Abstract

A speckle shear interferometer is presented which can be used to yield lateral, radial, rotational, and inversion shear fringes in real time in conjunction with a digital image processing system. A modification of the optical arrangement yields reversal or folding shear as well. Experiments are conducted on an edge-clamped diaphragm with concentrated load. Unit contrast fringes have been obtained by resorting to nonlinear processing techniques such as level slicing. The results are presented for various types of shear.

© 1988 Optical Society of America

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References

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  1. R. S. Sirohi, “Speckle Shear Interferometry—A Review,” J. Opt. India 13, 95 (1984).
  2. R. S. Sirohi, “Speckle Shear Interferometry,” Opt. Laser Technol. 16, 251 (1984).
    [CrossRef]
  3. J. A. Leendertz, J. N. Butters, “An Image Shearing-Speckle Pattern Interferometer for Measuring Bending Moments,” J. Phys. E 6, 1107 (1973).
    [CrossRef]
  4. R. Krishnamurthy, R. K. Mohanty, R. S. Sirohi, M. P. Kothiyal, “Radial Speckle Shearing Interferometer and Its Engineering Applications,” Optik 67, 85 (1984).
  5. R. K. Mohanty, C. Joenathan, R. S. Sirohi, “Speckle-Shear Interferometry with Double Dove-Prisms,” Opt. Commun. 47, 27 (1983).
    [CrossRef]
  6. R. K. Mohanty, C. Joenathan, R. S. Sirohi, “High Sensitivity Tilt Measurement by Speckle Shear Interferometry,” Appl. Opt. 25, 1661 (1986).
    [CrossRef] [PubMed]
  7. S. Nakadate, T. Yatagai, H. Saito, “Digital Speckle-Pattern Shearing Interferometry,” Appl. Opt. 19, 4241 (1980).
    [CrossRef] [PubMed]
  8. R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U.P., London, 1983).
  9. S. Nakadate, T. Yatagai, H. Saito, “Electronic Speckle Pattern Interferometry Using Digital Image Processing Techniques,” Appl. Opt. 19, 1879 (1980).
    [CrossRef] [PubMed]

1986 (1)

1984 (3)

R. S. Sirohi, “Speckle Shear Interferometry—A Review,” J. Opt. India 13, 95 (1984).

R. S. Sirohi, “Speckle Shear Interferometry,” Opt. Laser Technol. 16, 251 (1984).
[CrossRef]

R. Krishnamurthy, R. K. Mohanty, R. S. Sirohi, M. P. Kothiyal, “Radial Speckle Shearing Interferometer and Its Engineering Applications,” Optik 67, 85 (1984).

1983 (1)

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

1980 (2)

1973 (1)

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

Butters, J. N.

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

Joenathan, C.

R. K. Mohanty, C. Joenathan, R. S. Sirohi, “High Sensitivity Tilt Measurement by Speckle Shear Interferometry,” Appl. Opt. 25, 1661 (1986).
[CrossRef] [PubMed]

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

Jones, R.

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U.P., London, 1983).

Kothiyal, M. P.

R. Krishnamurthy, R. K. Mohanty, R. S. Sirohi, M. P. Kothiyal, “Radial Speckle Shearing Interferometer and Its Engineering Applications,” Optik 67, 85 (1984).

Krishnamurthy, R.

R. Krishnamurthy, R. K. Mohanty, R. S. Sirohi, M. P. Kothiyal, “Radial Speckle Shearing Interferometer and Its Engineering Applications,” Optik 67, 85 (1984).

Leendertz, J. A.

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

Mohanty, R. K.

R. K. Mohanty, C. Joenathan, R. S. Sirohi, “High Sensitivity Tilt Measurement by Speckle Shear Interferometry,” Appl. Opt. 25, 1661 (1986).
[CrossRef] [PubMed]

R. Krishnamurthy, R. K. Mohanty, R. S. Sirohi, M. P. Kothiyal, “Radial Speckle Shearing Interferometer and Its Engineering Applications,” Optik 67, 85 (1984).

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

Nakadate, S.

Saito, H.

Sirohi, R. S.

R. K. Mohanty, C. Joenathan, R. S. Sirohi, “High Sensitivity Tilt Measurement by Speckle Shear Interferometry,” Appl. Opt. 25, 1661 (1986).
[CrossRef] [PubMed]

R. Krishnamurthy, R. K. Mohanty, R. S. Sirohi, M. P. Kothiyal, “Radial Speckle Shearing Interferometer and Its Engineering Applications,” Optik 67, 85 (1984).

R. S. Sirohi, “Speckle Shear Interferometry,” Opt. Laser Technol. 16, 251 (1984).
[CrossRef]

R. S. Sirohi, “Speckle Shear Interferometry—A Review,” J. Opt. India 13, 95 (1984).

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

Wykes, C.

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U.P., London, 1983).

Yatagai, T.

Appl. Opt. (3)

J. Opt. India (1)

R. S. Sirohi, “Speckle Shear Interferometry—A Review,” J. Opt. India 13, 95 (1984).

J. Phys. E (1)

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

Opt. Commun. (1)

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

Opt. Laser Technol. (1)

R. S. Sirohi, “Speckle Shear Interferometry,” Opt. Laser Technol. 16, 251 (1984).
[CrossRef]

Optik (1)

R. Krishnamurthy, R. K. Mohanty, R. S. Sirohi, M. P. Kothiyal, “Radial Speckle Shearing Interferometer and Its Engineering Applications,” Optik 67, 85 (1984).

Other (1)

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U.P., London, 1983).

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Figures (8)

Fig. 1
Fig. 1

Schematic of the shearing interferometer.

Fig. 2
Fig. 2

Lateral shear slope fringes obtained for an edge-clamped rectangular diaphragm centrally loaded: (a) (∂w)/(∂x) contours; (b) (∂w)/(∂y) contours; (c) [(∂w)/(∂x)]45° contours.

Fig. 3
Fig. 3

Radial shear fringes depicting contours of r[(∂w)/(∂r)] for a centrally loaded circular diaphragm.

Fig. 4
Fig. 4

Rotational shear fringes depicting contours of (∂w)/(∂θ) for an eccentrically loaded circular diaphragm.

Fig. 5
Fig. 5

Fringes obtained with inversion shear for an eccentrically loaded circular diaphragm: (a) small load and (b) larger load. Point of loading on the diaphragm is marked X.

Fig. 6
Fig. 6

Schematic of the modified optical arrangement for reversal shear. P 2 P 1 , is the image of the object P1P2 formed through mirror M while P 1 P 2 is the image formed through prism A.

Fig. 7
Fig. 7

Fringes obtained with reversal shear for an eccentrically loaded circular diaphragm: (a) small load and (b) larger load. Point of loading on the diaphragm is marked X.

Fig. 8
Fig. 8

High sensitivity tilt fringes obtained with the folding shear configuration.

Equations (7)

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Δ I = I 1 - I 2 = 4 I 1 I 2 sin ( θ + δ 2 ) sin δ 2 ,
δ = 4 π λ w x Δ x 0 ,
δ r = - ( 1 - M 1 M 2 ) r
δ = - 4 π λ w r δ r ,
δ = - 4 π λ w θ δ θ ,
δ = 4 π λ δ w ,
δ = 4 π λ δ w ,

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