Abstract

We present a novel optical configuration that yields a fringe pattern that represents the slope changes of a three-dimensional object with a twofold increase in sensitivity. The method offers controllable sensitivity over a wide range. We accomplish it by modifying the in-plane displacement sensitive configuration of speckle interferometry. The detailed theory and the experimental results are presented with a brief discussion on the limiting aspects of the configuration.

© 1998 Optical Society of America

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References

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  1. Y. Y. Hung, J. L. Turner, M. Tafralian, J. D. Hovanesian, C. E. Taylor, “Optical methods for measuring contour slopes of an object,” Appl. Opt. 17, 128–131 (1978).
    [CrossRef] [PubMed]
  2. R. S. Sirohi, ed., Speckle Metrology (Marcel Dekker, New York, 1993).
  3. A. R. Ganesan, R. S. Sirohi, “New method of contouring using digital speckle pattern interferometry,” in Optical Testing and Metrology II, C. Grover, ed., Proc. SPIE954, 327–332 (1988).
    [CrossRef]
  4. P. K. Rastogi, “A two-aperture dual source speckle interferometry for the measurement of the angular variations of a three-dimensional surface,” Opt. Laser Technol. 26, 195–197 (1994).
    [CrossRef]
  5. P. K. Rastogi, “Slope change contouring of a three-dimensional object using speckle interferometry,” Opt. Commun. 108, 37–41 (1994).
    [CrossRef]
  6. T. Santhanakrishnan, N. Krishna Mohan, P. Senthilkumaran, R. S. Sirohi, “Slope change contouring for 3D deeply curved objects by multi-aperture speckle shear interferometry,” Optik 104, 27–31 (1996).
  7. R. S. Sirohi, N. Krishna Mohan, “In-plane displacement measurement configuration with two-fold sensitivity,” Appl. Opt. 32, 6387–6390 (1993).
    [CrossRef] [PubMed]
  8. T. Santhanakrishnan, N. Krishna Mohan, R. S. Sirohi, “Oblique observation speckle shear interferometers for slope change contouring,” J. Mod. Opt. 44, 831–839 (1997).
    [CrossRef]
  9. A. Sohmer, C. Joenathan, “Two-fold increase in sensitivity with a dual-beam illumination arrangement for electronic speckle pattern interferometry,” Opt. Eng. 35, 1943–1948 (1996).
    [CrossRef]

1997 (1)

T. Santhanakrishnan, N. Krishna Mohan, R. S. Sirohi, “Oblique observation speckle shear interferometers for slope change contouring,” J. Mod. Opt. 44, 831–839 (1997).
[CrossRef]

1996 (2)

A. Sohmer, C. Joenathan, “Two-fold increase in sensitivity with a dual-beam illumination arrangement for electronic speckle pattern interferometry,” Opt. Eng. 35, 1943–1948 (1996).
[CrossRef]

T. Santhanakrishnan, N. Krishna Mohan, P. Senthilkumaran, R. S. Sirohi, “Slope change contouring for 3D deeply curved objects by multi-aperture speckle shear interferometry,” Optik 104, 27–31 (1996).

1994 (2)

P. K. Rastogi, “A two-aperture dual source speckle interferometry for the measurement of the angular variations of a three-dimensional surface,” Opt. Laser Technol. 26, 195–197 (1994).
[CrossRef]

P. K. Rastogi, “Slope change contouring of a three-dimensional object using speckle interferometry,” Opt. Commun. 108, 37–41 (1994).
[CrossRef]

1993 (1)

1978 (1)

Ganesan, A. R.

A. R. Ganesan, R. S. Sirohi, “New method of contouring using digital speckle pattern interferometry,” in Optical Testing and Metrology II, C. Grover, ed., Proc. SPIE954, 327–332 (1988).
[CrossRef]

Hovanesian, J. D.

Hung, Y. Y.

Joenathan, C.

A. Sohmer, C. Joenathan, “Two-fold increase in sensitivity with a dual-beam illumination arrangement for electronic speckle pattern interferometry,” Opt. Eng. 35, 1943–1948 (1996).
[CrossRef]

Krishna Mohan, N.

T. Santhanakrishnan, N. Krishna Mohan, R. S. Sirohi, “Oblique observation speckle shear interferometers for slope change contouring,” J. Mod. Opt. 44, 831–839 (1997).
[CrossRef]

T. Santhanakrishnan, N. Krishna Mohan, P. Senthilkumaran, R. S. Sirohi, “Slope change contouring for 3D deeply curved objects by multi-aperture speckle shear interferometry,” Optik 104, 27–31 (1996).

R. S. Sirohi, N. Krishna Mohan, “In-plane displacement measurement configuration with two-fold sensitivity,” Appl. Opt. 32, 6387–6390 (1993).
[CrossRef] [PubMed]

Rastogi, P. K.

