Abstract

Fringe sharpening is required to obtain a higher accuracy of measurement. Nonlinear recording and consequently filtering at the higher-order halos for image formation give sharpened fringes in the image. Furthermore, if the apertures during recording are properly arranged, cross-frequency orders appear, which when used for filtering provide moiré fringes of higher contrast due to intercoupling.

© 1984 Optical Society of America

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References

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  1. J. A. Leendertz, J. N. Butters, “An Image of Shearing Speckle Pattern Interferometer for Measuring Bending Moments,” J. Phys. E 6, 1107 (1973).
    [CrossRef]
  2. Y. Y. Hung, C. E. Taylor, “Measurement of Slopes of Structural Deflections by Speckle Shearing Interferometry,” Exp. Mech. 14, 281 (1974).
    [CrossRef]
  3. Y. Y. Yung, R. E. Rowlands, I. M. Daniel, “Speckle-Shearing Inteferometric Technique: a Full-Field Strain Gauge,” Appl. Opt. 14, 618 (1975).
    [CrossRef]
  4. P. Hariharan, “Speckle-Shearing Interferometry: a Simplified Sandwich Technique,” Appl. Opt. 14, 2563 (1975).
    [CrossRef] [PubMed]
  5. F. P. Chiang, R. M. Juang, “Laser Speckle Interferometry for Plate Bending Problems,” Appl. Opt. 15, 2199 (1976).
    [CrossRef] [PubMed]
  6. Y. Y. Hung, I. M. Daniel, R. E. Rowlands, “Full-Field Optical Strain Measurement Having Post Recording Sensitivity and Direction Selectivity,” Exp. Mech. 18, 56 (1978).
    [CrossRef]
  7. Y. Y. Hung, C. Y. Liang, “Image-Shearing Camera for Direct Measurement of Surface Strains,” Appl. Opt. 18, 1046 (1979).
    [CrossRef] [PubMed]
  8. Y. Y. Hung, A. J. Durelli, “Simultaneous Measurement of Three Displacement Derivatives Using a Multiple Image Shearing Interferometric Camera,” J. Strain Anal. 14, 81 (1979).
    [CrossRef]
  9. R. Krishna Murthy, R. S. Sirohi, M. P. Kothiyal, “Speckle Shearing Interferometry: a New Method,” Appl. Opt. 21, 2865 (1982).
  10. R. Krishna Murthy, Ph.D. Thesis, IIT, Madras, India (1983).
  11. R. K. Mohanty, C. Joenathan, R. S. Sirohi, “Speckle Shear Interferometry by Double Dove Prism,” Opt. Commun. 47, 27 (1983).
    [CrossRef]
  12. D. K. Sharma, R. S. Sirohi, M. P. Kothiyal, “Simultaneous Measurement of Slope and Curvature with a Three-Aperture Speckle Shearing Interferometer,” Appl. Opt. 23, 1542 (1984).
    [CrossRef] [PubMed]
  13. C. Joenathan, R. K. Mohanty, R. S. Sirohi, “Multiplexing in Speckle Shear Interferometry,” to appear in Opt. Acta (1984).
    [CrossRef]
  14. C. Joenathan, R. K. Mohanty, R. S. Sirohi, “On Methods of Multiplexing in Speckle Shear Interferometry,” to appear in Optik (1985).
  15. D. E. Duffy, “Moiré Gauging of In-Plane Displacement Using Double Aperture Imaging,” Appl. Opt. 11, 17781 (1972).
    [CrossRef] [PubMed]
  16. E. Archbold, J. M. Burch, A. E. Ennos, “Recording of In-Plane Displacement by Double Exposure Speckle Photography,” Opt. Acta 17, 883 (1970).
    [CrossRef]
  17. P. L. Baker, D. C. Hogan, G. J. Troup, R. G. Turner, “The Variation of Speckle Size with Film Density: An Example of Babinet’s Principle,” Opt. Commun. 29, 265 (1979).
    [CrossRef]

1984

1983

R. K. Mohanty, C. Joenathan, R. S. Sirohi, “Speckle Shear Interferometry by Double Dove Prism,” Opt. Commun. 47, 27 (1983).
[CrossRef]

1982

1979

Y. Y. Hung, C. Y. Liang, “Image-Shearing Camera for Direct Measurement of Surface Strains,” Appl. Opt. 18, 1046 (1979).
[CrossRef] [PubMed]

