Abstract

Expressions to eliminate the diffraction halo effects in speckle photography of sinusoidal vibration are derived. Both maxima and minima positions in Young’s fringes pattern are considered, and only the experimental halo intensity variation is assumed known.

© 1990 Optical Society of America

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References

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  1. J. M. Burch, J. M. J. Tokarski, “Production of Multiple Beam Fringes from Photographic Scatterers,” Opt. Acta 15, 101–111 (1968).
  2. E. Archbold, J. M. Burch, A. E. Ennos, “Recording of In-Plane Surface Displacement by Double-Exposure Speckle Photography,” Opt. Acta 17, 883–898 (1970).
    [Crossref]
  3. G. H. Kaufmann, “On the Numerical Processing of Speckle Photography Fringes,” Opt. Laser Technol. 12, 207–209 (1980).
    [Crossref]
  4. C. S. Vikram, K. Vedam, “Speckle Photography of Lateral Sinusoidal Vibrations: Error due to Varying Halo Intensity,” Appl. Opt. 20, 3388–3391 (1981).
    [Crossref] [PubMed]
  5. J. Georgieva, “Removing the Diffraction Halo Effect in Speckle Photography,” Appl. Opt. 28, 21–24 (1989).
    [Crossref] [PubMed]
  6. C. S. Vikram, K. Vedam, “Selective Counting Path of Young’s Fringes in Speckle Photography for Eliminating Diffraction Halo Effects,” Appl. Opt. 22, 2242–2243 (1983).
    [Crossref] [PubMed]
  7. C. J. Joenathan, R. S. Sirohi, “Elimination of Error in Speckle Photography,” Appl. Opt. 25, 1791–1794 (1986).
    [Crossref] [PubMed]
  8. R. Meynart, “Diffraction Halo in Speckle Photography,” Appl. Opt. 23, 2235–2236 (1984).
    [Crossref] [PubMed]
  9. F.-P. Chiang, D. W. Li, “Diffraction Halo Functions of Coherent and Incoherent Random Speckle Patterns,” Appl. Opt. 24, 2166–2171 (1985).
    [Crossref] [PubMed]
  10. C. S. Vikram, “Error in Speckle Photography of Lateral Sinusoidal Vibrations: A Simple Analytical Solution,” Appl. Opt. 21, 1710–1712 (1982).
    [Crossref] [PubMed]
  11. C. S. Vikram, “Interpretation of Young’s Fringes in Speckle Photography for Lateral Vibration Analysis: Imaging with Circular Aperture,” Optik 65, 263–268 (1983).
  12. C. S. Vikram, “Analysis of Young’s Fringes in Speckle Photography: Generalized Square Imaging Aperture,” Appl. Phys. B 31, 221–224 (1983).
    [Crossref]
  13. K. Hinsch, “Fringe Positions in Double-Exposure Speckle Photography,” Appl. Opt. 28, 5298–5304 (1989).
    [Crossref] [PubMed]
  14. N. Deng, I. Yamaguchi, “Automated Analysis of Speckle Photographs with Extended Range and Improved Accuracy,” Appl. Opt. 29, 296–303 (1990).
    [Crossref] [PubMed]

1990 (1)

1989 (2)

1986 (1)

1985 (1)

1984 (1)

1983 (3)

C. S. Vikram, K. Vedam, “Selective Counting Path of Young’s Fringes in Speckle Photography for Eliminating Diffraction Halo Effects,” Appl. Opt. 22, 2242–2243 (1983).
[Crossref] [PubMed]

C. S. Vikram, “Interpretation of Young’s Fringes in Speckle Photography for Lateral Vibration Analysis: Imaging with Circular Aperture,” Optik 65, 263–268 (1983).

C. S. Vikram, “Analysis of Young’s Fringes in Speckle Photography: Generalized Square Imaging Aperture,” Appl. Phys. B 31, 221–224 (1983).
[Crossref]

1982 (1)

1981 (1)

1980 (1)

G. H. Kaufmann, “On the Numerical Processing of Speckle Photography Fringes,” Opt. Laser Technol. 12, 207–209 (1980).
[Crossref]

1970 (1)

E. Archbold, J. M. Burch, A. E. Ennos, “Recording of In-Plane Surface Displacement by Double-Exposure Speckle Photography,” Opt. Acta 17, 883–898 (1970).
[Crossref]

1968 (1)

J. M. Burch, J. M. J. Tokarski, “Production of Multiple Beam Fringes from Photographic Scatterers,” Opt. Acta 15, 101–111 (1968).

Archbold, E.

E. Archbold, J. M. Burch, A. E. Ennos, “Recording of In-Plane Surface Displacement by Double-Exposure Speckle Photography,” Opt. Acta 17, 883–898 (1970).
[Crossref]

Burch, J. M.

