Abstract

When an object and collecting pupil are separated by a medium that has random spatial and temporal variations of refractive index, a conventionally formed image may be severely degraded over the entire field of view of the imaging system. By using lensless Fourier-transform holography, considerable improvement of image resolution can be obtained within a limited field of view. The nature of the degradation of the reconstructed images is analyzed for both long and short exposures under the assumption that the random log amplitude and phase fluctuations across the collecting pupil are locally stationary processes with gaussian statistics. Experimental results support the analysis in a qualitative manner.

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  1. R. E. Hufnagel and N. R. Stanley, J. Opt. Soc. Am. 54, 52 (1964).
  2. G. O. Reynolds and T. J. Skinner, J. Opt. Soc. Am. 54, 1302 (1964).
  3. D. L. Fried, J. Opt. Soc. Am. 56, 1372 (1966).
  4. D. L. Fried, J. Opt. Soc. Am. 56, 1381 (1966).
  5. J. W. Goodman, W. H. Huntley, Jr., D. W. Jackson, and M. Lehmann, Appl. Phys. Letters 8, 311 (1966).
  6. M. J. Beran and G. B. Parrent, Jr., Theory of Partial Coherence, (Prentice-Hall, Inc., Englewood Cliffs, N. J., 1964), p. 175.
  7. Here we are not concerned with the practical aspects of how the object illumination and reference are provided. However, we do assume that both are linearly polarized in the same direction and that the state of polarization is not changed by the perturbing medium. 600
  8. See Ref. 3, p. 1374.
  9. A. Kozma, J. Opt. Soc. Am. 56, 428 (1966).
  10. Here we neglect a constant as well as a quadratic phase factor that would vanish later.
  11. D. L. Fried, J. Opt. Soc. Am. 57, 175 (1967).
  12. The analysis of this section becomes invalid if the irradiance fluctuations across the reference beam are sufficiently large to drive the hologram exposure out of the linear region of the transmittance-exposure curve. However, this problem can be eliminated by pre-exposing the photographic plate.
  13. Ref. 3, p. 1375.
  14. Ref. 11, Eq. (3.3). This equation cannot be strictly correct because of its behavior for large r2, but its use is justified for the purpose of computing image resolution.
  15. A Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill Book Company, New York, 1965), p. 226, Eq. (7-14).

Beran, M. J.

M. J. Beran and G. B. Parrent, Jr., Theory of Partial Coherence, (Prentice-Hall, Inc., Englewood Cliffs, N. J., 1964), p. 175.

Fried, D. L.

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

D. L. Fried, J. Opt. Soc. Am. 57, 175 (1967).

D. L. Fried, J. Opt. Soc. Am. 56, 1381 (1966).

Goodman, J. W.

J. W. Goodman, W. H. Huntley, Jr., D. W. Jackson, and M. Lehmann, Appl. Phys. Letters 8, 311 (1966).

Hufnagel, R. E.

R. E. Hufnagel and N. R. Stanley, J. Opt. Soc. Am. 54, 52 (1964).

Huntley, Jr., W. H.

J. W. Goodman, W. H. Huntley, Jr., D. W. Jackson, and M. Lehmann, Appl. Phys. Letters 8, 311 (1966).

Jackson, D. W.

J. W. Goodman, W. H. Huntley, Jr., D. W. Jackson, and M. Lehmann, Appl. Phys. Letters 8, 311 (1966).

Kozma, A.

A. Kozma, J. Opt. Soc. Am. 56, 428 (1966).

Lehmann, M.

J. W. Goodman, W. H. Huntley, Jr., D. W. Jackson, and M. Lehmann, Appl. Phys. Letters 8, 311 (1966).

Papoulis, A

A Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill Book Company, New York, 1965), p. 226, Eq. (7-14).

Parrent, Jr., G. B.

M. J. Beran and G. B. Parrent, Jr., Theory of Partial Coherence, (Prentice-Hall, Inc., Englewood Cliffs, N. J., 1964), p. 175.

Reynolds, G. O.

G. O. Reynolds and T. J. Skinner, J. Opt. Soc. Am. 54, 1302 (1964).

Skinner, T. J.

G. O. Reynolds and T. J. Skinner, J. Opt. Soc. Am. 54, 1302 (1964).

Stanley, N. R.

R. E. Hufnagel and N. R. Stanley, J. Opt. Soc. Am. 54, 52 (1964).

Other

R. E. Hufnagel and N. R. Stanley, J. Opt. Soc. Am. 54, 52 (1964).

G. O. Reynolds and T. J. Skinner, J. Opt. Soc. Am. 54, 1302 (1964).

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

D. L. Fried, J. Opt. Soc. Am. 56, 1381 (1966).

J. W. Goodman, W. H. Huntley, Jr., D. W. Jackson, and M. Lehmann, Appl. Phys. Letters 8, 311 (1966).

M. J. Beran and G. B. Parrent, Jr., Theory of Partial Coherence, (Prentice-Hall, Inc., Englewood Cliffs, N. J., 1964), p. 175.

Here we are not concerned with the practical aspects of how the object illumination and reference are provided. However, we do assume that both are linearly polarized in the same direction and that the state of polarization is not changed by the perturbing medium. 600

See Ref. 3, p. 1374.

A. Kozma, J. Opt. Soc. Am. 56, 428 (1966).

Here we neglect a constant as well as a quadratic phase factor that would vanish later.

D. L. Fried, J. Opt. Soc. Am. 57, 175 (1967).

The analysis of this section becomes invalid if the irradiance fluctuations across the reference beam are sufficiently large to drive the hologram exposure out of the linear region of the transmittance-exposure curve. However, this problem can be eliminated by pre-exposing the photographic plate.

Ref. 3, p. 1375.

Ref. 11, Eq. (3.3). This equation cannot be strictly correct because of its behavior for large r2, but its use is justified for the purpose of computing image resolution.

A Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill Book Company, New York, 1965), p. 226, Eq. (7-14).

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