Abstract

A technique for a tilt-angle measurement of reflecting objects based on the Lau interferometry coupled with the moiré readout has been proposed. A white-light incoherent source illuminates a set of two gratings, resulting in the generation of the Fresnel image due to the Lau effect. The Fresnel image is projected onto a reflecting object. The image reflected from the object is superimposed onto an identical grating, which results in the formation of a moiré fringe pattern. The inclination angle of moiré fringes is a function of tilt angle of the object. Theory and experimental arrangement of the proposed technique is presented and results of the investigation are reported.

© 2005 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]

2004 (1)

2003 (3)

Ge Zongtao, M. Takeda, “High-resolution 2D-angle measurement technique based on fringe analysis,” Appl. Opt. 42, 6859–6868 (2003).
[CrossRef]

O. Sasaki, C. Togashi, T. Suzuki, “Two-dimensional rotation angle measurement using a sinusoidal phase-modulating laser diode interferometer,” Opt. Eng. 42, 1132–1136 (2003).
[CrossRef]

M. Thakur, S. K. Angra, C. Shakher, “Measurement of the temperature profile of a two-dimensional slot burner using a Lau phase interferometer with linear gratings,” Opt. Eng. 42, 86–91 (2003).
[CrossRef]

2002 (1)

2001 (2)

T. Suzuki, H. Nakamura, O. Sasaki, J. E. Greivenkamp, “Small-rotation-angle measurement using an imaging method,” Opt. Eng. 40, 426–432 (2001).
[CrossRef]

K. S. Dharmsaktu, A. Kumar, K. Singh, “Measurement of tilt of a diffuse object by double-exposure speckle photography using speckle fanning in a photo refractive BaTiO3crystal,” Opt. Lasers Eng. 36, 331–344 (2001).
[CrossRef]

1998 (1)

R. Tripathi, G. S. Pati, A. Kumar, K. Singh, “Object tilt measurement using a photo-refractive speckle correlator: theoretical and experimental analysis,” Opt. Eng. 37, 2988–2997 (1998).
[CrossRef]

1997 (1)

1996 (1)

1993 (1)

1992 (1)

R. S. Sirohi, A. R. Ganesan, B. C. Tan, “Tilt measurement using digital speckle shear interferometry,” Opt. Laser Technol. 24, 257–261 (1992).
[CrossRef]

1990 (1)

T. Takano, S. Yonehara, “Basic investigations on an angle measurement system using a laser,” IEEE Trans. Aerosp. Electron. Syst. 26, 657–662 (1990).
[CrossRef]

1986 (1)

1984 (1)

K. Patorski, “Heuristic explanation of grating shearing interferometry using incoherent illumination,” Opt. Acta 31, 33–38 (1984).
[CrossRef]

1975 (1)

1970 (1)

Angra, S. K.

M. Thakur, S. K. Angra, C. Shakher, “Measurement of the temperature profile of a two-dimensional slot burner using a Lau phase interferometer with linear gratings,” Opt. Eng. 42, 86–91 (2003).
[CrossRef]

Chickvary, J. L.

Dai, X.

Dharmsaktu, K. S.

K. S. Dharmsaktu, A. Kumar, K. Singh, “Measurement of tilt of a diffuse object by double-exposure speckle photography using speckle fanning in a photo refractive BaTiO3crystal,” Opt. Lasers Eng. 36, 331–344 (2001).
[CrossRef]

Ganesan, A. R.

R. S. Sirohi, A. R. Ganesan, B. C. Tan, “Tilt measurement using digital speckle shear interferometry,” Opt. Laser Technol. 24, 257–261 (1992).
[CrossRef]

Greivenkamp, J. E.

T. Suzuki, H. Nakamura, O. Sasaki, J. E. Greivenkamp, “Small-rotation-angle measurement using an imaging method,” Opt. Eng. 40, 426–432 (2001).
[CrossRef]

X. Dai, O. Sasaki, J. E. Greivenkamp, T. Suzuki, “High accuracy, wide range, rotation angle measurement by the use of two parallel interference patterns,” Appl. Opt. 36, 6190–6195 (1997).
[CrossRef]

Hammam, H.

Harris, O.

Huang, P. S.

Kumar, A.

K. S. Dharmsaktu, A. Kumar, K. Singh, “Measurement of tilt of a diffuse object by double-exposure speckle photography using speckle fanning in a photo refractive BaTiO3crystal,” Opt. Lasers Eng. 36, 331–344 (2001).
[CrossRef]

R. Tripathi, G. S. Pati, A. Kumar, K. Singh, “Object tilt measurement using a photo-refractive speckle correlator: theoretical and experimental analysis,” Opt. Eng. 37, 2988–2997 (1998).
[CrossRef]

Malacara, D.