P. L. Baker, D. C. Hogan, G. J. Troup, R. G. Turner, “The Variation of Speckle Size with Film Density: An Example of Babinet’s Principle,” Opt. Commun. 29, 265 (1979).
[CrossRef]

Y. Y. Hung, A. J. Durelli, “Simultaneous Measurement of Three Displacement Derivatives Using a Multiple Image Shearing Interferometric Camera,” J. Strain Anal. 14, 81 (1979).
[CrossRef]

1978

Y. Y. Hung, I. M. Daniel, R. E. Rowlands, “Full-Field Optical Strain Measurement Having Post Recording Sensitivity and Direction Selectivity,” Exp. Mech. 18, 56 (1978).
[CrossRef]

1976

1975

1974

Y. Y. Hung, C. E. Taylor, “Measurement of Slopes of Structural Deflections by Speckle Shearing Interferometry,” Exp. Mech. 14, 281 (1974).
[CrossRef]

1973

J. A. Leendertz, J. N. Butters, “An Image of Shearing Speckle Pattern Interferometer for Measuring Bending Moments,” J. Phys. E 6, 1107 (1973).
[CrossRef]

1972

D. E. Duffy, “Moiré Gauging of In-Plane Displacement Using Double Aperture Imaging,” Appl. Opt. 11, 17781 (1972).
[CrossRef] [PubMed]

1970

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

Archbold, E.

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

Baker, P. L.

P. L. Baker, D. C. Hogan, G. J. Troup, R. G. Turner, “The Variation of Speckle Size with Film Density: An Example of Babinet’s Principle,” Opt. Commun. 29, 265 (1979).
[CrossRef]

Burch, J. M.

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

Butters, J. N.

J. A. Leendertz, J. N. Butters, “An Image of Shearing Speckle Pattern Interferometer for Measuring Bending Moments,” J. Phys. E 6, 1107 (1973).
[CrossRef]

Chiang, F. P.

Daniel, I. M.

Y. Y. Hung, I. M. Daniel, R. E. Rowlands, “Full-Field Optical Strain Measurement Having Post Recording Sensitivity and Direction Selectivity,” Exp. Mech. 18, 56 (1978).
[CrossRef]

Y. Y. Yung, R. E. Rowlands, I. M. Daniel, “Speckle-Shearing Inteferometric Technique: a Full-Field Strain Gauge,” Appl. Opt. 14, 618 (1975).
[CrossRef]

Duffy, D. E.

D. E. Duffy, “Moiré Gauging of In-Plane Displacement Using Double Aperture Imaging,” Appl. Opt. 11, 17781 (1972).
[CrossRef] [PubMed]

Durelli, A. J.

Y. Y. Hung, A. J. Durelli, “Simultaneous Measurement of Three Displacement Derivatives Using a Multiple Image Shearing Interferometric Camera,” J. Strain Anal. 14, 81 (1979).
[CrossRef]

Ennos, A. E.

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

Hariharan, P.

Hogan, D. C.

P. L. Baker, D. C. Hogan, G. J. Troup, R. G. Turner, “The Variation of Speckle Size with Film Density: An Example of Babinet’s Principle,” Opt. Commun. 29, 265 (1979).
[CrossRef]

Hung, Y. Y.

Y. Y. Hung, A. J. Durelli, “Simultaneous Measurement of Three Displacement Derivatives Using a Multiple Image Shearing Interferometric Camera,” J. Strain Anal. 14, 81 (1979).
[CrossRef]

Y. Y. Hung, C. Y. Liang, “Image-Shearing Camera for Direct Measurement of Surface Strains,” Appl. Opt. 18, 1046 (1979).
[CrossRef] [PubMed]

Y. Y. Hung, I. M. Daniel, R. E. Rowlands, “Full-Field Optical Strain Measurement Having Post Recording Sensitivity and Direction Selectivity,” Exp. Mech. 18, 56 (1978).
[CrossRef]

Y. Y. Hung, C. E. Taylor, “Measurement of Slopes of Structural Deflections by Speckle Shearing Interferometry,” Exp. Mech. 14, 281 (1974).
[CrossRef]

Joenathan, C.

R. K. Mohanty, C. Joenathan, R. S. Sirohi, “Speckle Shear Interferometry by Double Dove Prism,” Opt. Commun. 47, 27 (1983).
[CrossRef]

C. Joenathan, R. K. Mohanty, R. S. Sirohi, “Multiplexing in Speckle Shear Interferometry,” to appear in Opt. Acta (1984).
[CrossRef]

C. Joenathan, R. K. Mohanty, R. S. Sirohi, “On Methods of Multiplexing in Speckle Shear Interferometry,” to appear in Optik (1985).

