dean and L. T. James, "Adaptive Laser Optics Techniques (ALOT)," in Proceedings of the High Energy Laser Conference, San Diego, Calif., October 1975 (unpublished).

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 465.

C. B. Hogge and R. R. Butts, IEEE Trans. Antennas Propag. AP-24, 144 (1976).

R. J. Noll, J. Opt. Soc. Am. 66, 207 (1976).

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).

A. D. Varvatsis and M. I. Sancer, Can. J. Phys. 49, 1233 (1971).

W. P. Brown, Jr., J. Opt. Soc. Am. 61, 1051 (1971).

H. T. Yura, Appl. Opt. 10, 2771 (1971).

D. A. deWolf, "Effects of Turbulence Instabilities on Laser Propagation," RADC-TR-72-119 (April 1972) (unpublished).

D. L. Fried, J. Opt. Soc. Am. 56, 1372 (1966).

D. L. Fried, Proc. IEEE 55, 57 (1967).

R. F. Lutomirski and H. T. Yura, Appl. Opt. 10, 1652 (1971).

G. R. Heidbreder, IEEE Trans. Antennas Propag. AP-15, 90 (1967).

H. T. Yura, J. Opt. Soc. Am. 63, 567 (1973).

T. Chiba, Appl. Opt. 10, 2456 (1971).

J. A. Dowling and P. M. Livingston, J. Opt. Soc. Am. 63, 846 (1973).

J. R. Dunphy and J. R. Kerr, J. Opt. Soc. Am. 64, 1015 (1974).

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

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

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