Murata, K.

Nakamura, H.

T. Suzuki, H. Nakamura, O. Sasaki, J. E. Greivenkamp, “Small-rotation-angle measurement using an imaging method,” Opt. Eng. 40, 426–432 (2001).
[CrossRef]

Nakano, Y.

Ni, J.

Pati, G. S.

R. Tripathi, G. S. Pati, A. Kumar, K. Singh, “Object tilt measurement using a photo-refractive speckle correlator: theoretical and experimental analysis,” Opt. Eng. 37, 2988–2997 (1998).
[CrossRef]

Patorski, K.

K. Patorski, “Heuristic explanation of grating shearing interferometry using incoherent illumination,” Opt. Acta 31, 33–38 (1984).
[CrossRef]

Prakash, S.

S. Singh, S. Rana, S. Prakash, “Design, development and performance evaluation of Lau based array illuminators,” presented at the International Conference on Photonics, International School of Photonics, Cochin, India, December 9–11, 2004.

Rana, S.

S. Singh, S. Rana, S. Prakash, “Design, development and performance evaluation of Lau based array illuminators,” presented at the International Conference on Photonics, International School of Photonics, Cochin, India, December 9–11, 2004.

Sasaki, O.

O. Sasaki, C. Togashi, T. Suzuki, “Two-dimensional rotation angle measurement using a sinusoidal phase-modulating laser diode interferometer,” Opt. Eng. 42, 1132–1136 (2003).
[CrossRef]

T. Suzuki, H. Nakamura, O. Sasaki, J. E. Greivenkamp, “Small-rotation-angle measurement using an imaging method,” Opt. Eng. 40, 426–432 (2001).
[CrossRef]

X. Dai, O. Sasaki, J. E. Greivenkamp, T. Suzuki, “High accuracy, wide range, rotation angle measurement by the use of two parallel interference patterns,” Appl. Opt. 36, 6190–6195 (1997).
[CrossRef]

Schlesinger, E. R.

Shakher, C.

M. Thakur, S. K. Angra, C. Shakher, “Measurement of the temperature profile of a two-dimensional slot burner using a Lau phase interferometer with linear gratings,” Opt. Eng. 42, 86–91 (2003).
[CrossRef]

M. Thakur, C. Shakher, “Evaluation of the focal distance of lenses by white light Lau phase interferometry,” Appl. Opt. 41, 1841–1845 (2002).
[CrossRef] [PubMed]

Shi, P.

Singh, K.

K. S. Dharmsaktu, A. Kumar, K. Singh, “Measurement of tilt of a diffuse object by double-exposure speckle photography using speckle fanning in a photo refractive BaTiO3crystal,” Opt. Lasers Eng. 36, 331–344 (2001).
[CrossRef]

R. Tripathi, G. S. Pati, A. Kumar, K. Singh, “Object tilt measurement using a photo-refractive speckle correlator: theoretical and experimental analysis,” Opt. Eng. 37, 2988–2997 (1998).
[CrossRef]

Singh, S.

S. Singh, S. Rana, S. Prakash, “Design, development and performance evaluation of Lau based array illuminators,” presented at the International Conference on Photonics, International School of Photonics, Cochin, India, December 9–11, 2004.

Sirohi, R. S.

R. S. Sirohi, A. R. Ganesan, B. C. Tan, “Tilt measurement using digital speckle shear interferometry,” Opt. Laser Technol. 24, 257–261 (1992).
[CrossRef]

Stijns, E.

Suzuki, T.

O. Sasaki, C. Togashi, T. Suzuki, “Two-dimensional rotation angle measurement using a sinusoidal phase-modulating laser diode interferometer,” Opt. Eng. 42, 1132–1136 (2003).
[CrossRef]

T. Suzuki, H. Nakamura, O. Sasaki, J. E. Greivenkamp, “Small-rotation-angle measurement using an imaging method,” Opt. Eng. 40, 426–432 (2001).
[CrossRef]

X. Dai, O. Sasaki, J. E. Greivenkamp, T. Suzuki, “High accuracy, wide range, rotation angle measurement by the use of two parallel interference patterns,” Appl. Opt. 36, 6190–6195 (1997).
[CrossRef]

Takano, T.

T. Takano, S. Yonehara, “Basic investigations on an angle measurement system using a laser,” IEEE Trans. Aerosp. Electron. Syst. 26, 657–662 (1990).
[CrossRef]

Takeda, M.

Tan, B. C.

R. S. Sirohi, A. R. Ganesan, B. C. Tan, “Tilt measurement using digital speckle shear interferometry,” Opt. Laser Technol. 24, 257–261 (1992).
[CrossRef]

Thakur, M.