Juang, R. M.

Kothiyal, M. P.

Krishna Murthy, R.

Leendertz, J. A.

J. A. Leendertz, J. N. Butters, “An Image of Shearing Speckle Pattern Interferometer for Measuring Bending Moments,” J. Phys. E 6, 1107 (1973).
[CrossRef]

Liang, C. Y.

Mohanty, R. K.

R. K. Mohanty, C. Joenathan, R. S. Sirohi, “Speckle Shear Interferometry by Double Dove Prism,” Opt. Commun. 47, 27 (1983).
[CrossRef]

C. Joenathan, R. K. Mohanty, R. S. Sirohi, “Multiplexing in Speckle Shear Interferometry,” to appear in Opt. Acta (1984).
[CrossRef]

C. Joenathan, R. K. Mohanty, R. S. Sirohi, “On Methods of Multiplexing in Speckle Shear Interferometry,” to appear in Optik (1985).

Rowlands, R. E.

Y. Y. Hung, I. M. Daniel, R. E. Rowlands, “Full-Field Optical Strain Measurement Having Post Recording Sensitivity and Direction Selectivity,” Exp. Mech. 18, 56 (1978).
[CrossRef]

Y. Y. Yung, R. E. Rowlands, I. M. Daniel, “Speckle-Shearing Inteferometric Technique: a Full-Field Strain Gauge,” Appl. Opt. 14, 618 (1975).
[CrossRef]

Sharma, D. K.

Sirohi, R. S.

D. K. Sharma, R. S. Sirohi, M. P. Kothiyal, “Simultaneous Measurement of Slope and Curvature with a Three-Aperture Speckle Shearing Interferometer,” Appl. Opt. 23, 1542 (1984).
[CrossRef] [PubMed]

R. K. Mohanty, C. Joenathan, R. S. Sirohi, “Speckle Shear Interferometry by Double Dove Prism,” Opt. Commun. 47, 27 (1983).
[CrossRef]

R. Krishna Murthy, R. S. Sirohi, M. P. Kothiyal, “Speckle Shearing Interferometry: a New Method,” Appl. Opt. 21, 2865 (1982).

C. Joenathan, R. K. Mohanty, R. S. Sirohi, “On Methods of Multiplexing in Speckle Shear Interferometry,” to appear in Optik (1985).

C. Joenathan, R. K. Mohanty, R. S. Sirohi, “Multiplexing in Speckle Shear Interferometry,” to appear in Opt. Acta (1984).
[CrossRef]

Taylor, C. E.

Y. Y. Hung, C. E. Taylor, “Measurement of Slopes of Structural Deflections by Speckle Shearing Interferometry,” Exp. Mech. 14, 281 (1974).
[CrossRef]

Troup, G. J.

P. L. Baker, D. C. Hogan, G. J. Troup, R. G. Turner, “The Variation of Speckle Size with Film Density: An Example of Babinet’s Principle,” Opt. Commun. 29, 265 (1979).
[CrossRef]

Turner, R. G.

P. L. Baker, D. C. Hogan, G. J. Troup, R. G. Turner, “The Variation of Speckle Size with Film Density: An Example of Babinet’s Principle,” Opt. Commun. 29, 265 (1979).
[CrossRef]

Yung, Y. Y.

Appl. Opt.

Exp. Mech.

Y. Y. Hung, C. E. Taylor, “Measurement of Slopes of Structural Deflections by Speckle Shearing Interferometry,” Exp. Mech. 14, 281 (1974).
[CrossRef]

Y. Y. Hung, I. M. Daniel, R. E. Rowlands, “Full-Field Optical Strain Measurement Having Post Recording Sensitivity and Direction Selectivity,” Exp. Mech. 18, 56 (1978).
[CrossRef]

J. Phys. E

J. A. Leendertz, J. N. Butters, “An Image of Shearing Speckle Pattern Interferometer for Measuring Bending Moments,” J. Phys. E 6, 1107 (1973).
[CrossRef]

J. Strain Anal.

Y. Y. Hung, A. J. Durelli, “Simultaneous Measurement of Three Displacement Derivatives Using a Multiple Image Shearing Interferometric Camera,” J. Strain Anal. 14, 81 (1979).
[CrossRef]

Opt. Acta

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

Opt. Commun.