P. K. Rastogi, “A two-aperture dual source speckle interferometry for the measurement of the angular variations of a three-dimensional surface,” Opt. Laser Technol. 26, 195–197 (1994).
[CrossRef]

P. K. Rastogi, “Slope change contouring of a three-dimensional object using speckle interferometry,” Opt. Commun. 108, 37–41 (1994).
[CrossRef]

Santhanakrishnan, T.

T. Santhanakrishnan, N. Krishna Mohan, R. S. Sirohi, “Oblique observation speckle shear interferometers for slope change contouring,” J. Mod. Opt. 44, 831–839 (1997).
[CrossRef]

T. Santhanakrishnan, N. Krishna Mohan, P. Senthilkumaran, R. S. Sirohi, “Slope change contouring for 3D deeply curved objects by multi-aperture speckle shear interferometry,” Optik 104, 27–31 (1996).

Senthilkumaran, P.

T. Santhanakrishnan, N. Krishna Mohan, P. Senthilkumaran, R. S. Sirohi, “Slope change contouring for 3D deeply curved objects by multi-aperture speckle shear interferometry,” Optik 104, 27–31 (1996).

Sirohi, R. S.

T. Santhanakrishnan, N. Krishna Mohan, R. S. Sirohi, “Oblique observation speckle shear interferometers for slope change contouring,” J. Mod. Opt. 44, 831–839 (1997).
[CrossRef]

T. Santhanakrishnan, N. Krishna Mohan, P. Senthilkumaran, R. S. Sirohi, “Slope change contouring for 3D deeply curved objects by multi-aperture speckle shear interferometry,” Optik 104, 27–31 (1996).

R. S. Sirohi, N. Krishna Mohan, “In-plane displacement measurement configuration with two-fold sensitivity,” Appl. Opt. 32, 6387–6390 (1993).
[CrossRef] [PubMed]

A. R. Ganesan, R. S. Sirohi, “New method of contouring using digital speckle pattern interferometry,” in Optical Testing and Metrology II, C. Grover, ed., Proc. SPIE954, 327–332 (1988).
[CrossRef]

Sohmer, A.

A. Sohmer, C. Joenathan, “Two-fold increase in sensitivity with a dual-beam illumination arrangement for electronic speckle pattern interferometry,” Opt. Eng. 35, 1943–1948 (1996).
[CrossRef]

Tafralian, M.

Taylor, C. E.

Turner, J. L.

Appl. Opt. (2)

J. Mod. Opt. (1)

T. Santhanakrishnan, N. Krishna Mohan, R. S. Sirohi, “Oblique observation speckle shear interferometers for slope change contouring,” J. Mod. Opt. 44, 831–839 (1997).
[CrossRef]

Opt. Commun. (1)

P. K. Rastogi, “Slope change contouring of a three-dimensional object using speckle interferometry,” Opt. Commun. 108, 37–41 (1994).
[CrossRef]

Opt. Eng. (1)

A. Sohmer, C. Joenathan, “Two-fold increase in sensitivity with a dual-beam illumination arrangement for electronic speckle pattern interferometry,” Opt. Eng. 35, 1943–1948 (1996).
[CrossRef]

Opt. Laser Technol. (1)

P. K. Rastogi, “A two-aperture dual source speckle interferometry for the measurement of the angular variations of a three-dimensional surface,” Opt. Laser Technol. 26, 195–197 (1994).
[CrossRef]

Optik (1)

T. Santhanakrishnan, N. Krishna Mohan, P. Senthilkumaran, R. S. Sirohi, “Slope change contouring for 3D deeply curved objects by multi-aperture speckle shear interferometry,” Optik 104, 27–31 (1996).

Other (2)

R. S. Sirohi, ed., Speckle Metrology (Marcel Dekker, New York, 1993).

A. R. Ganesan, R. S. Sirohi, “New method of contouring using digital speckle pattern interferometry,” in Optical Testing and Metrology II, C. Grover, ed., Proc. SPIE954, 327–332 (1988).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Experimental arrangement for slope change contouring with a two-fold increase in sensitivity.

Fig. 2
Fig. 2

Partial x-slope fringes obtained when filtered through one of the first-order halos for an angle of rotation ψ = 0.33 mrad.

Fig. 3
Fig. 3

Experimental arrangement for an oblique observation speckle shear interferometer.

Fig. 4
Fig. 4

Partial x-slope fringes obtained when Fig. 3 for ψ = 0.33 mrad is used.

Equations (8)

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I = 2 I 1 + I 2 + 2 I 1 I 2 1 / 2 cos ϕ 21 + 2 π μ x + δ 21 2 cos δ 21 2 ,
δ 21 = - 2 K · L x   Δ x o .
δ 21 = 4 π λ u x sin   θ + w x cos   θ Δ x o .
u = z ψ ,     u x = z x ψ ,     w = x ψ ,     w x = constant .
δ 21 = 4 π λ ψ   z x   Δ x o sin   θ ,
4 π λ ψ   z x   Δ x o sin   θ = 2 m π ,
z x = m λ 2 ψ Δ x o sin   θ .
Δ z x = λ 2 ψ Δ x o sin   θ .

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