Abstract

This paper presents a method of eliminating the error introduced by the nonuniform diffraction halo in speckle photography. It is shown that, by proper aperturing of the imaging lens, the intensity distribution in the diffraction halo can be made constant over a certain frequency range. The measurements made on Young's fringes, present in this region, would be free from error due to varying intensity in the diffraction halo.

© 1986 Optical Society of America

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References

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  1. G. H. Kaufmann, “On the Numerical Processing of Speckle Photograph Fringes,” Opt. Laser Technol. 12, 207 (1980).
    [CrossRef]
  2. C. S. Vikram, K. Vedam, “Speckle Photography of Lateral Sinusoidal Vibrations: Error due to Varying Halo Intensity,” Appl. Opt. 20, 3388 (1981).
    [CrossRef] [PubMed]
  3. G. H. Kaufmann, A. E. Ennos, B. Gale, D. G. Pugh, “An Electrooptic Readout System for Speckle Photographs,” J. Phys. E 13, 579 (1980).
    [CrossRef]
  4. B. Ineichen, P. Eglin, R. Dandliker, “Hybrid Optical and Electronic Image Processing for Strain Measurements by Speckle Photography,” Appl. Opt. 19, 2191 (1980).
    [CrossRef] [PubMed]
  5. W. R. J. Funnell, “Image Processing Applied to the Interactive Analysis of Interferometric Fringes,” Appl. Opt. 20, 3245 (1981).
    [CrossRef] [PubMed]
  6. G. H. Kaufmann, “Digital Analysis of Speckle Photography Fringes: Processing of Experimental Data,” Appl. Opt. 20, 4277 (1981).
    [CrossRef] [PubMed]
  7. R. Meynart, “Instantaneous Velocity Field Measurements in Unsteady Gas Flow by Speckle Velocimetry,” Appl. Opt. 22, 535 (1983).
    [CrossRef] [PubMed]
  8. C. S. Vikram, K. Vedam, “Processing Speckle Photography Data: Circular Imaging Aperture,” Appl. Opt. 22, 653 (1983).
    [CrossRef] [PubMed]
  9. C. S. Vikram, “Errors in Speckle Photography of Lateral Sinusoidal Vibrations: a Simple Analytical Solution,” Appl. Opt. 21, 1710 (1982).
    [CrossRef] [PubMed]
  10. C. S. Vikram, “Simple Approach to Process Speckle-Photography Data,” Opt. Lett. 7, 374 (1982).
    [CrossRef] [PubMed]
  11. C. S. Vikram, “Analysis of Young's Fringes in Speckle Photography: Generalized Square Aperture Imaging,” Appl.Phys. B 31, 221 (1983).
    [CrossRef]
  12. C. S. Vikram, K. Vedam, “Selective Counting Path of Young's Fringes in Speckle Photography for Eliminating Diffraction Halo Effects,” Appl. Opt. 22, 2242 (1983).
    [CrossRef] [PubMed]
  13. F. P. Chiang, R. P. Khetan, “Strain Analysis by One-Beam Laser Speckle Interferometry. 2: Multiaperture Method,” Appl. Opt. 18, 2175 (1979).
    [CrossRef] [PubMed]
  14. L. I. Goldfischer, “Autocorrelation Function and Power Spectral Density of Laser-Produced Speckle Patterns,” J. Opt. Soc. Am. 55, 247 (1965).
    [CrossRef]
  15. J. W. Goodman, “Statistical Properties of Laser Speckle Pattern,” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer-Verlag, New York, 1975), p. 9.
    [CrossRef]
  16. S. Lowenthal, H. H. Arsenault, “Image Formation for Coherent Diffuse Objects and Statistical Properties,” J. Opt. Soc. Am. 60, 1478 (1970).
    [CrossRef]
  17. R. Meynart, “Diffraction Halo in Speckle Photography,” Appl. Opt. 23, 2235 (1984).
    [CrossRef] [PubMed]
  18. F. P. Chiang, D. W. Li, “Diffraction Halo Functions of Coherent and Incoherent Random Speckle Patterns,” Appl. Opt. 24, 2166 (1985).
    [CrossRef] [PubMed]
  19. E. L. O'Neill, “Transfer Function for an Annular Aperture,”J. Opt. Soc. Am. 46, 285 (1956).
    [CrossRef]