P. L. Baker, D. C. Hogan, G. J. Troup, R. G. Turner, “The Variation of Speckle Size with Film Density: An Example of Babinet’s Principle,” Opt. Commun. 29, 265 (1979).
[CrossRef]

R. K. Mohanty, C. Joenathan, R. S. Sirohi, “Speckle Shear Interferometry by Double Dove Prism,” Opt. Commun. 47, 27 (1983).
[CrossRef]

Other

R. Krishna Murthy, Ph.D. Thesis, IIT, Madras, India (1983).

C. Joenathan, R. K. Mohanty, R. S. Sirohi, “Multiplexing in Speckle Shear Interferometry,” to appear in Opt. Acta (1984).
[CrossRef]

C. Joenathan, R. K. Mohanty, R. S. Sirohi, “On Methods of Multiplexing in Speckle Shear Interferometry,” to appear in Optik (1985).

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Figures (4)

Fig. 1
Fig. 1

Photograph of (∂w/∂x) fringes for an edge-clamped centrally loaded rectangular diaphragm obtained by filtering at a first-order halo under linear recording.

Fig. 2
Fig. 2

(a) FT plane halo distribution for a nonlinear specklegram showing halos up to the third order. (b), (c) Slope patterns for the rectangular diaphragm obtained by filtering at the second- and third-order halos showing fringe sharpening relative to Fig. 1.

Fig. 3
Fig. 3

(a) Schematic of the three-aperture arrangement. (b), (c) FT plane halo distributions corresponding to the three-aperture arrangement for linear and nonlinear recordings, respectively.

Fig. 4
Fig. 4

Moiré curvature fringes for an edge-clamped centrally loaded circular diaphragm obtained by filtering at the addition frequency halo centered at μ ¯ 12 + μ ¯ 32.

Equations (12)

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I = I 1 + I 2 = 2 a 1 2 + 2 a 2 2 + 4 a 1 a 2 cos ( δ 12 2 ) cos ( ϕ 12 + δ 12 2 ) ,
t = t 0 - β I + γ I 2 ,
I 2 = a 2 + C 1 cos 2 δ 12 2 [ 1 + cos ( 2 ϕ 12 + δ 12 ) ] + C 2 cos 12 2 cos ( ϕ 12 + δ 12 2 ) ,
a = 2 ( a 1 2 + a 2 2 ) , C 1 = 8 a 1 2 a 2 2 , C 2 = 8 a a 1 a 2 .
t = t 1 - C 3 cos δ 12 2 cos ( ϕ 12 + δ 12 2 ) + C 1 cos 2 δ 12 2 cos ( 2 ϕ 12 + δ 12 ) ,
t 1 = t 0 - β a + γ a 2 + γ C 1 cos 2 δ 12 / 2 ,
C 3 = 4 β a 1 a 2 - γ C 2 .
I 1 = a 1 exp ( i ϕ 1 ) + a 2 exp ( i ϕ 2 ) + a 3 exp ( i ϕ 3 ) 2 , I 2 = a 1 exp [ i ( ϕ 1 + δ 1 ) ] + a 2 exp [ i ( ϕ 2 + δ 2 ) ] + a 3 exp [ i ( ϕ 3 + δ 3 ) ] 2 ,
I = A + B + C + D ,
A = 2 ( a 1 2 + a 2 2 + a 3 2 ) , B = 4 a 1 a 2 cos ( δ 12 2 ) cos ( ϕ 12 + δ 12 2 ) , C = 4 a 1 a 3 cos ( δ 13 2 ) cos ( ϕ 13 + δ 13 2 ) , D = 4 a 2 a 3 cos ( ϕ 23 2 ) cos ( ϕ 23 + δ 23 2 ) , ϕ i j = ϕ i - ϕ j , δ i j = δ i - δ j .
t = t 0 - β ( A + B + C + D ) + γ [ A 2 + B 2 + C 2 + D 2 + 2 A ( B + C + D ) + 2 B C + 2 C D + 2 B D ] .
B D = 8 a 1 a 2 2 a 3 cos δ 12 2 cos δ 23 2 { cos [ ( ϕ 12 - ϕ 23 ) + δ 12 - δ 23 2 ] + cos [ ( ϕ 12 + ϕ 23 ) + δ 12 + δ 23 2 ] } .

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