M. Thakur, S. K. Angra, C. Shakher, “Measurement of the temperature profile of a two-dimensional slot burner using a Lau phase interferometer with linear gratings,” Opt. Eng. 42, 86–91 (2003).
[CrossRef]

M. Thakur, C. Shakher, “Evaluation of the focal distance of lenses by white light Lau phase interferometry,” Appl. Opt. 41, 1841–1845 (2002).
[CrossRef] [PubMed]

Togashi, C.

O. Sasaki, C. Togashi, T. Suzuki, “Two-dimensional rotation angle measurement using a sinusoidal phase-modulating laser diode interferometer,” Opt. Eng. 42, 1132–1136 (2003).
[CrossRef]

Tripathi, R.

R. Tripathi, G. S. Pati, A. Kumar, K. Singh, “Object tilt measurement using a photo-refractive speckle correlator: theoretical and experimental analysis,” Opt. Eng. 37, 2988–2997 (1998).
[CrossRef]

Yoder, P. R.

Yonehara, S.

T. Takano, S. Yonehara, “Basic investigations on an angle measurement system using a laser,” IEEE Trans. Aerosp. Electron. Syst. 26, 657–662 (1990).
[CrossRef]

Zongtao, Ge

Appl. Opt. (9)

IEEE Trans. Aerosp. Electron. Syst. (1)

T. Takano, S. Yonehara, “Basic investigations on an angle measurement system using a laser,” IEEE Trans. Aerosp. Electron. Syst. 26, 657–662 (1990).
[CrossRef]

Opt. Acta (1)

K. Patorski, “Heuristic explanation of grating shearing interferometry using incoherent illumination,” Opt. Acta 31, 33–38 (1984).
[CrossRef]

Opt. Eng. (4)

M. Thakur, S. K. Angra, C. Shakher, “Measurement of the temperature profile of a two-dimensional slot burner using a Lau phase interferometer with linear gratings,” Opt. Eng. 42, 86–91 (2003).
[CrossRef]

T. Suzuki, H. Nakamura, O. Sasaki, J. E. Greivenkamp, “Small-rotation-angle measurement using an imaging method,” Opt. Eng. 40, 426–432 (2001).
[CrossRef]

R. Tripathi, G. S. Pati, A. Kumar, K. Singh, “Object tilt measurement using a photo-refractive speckle correlator: theoretical and experimental analysis,” Opt. Eng. 37, 2988–2997 (1998).
[CrossRef]

O. Sasaki, C. Togashi, T. Suzuki, “Two-dimensional rotation angle measurement using a sinusoidal phase-modulating laser diode interferometer,” Opt. Eng. 42, 1132–1136 (2003).
[CrossRef]

Opt. Laser Technol. (1)

R. S. Sirohi, A. R. Ganesan, B. C. Tan, “Tilt measurement using digital speckle shear interferometry,” Opt. Laser Technol. 24, 257–261 (1992).
[CrossRef]

Opt. Lasers Eng. (1)

K. S. Dharmsaktu, A. Kumar, K. Singh, “Measurement of tilt of a diffuse object by double-exposure speckle photography using speckle fanning in a photo refractive BaTiO3crystal,” Opt. Lasers Eng. 36, 331–344 (2001).
[CrossRef]

Other (1)

S. Singh, S. Rana, S. Prakash, “Design, development and performance evaluation of Lau based array illuminators,” presented at the International Conference on Photonics, International School of Photonics, Cochin, India, December 9–11, 2004.

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram for measuring small tilt-angle variation using Lau phase interferometry.

Fig. 2
Fig. 2

Schematic diagram of the experimental arrangement for small tilt-angle measurement using Lau interferometry.

Fig. 3
Fig. 3

Image acquired directly by a CCD camera without any image processing operations.

Fig. 4
Fig. 4

Moiré fringe patterns obtained after undertaking image-processing operations for (a) α1 = 13.7° and (b) α2 = 21.9°.

Fig. 5
Fig. 5

Theoretical curves representing the relationship between the tilt angle δ of the object surface and the inclination angle α of the moiré fringes, corresponding to different values of crossed angle θ between the gratings.

Fig. 6
Fig. 6

Theoretical curves indicating variation of sensitivity |dα/dδ|, with the tilt angle of the object δ, for different values of the crossed angle θ.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

p = p cos 2 δ = p sin 2 δ .
p = p cos α 1 cos ( α 1 + θ ) .
sin 2 δ = cos ( α 1 + θ ) cos α 1 .
p = p sin 2 ( δ + Δ δ ) .
sin 2 ( δ + Δ δ ) = cos ( α 2 + θ ) cos α 2 .
Δ δ = 1 2 { sin - 1 [ cos ( α 2 + θ ) cos α 2 ] - sin - 1 [ cos ( α 1 + θ ) cos α 1 ] } .

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