Abstract

This paper proposes a tilt sensor that measures the small two-dimensional tilt of a plane reflective object using the Talbot effect. It is an extension of a previously proposed one-dimensional tilt sensor. The light beam reflected from the object impinges on a hexagonal grating, and the intensity of the diffracted wave is detected on an image sensor located at a Talbot distance from the grating. The diffraction intensity displaces due to the tilt of the object. The displacement is calculated by the Fourier transform method to obtain the two-dimensional tilt. This sensor is very simple and compact. The principle of the sensor is explained for a grating with a general pattern. An experiment using a hexagonal grating shows its validity. Discussions are given for making it more practical.

© 2011 Optical Society of America

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2009

2006

T. Suzuki, T. Endo, O. Sasaki, and J. E. Greivenkamp, “Two-dimensional small-rotation-angle measurement using an imaging method,” Opt. Eng. 45, 043604 (2006).
[CrossRef]

2005

2003

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

J. Yuana and X. Long, “CCD-area-based autocollimator for precision small-angle measurement,” Rev. Sci. Instrum. 74, 1362–1365 (2003).
[CrossRef]

1997

M.-H. Chiu and D.-C. Su, “Angle measurement using total-internal-reflection heterodyne interferometry,” Opt. Eng. 36, 1750–1753 (1997).
[CrossRef]

1992

1965

Chiu, M.-H.

M.-H. Chiu and D.-C. Su, “Angle measurement using total-internal-reflection heterodyne interferometry,” Opt. Eng. 36, 1750–1753 (1997).
[CrossRef]

Endo, T.

T. Suzuki, T. Endo, O. Sasaki, and J. E. Greivenkamp, “Two-dimensional small-rotation-angle measurement using an imaging method,” Opt. Eng. 45, 043604 (2006).
[CrossRef]

Fukuda, H.

Ge, Z.

Greivenkamp, J. E.

T. Suzuki, T. Endo, O. Sasaki, and J. E. Greivenkamp, “Two-dimensional small-rotation-angle measurement using an imaging method,” Opt. Eng. 45, 043604 (2006).
[CrossRef]

Huang, P. S.

Iwata, K.

K. Iwata, H. Fukuda, and K. Moriwaki, “Transmission-grating-based wave-front tilt sensor,” Appl. Opt. 48, 3961–3966 (2009).
[CrossRef]

K. Iwata, K. Satoh, and K. Moriwaki, “Two-dimensional wave-front tilt sensor using a two-dimensional transmission grating,” in AIP Proceedings of the International Conference on Advanced Phase Measurement Methods in Optics and Imaging, P.K.Rastogi and E.Hack, eds. (AIP, 2010), Vol. 1236, pp. 254–258.

Kamada, O.

Kiyono, S.

Long, X.

J. Yuana and X. Long, “CCD-area-based autocollimator for precision small-angle measurement,” Rev. Sci. Instrum. 74, 1362–1365 (2003).
[CrossRef]

Moriwaki, K.

K. Iwata, H. Fukuda, and K. Moriwaki, “Transmission-grating-based wave-front tilt sensor,” Appl. Opt. 48, 3961–3966 (2009).
[CrossRef]

K. Iwata, K. Satoh, and K. Moriwaki, “Two-dimensional wave-front tilt sensor using a two-dimensional transmission grating,” in AIP Proceedings of the International Conference on Advanced Phase Measurement Methods in Optics and Imaging, P.K.Rastogi and E.Hack, eds. (AIP, 2010), Vol. 1236, pp. 254–258.

Prakash, S.

Rana, S.

Sasaki, O.

T. Suzuki, T. Endo, O. Sasaki, and J. E. Greivenkamp, “Two-dimensional small-rotation-angle measurement using an imaging method,” Opt. Eng. 45, 043604 (2006).
[CrossRef]

Satoh, K.

K. Iwata, K. Satoh, and K. Moriwaki, “Two-dimensional wave-front tilt sensor using a two-dimensional transmission grating,” in AIP Proceedings of the International Conference on Advanced Phase Measurement Methods in Optics and Imaging, P.K.Rastogi and E.Hack, eds. (AIP, 2010), Vol. 1236, pp. 254–258.

Singh, S.

Su, D.-C.

M.-H. Chiu and D.-C. Su, “Angle measurement using total-internal-reflection heterodyne interferometry,” Opt. Eng. 36, 1750–1753 (1997).
[CrossRef]

Suzuki, T.

T. Suzuki, T. Endo, O. Sasaki, and J. E. Greivenkamp, “Two-dimensional small-rotation-angle measurement using an imaging method,” Opt. Eng. 45, 043604 (2006).
[CrossRef]

Takeda, M.

Winthrop, J. T.

Worthington, C. R.

Yuana, J.

J. Yuana and X. Long, “CCD-area-based autocollimator for precision small-angle measurement,” Rev. Sci. Instrum. 74, 1362–1365 (2003).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am.

Opt. Eng.

M.-H. Chiu and D.-C. Su, “Angle measurement using total-internal-reflection heterodyne interferometry,” Opt. Eng. 36, 1750–1753 (1997).
[CrossRef]

T. Suzuki, T. Endo, O. Sasaki, and J. E. Greivenkamp, “Two-dimensional small-rotation-angle measurement using an imaging method,” Opt. Eng. 45, 043604 (2006).
[CrossRef]

Rev. Sci. Instrum.

J. Yuana and X. Long, “CCD-area-based autocollimator for precision small-angle measurement,” Rev. Sci. Instrum. 74, 1362–1365 (2003).
[CrossRef]

Other

K. Iwata, K. Satoh, and K. Moriwaki, “Two-dimensional wave-front tilt sensor using a two-dimensional transmission grating,” in AIP Proceedings of the International Conference on Advanced Phase Measurement Methods in Optics and Imaging, P.K.Rastogi and E.Hack, eds. (AIP, 2010), Vol. 1236, pp. 254–258.

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