E. Archbold, J. M. Burch, A. E. Ennos, “Recording of In-Plane Surface Displacement by Double-Exposure Speckle Photography,” Opt. Acta 17, 883–898 (1970).
[Crossref]

J. M. Burch, J. M. J. Tokarski, “Production of Multiple Beam Fringes from Photographic Scatterers,” Opt. Acta 15, 101–111 (1968).

Chiang, F.-P.

Deng, N.

Ennos, A. E.

E. Archbold, J. M. Burch, A. E. Ennos, “Recording of In-Plane Surface Displacement by Double-Exposure Speckle Photography,” Opt. Acta 17, 883–898 (1970).
[Crossref]

Georgieva, J.

Hinsch, K.

Joenathan, C. J.

Kaufmann, G. H.

G. H. Kaufmann, “On the Numerical Processing of Speckle Photography Fringes,” Opt. Laser Technol. 12, 207–209 (1980).
[Crossref]

Li, D. W.

Meynart, R.

Sirohi, R. S.

Tokarski, J. M. J.

J. M. Burch, J. M. J. Tokarski, “Production of Multiple Beam Fringes from Photographic Scatterers,” Opt. Acta 15, 101–111 (1968).

Vedam, K.

Vikram, C. S.

Yamaguchi, I.

Appl. Opt. (9)

Appl. Phys. B (1)

C. S. Vikram, “Analysis of Young’s Fringes in Speckle Photography: Generalized Square Imaging Aperture,” Appl. Phys. B 31, 221–224 (1983).
[Crossref]

Opt. Acta (2)

J. M. Burch, J. M. J. Tokarski, “Production of Multiple Beam Fringes from Photographic Scatterers,” Opt. Acta 15, 101–111 (1968).

E. Archbold, J. M. Burch, A. E. Ennos, “Recording of In-Plane Surface Displacement by Double-Exposure Speckle Photography,” Opt. Acta 17, 883–898 (1970).
[Crossref]

Opt. Laser Technol. (1)

G. H. Kaufmann, “On the Numerical Processing of Speckle Photography Fringes,” Opt. Laser Technol. 12, 207–209 (1980).
[Crossref]

Optik (1)

C. S. Vikram, “Interpretation of Young’s Fringes in Speckle Photography for Lateral Vibration Analysis: Imaging with Circular Aperture,” Optik 65, 263–268 (1983).

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Equations (15)

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I ( x ) = I 0 ( x ) j 0 2 ( 2 π A M x λ L ) ,
2 π A M x n 0 λ L = j 1 , n ; n = 1 , 2 , 3 , ,
2 π A M x n 0 λ L = j 0 , n ; n = 1 , 2 , 3 , ,
I ( x ) = I 0 ( x ) [ 1 - ν 1 + ν + 2 ν 1 + ν J 0 2 ( 2 π A M x λ L ) ] ,
ν c = I max - I min I max + I min = ν J 0 2 ( j 1 , n ) 1 - ν + ν J 0 2 ( j 1 , n ) .
I 0 ( x ) [ 1 - ν 2 ν + J 0 2 ( 2 π A M x n λ L ) ] - I 0 ( x ) · 4 π A M x n λ L · J 0 ( 2 π A M x n λ L ) J 1 ( 2 π A M x n λ L ) = 0.
x n = x n 0 + Δ x n .
J 0 ( 2 π A M x n λ L ) J 0 ( j 1 , n ) - 1 2 J 0 ( j 1 , n ) ( Δ j 1 , n ) 2 ,
J 1 ( 2 π A M x n λ L ) J 0 ( j 1 , n ) ( Δ j 1 , n ) - 1 2 j 1 , n J 0 ( j 1 , n ) ( Δ j 1 , n ) 2 ,
Δ j 1 , n = 2 π A M Δ x n λ L .
[ 1 + I 0 ( x n ) I 0 ( x n ) ] J 0 2 ( j 1 , n ) ( Δ j 1 , n ) 2 + 2 j 1 , n J 0 2 ( j 1 , n ) ( Δ j 1 , n ) - I 0 ( x n ) I 0 ( x n ) [ 1 - ν 2 ν + j 0 2 ( j 1 , n ) ] = 0.
J 0 ( 2 π A M x n λ L ) - J 1 ( j 0 , n ) ( Δ j 0 , n ) + 1 4 J 2 ( j 0 , n ) ( Δ j 0 , n ) 2 ,
J 1 ( 2 π A M x n λ L ) J 1 ( j 0 , n ) - 1 2 J 2 ( j 0 , n ) ( Δ j 0 , n ) + [ J 3 ( j o , n ) - 3 J 1 ( j 0 , n ) ] ( Δ j 0 , n ) 2 ,
Δ j 0 , n = 2 π A M Δ x n λ L .
[ I 0 ( x n ) I 0 ( x n ) - 1 ] J 0 2 ( j 0 , n ) ( Δ j 0 , n ) 2 + 2 j 0 , n J 1 2 ( j 0 , n ) ( Δ j 0 , n ) + I 0 ( x n ) I 0 ( x n ) · 1 - ν 2 ν = 0.

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