1985 (1)

1984 (1)

1983 (4)

1982 (2)

1981 (3)

1980 (3)

G. H. Kaufmann, “On the Numerical Processing of Speckle Photograph Fringes,” Opt. Laser Technol. 12, 207 (1980).
[CrossRef]

G. H. Kaufmann, A. E. Ennos, B. Gale, D. G. Pugh, “An Electrooptic Readout System for Speckle Photographs,” J. Phys. E 13, 579 (1980).
[CrossRef]

B. Ineichen, P. Eglin, R. Dandliker, “Hybrid Optical and Electronic Image Processing for Strain Measurements by Speckle Photography,” Appl. Opt. 19, 2191 (1980).
[CrossRef] [PubMed]

1979 (1)

1970 (1)

1965 (1)

1956 (1)

Arsenault, H. H.

Chiang, F. P.

Dandliker, R.

Eglin, P.

Ennos, A. E.

G. H. Kaufmann, A. E. Ennos, B. Gale, D. G. Pugh, “An Electrooptic Readout System for Speckle Photographs,” J. Phys. E 13, 579 (1980).
[CrossRef]

Funnell, W. R. J.

Gale, B.

G. H. Kaufmann, A. E. Ennos, B. Gale, D. G. Pugh, “An Electrooptic Readout System for Speckle Photographs,” J. Phys. E 13, 579 (1980).
[CrossRef]

Goldfischer, L. I.

Goodman, J. W.

J. W. Goodman, “Statistical Properties of Laser Speckle Pattern,” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer-Verlag, New York, 1975), p. 9.
[CrossRef]

Ineichen, B.

Kaufmann, G. H.

G. H. Kaufmann, “Digital Analysis of Speckle Photography Fringes: Processing of Experimental Data,” Appl. Opt. 20, 4277 (1981).
[CrossRef] [PubMed]

G. H. Kaufmann, A. E. Ennos, B. Gale, D. G. Pugh, “An Electrooptic Readout System for Speckle Photographs,” J. Phys. E 13, 579 (1980).
[CrossRef]

G. H. Kaufmann, “On the Numerical Processing of Speckle Photograph Fringes,” Opt. Laser Technol. 12, 207 (1980).
[CrossRef]

Khetan, R. P.

Li, D. W.

Lowenthal, S.

Meynart, R.

O'Neill, E. L.

Pugh, D. G.

G. H. Kaufmann, A. E. Ennos, B. Gale, D. G. Pugh, “An Electrooptic Readout System for Speckle Photographs,” J. Phys. E 13, 579 (1980).
[CrossRef]

Vedam, K.

Vikram, C. S.

Appl. Opt. (11)

F. P. Chiang, R. P. Khetan, “Strain Analysis by One-Beam Laser Speckle Interferometry. 2: Multiaperture Method,” Appl. Opt. 18, 2175 (1979).
[CrossRef] [PubMed]

W. R. J. Funnell, “Image Processing Applied to the Interactive Analysis of Interferometric Fringes,” Appl. Opt. 20, 3245 (1981).
[CrossRef] [PubMed]

C. S. Vikram, K. Vedam, “Speckle Photography of Lateral Sinusoidal Vibrations: Error due to Varying Halo Intensity,” Appl. Opt. 20, 3388 (1981).
[CrossRef] [PubMed]

G. H. Kaufmann, “Digital Analysis of Speckle Photography Fringes: Processing of Experimental Data,” Appl. Opt. 20, 4277 (1981).
[CrossRef] [PubMed]

C. S. Vikram, “Errors in Speckle Photography of Lateral Sinusoidal Vibrations: a Simple Analytical Solution,” Appl. Opt. 21, 1710 (1982).
[CrossRef] [PubMed]

