Abstract

It has been observed that in case of an imaging geometry, the speckle size and shape depend upon the aberrations, provided the scattering spot size is smaller than the point-spread function of the optical system. In the presence of spherical aberration the speckle pattern becomes radially streaky. Photographs of the patterns at paraxial, marginal, least-confusion, and defocused planes are given. When the diffuser is given a translatory motion the speckle at a point in the observation plane moves along the shadow of a knife edge (with its edge parallel to the direction of translation) placed at a suitable position in the pupil plane. Experiments with the atropinized eye also yielded the same results. A heuristic explanation for these results is included.

© 1979 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. W. Goodman, “Statistical properties of lasers speckle pattern,” in Topics in Applied Physics, Vol. 9. Laser Speckle and Related Phenomena,edited by J. C. Dainty (Springer-Verlag, Berlin1975), pp. 9–75.
    [Crossref]
  2. J. C. Dainty, “The statistics of speckle patterns,” in Progress in Optics, Vol. XIV, edited by E. Wolf (North-Holland, Amsterdam, (1976), pp. 1–44.
  3. K. A. Stetson, “The vulnerability of speckle photography to lens aberrations,” J. Opt. Soc. Am.,  67, 1587–1590 (1977).
    [Crossref]
  4. L. H. Tanner, “Camera testing by use of speckle patterns,” Appl. Opt. 13, 2026–2034 (1974).
    [Crossref] [PubMed]
  5. W. M. Rosenblum and J. L. Christensen “Objective and subjective spherical aberration measurements of the human eye,” in Progress in Optics Vol. XIII, edited by E. Wolf (North-Holland, Amsterdam, 1976), pp. 69–91.
    [Crossref]
  6. T. M. Sporton, “The scattering of coherent light from a rough surface,” J. Phy. D. 2, 1027–1034 (1969).
    [Crossref]
  7. H. H. Emsley, Visual Optics (Butterworths, London, 1977) 5th ed. p. 414.
  8. R. D. Bahuguna, K. K. Gupta, and K. Singh, “Some psychophysical experiments using diffraction patterns,” (unpublished).

1977 (1)

1974 (1)

1969 (1)

T. M. Sporton, “The scattering of coherent light from a rough surface,” J. Phy. D. 2, 1027–1034 (1969).
[Crossref]

Bahuguna, R. D.

R. D. Bahuguna, K. K. Gupta, and K. Singh, “Some psychophysical experiments using diffraction patterns,” (unpublished).

Christensen, J. L.

W. M. Rosenblum and J. L. Christensen “Objective and subjective spherical aberration measurements of the human eye,” in Progress in Optics Vol. XIII, edited by E. Wolf (North-Holland, Amsterdam, 1976), pp. 69–91.
[Crossref]

Dainty, J. C.

J. C. Dainty, “The statistics of speckle patterns,” in Progress in Optics, Vol. XIV, edited by E. Wolf (North-Holland, Amsterdam, (1976), pp. 1–44.

Emsley, H. H.

H. H. Emsley, Visual Optics (Butterworths, London, 1977) 5th ed. p. 414.

Goodman, J. W.

J. W. Goodman, “Statistical properties of lasers speckle pattern,” in Topics in Applied Physics, Vol. 9. Laser Speckle and Related Phenomena,edited by J. C. Dainty (Springer-Verlag, Berlin1975), pp. 9–75.
[Crossref]

Gupta, K. K.

R. D. Bahuguna, K. K. Gupta, and K. Singh, “Some psychophysical experiments using diffraction patterns,” (unpublished).

Rosenblum, W. M.

W. M. Rosenblum and J. L. Christensen “Objective and subjective spherical aberration measurements of the human eye,” in Progress in Optics Vol. XIII, edited by E. Wolf (North-Holland, Amsterdam, 1976), pp. 69–91.
[Crossref]

Singh, K.

R. D. Bahuguna, K. K. Gupta, and K. Singh, “Some psychophysical experiments using diffraction patterns,” (unpublished).

Sporton, T. M.

T. M. Sporton, “The scattering of coherent light from a rough surface,” J. Phy. D. 2, 1027–1034 (1969).
[Crossref]

Stetson, K. A.

Tanner, L. H.

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

J. Phy. D. (1)

T. M. Sporton, “The scattering of coherent light from a rough surface,” J. Phy. D. 2, 1027–1034 (1969).
[Crossref]

Other (5)

H. H. Emsley, Visual Optics (Butterworths, London, 1977) 5th ed. p. 414.

R. D. Bahuguna, K. K. Gupta, and K. Singh, “Some psychophysical experiments using diffraction patterns,” (unpublished).

W. M. Rosenblum and J. L. Christensen “Objective and subjective spherical aberration measurements of the human eye,” in Progress in Optics Vol. XIII, edited by E. Wolf (North-Holland, Amsterdam, 1976), pp. 69–91.
[Crossref]

J. W. Goodman, “Statistical properties of lasers speckle pattern,” in Topics in Applied Physics, Vol. 9. Laser Speckle and Related Phenomena,edited by J. C. Dainty (Springer-Verlag, Berlin1975), pp. 9–75.
[Crossref]

J. C. Dainty, “The statistics of speckle patterns,” in Progress in Optics, Vol. XIV, edited by E. Wolf (North-Holland, Amsterdam, (1976), pp. 1–44.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

FIG. 1
FIG. 1

Schematic diagram showing the optical system.

FIG. 2
FIG. 2

Speckle patterns in the paraxial plane, (a) for angular size Ω1; (b) for angular size Ω2; (c) for angular size Ω3.

FIG. 3
FIG. 3

Speckle patterns in the marginal plane (a) for angular size Ω1; (b) for angular size Ω2; (c) for angular size Ω3.

FIG. 4
FIG. 4

Speckle patterns in the plane of least confusion, (a) for angular size Ω1; (b) for angular size Ω2; (c) for angular size Ω3.

FIG. 5
FIG. 5

Speckle patterns in the defocused plane, (a) for angular size Ω1; (b) for angular size Ω2; (c) for angular size Ω3.

FIG. 6
FIG. 6

Appearance of speckles for horizontal translatory motion of the scattering spot of angular size Ω1 for defocused plane.

FIG. 7
FIG. 7

The maximum angular subtense in the presence of spherical aberration (a) large diffuser θ1θ2; (b) small diffuser θ1> θ2.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

V paraxial = c [ ( η / c a ) ( 9 η / c a 8 a 2 ) ] 1 / 2 V pupil , c a 3 η c R 2 a .
V paraxial 2 = ( d ξ d t | y = a ) 2 + ( d η d t | y = a ) 2
ξ = c ( x 2 + y 2 ) x , η = c ( x 2 + y 2 ) y ,
V pupil = d x / d t .