R. Meynart, “Instantaneous Velocity Field Measurements in Unsteady Gas Flow by Speckle Velocimetry,” Appl. Opt. 22, 535 (1983).
[CrossRef] [PubMed]

C. S. Vikram, K. Vedam, “Processing Speckle Photography Data: Circular Imaging Aperture,” Appl. Opt. 22, 653 (1983).
[CrossRef] [PubMed]

C. S. Vikram, K. Vedam, “Selective Counting Path of Young's Fringes in Speckle Photography for Eliminating Diffraction Halo Effects,” Appl. Opt. 22, 2242 (1983).
[CrossRef] [PubMed]

R. Meynart, “Diffraction Halo in Speckle Photography,” Appl. Opt. 23, 2235 (1984).
[CrossRef] [PubMed]

F. P. Chiang, D. W. Li, “Diffraction Halo Functions of Coherent and Incoherent Random Speckle Patterns,” Appl. Opt. 24, 2166 (1985).
[CrossRef] [PubMed]

B. Ineichen, P. Eglin, R. Dandliker, “Hybrid Optical and Electronic Image Processing for Strain Measurements by Speckle Photography,” Appl. Opt. 19, 2191 (1980).
[CrossRef] [PubMed]

Appl.Phys. B (1)

C. S. Vikram, “Analysis of Young's Fringes in Speckle Photography: Generalized Square Aperture Imaging,” Appl.Phys. B 31, 221 (1983).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Phys. E (1)

G. H. Kaufmann, A. E. Ennos, B. Gale, D. G. Pugh, “An Electrooptic Readout System for Speckle Photographs,” J. Phys. E 13, 579 (1980).
[CrossRef]

Opt. Laser Technol. (1)

G. H. Kaufmann, “On the Numerical Processing of Speckle Photograph Fringes,” Opt. Laser Technol. 12, 207 (1980).
[CrossRef]

Opt. Lett. (1)

Other (1)

J. W. Goodman, “Statistical Properties of Laser Speckle Pattern,” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer-Verlag, New York, 1975), p. 9.
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

(a) Schematic of the experimental setup to record specklegrams. (b) Rectangular aperture with two open sections of width η1a and (1 − η2)a.

Fig. 2
Fig. 2

Plot of the autocorrelation for the aperture shown in Fig. 1. Both the theoretical and experimental plots are given for η1 = 1/2 and η2 = 3/4.

Fig. 3
Fig. 3

(a) Intensity distribution of the diffraction halo for the aperture shown in Fig. 1. When η1 = 1/2 and η2 = 3/4 or η1 = 3/4 and η2 = 1/2. (b) Such a halo distribution modulated by cos2 fringes, where a = 32 mm, λ = 0.6328 μm, and u = 30 μm.

Equations (7)

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I ( x ) = [ 1 ν 1 + ν + 2 ν 1 + ν cos 2 ( D x ) ] I 0 ( x ) ,
D = π ua m λ z , x = | x | a ,
I 0 ( x ) = 1 ( 1 η 2 + η 1 ) [ A 1 + B 1 + C 1 + C 2 C 3 C 4 ] .
A 1 = { η 1 [ 1 x η 1 ] x < η 1 , 0 x η 1 , B 1 = { ( 1 η 2 ) [ 1 x 1 η 2 ] x < 1 η 2 , 0 x 1 η 2 , C 1 = { 1 η 1 0 < 1 η 1 x 1 , x 0 < x 1 η 1 , C 2 = { η 2 0 < η 2 x 1 , x 0 < x η 2 , C 3 = { η 2 η 1 0 < η 2 η 1 x 1 , x 0 < x η 2 η 1 , C 4 = { 1 0 < 1 x 1 , x 0 < x 1 .
d I 0 ( x ) d x = 1 1 η 2 + η 1 1 a [ 1 a | x < η 1 1 a | x < 1 η 2 + 1 a | 0 < x 1 η 1 + 1 a | 0 < x η 2 1 a | 0 < x η 2 η 1 1 a | 0 < x 1 ] .
d I 0 ( x ) dx
d I 0 ( x ) dx = 0

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