Abstract

We propose a single-shot phase-unwrapping method using two wavelengths in parallel phase-shifting digital holography (PPSDH). The proposed method enables one to solve the phase ambiguity problem in PPSDH. We conducted an experiment of the proposed method using two lasers whose wavelengths are 473 and 532 nm. An object having about 1.9 μm step, which is 7.1 times larger than the half wavelength of one of the lasers (266 nm), was fabricated by using vapor deposition of aluminum. Single-shot measurement of the height of the object was successfully demonstrated, and the validity of the proposed method was verified.

© 2014 Optical Society of America

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2013 (1)

2012 (1)

2011 (4)

2009 (1)

S. Murata, D. Harada, and Y. Tanaka, Jpn. J. Appl. Phys. 48, 09LB01 (2009).

2008 (1)

2007 (1)

2006 (3)

2004 (1)

Y. Awatsuji, M. Sasada, and T. Kubota, Appl. Phys. Lett. 85, 1069 (2004).
[CrossRef]

2003 (1)

2001 (2)

E. Tajahuerce, O. Matoba, and B. Javidi, Appl. Opt. 40, 3877 (2001).
[CrossRef]

I. Yamaguchi, J. Kato, and S. Ohta, Opt. Rev. 8, 85 (2001).
[CrossRef]

2000 (1)

1997 (1)

1994 (2)

1988 (1)

R. M. Goldstein, H. A. Zebker, and C. L. Werner, Radio Sci. 23, 713 (1988).
[CrossRef]

1982 (1)

1972 (1)

1967 (1)

J. W. Goodman and R. W. Lawrence, Appl. Phys. Lett. 11, 77 (1967).
[CrossRef]

Adachi, T.

Awatsuji, Y.

Charrière, F.

Colomb, T.

Cuche, E.

Dakoff, A.

de la Torre-Ibarra, M.

Depeursinge, C.

Emery, Y.

Endo, Y.

Fujii, A.

Gass, J.

Ghiglia, D. C.

Goldstein, R. M.

R. M. Goldstein, H. A. Zebker, and C. L. Werner, Radio Sci. 23, 713 (1988).
[CrossRef]

Goodman, J. W.

J. W. Goodman and R. W. Lawrence, Appl. Phys. Lett. 11, 77 (1967).
[CrossRef]

Harada, D.

S. Murata, D. Harada, and Y. Tanaka, Jpn. J. Appl. Phys. 48, 09LB01 (2009).

Hirayama, R.

Ichioka, Y.

Ida, T.

Inoue, J.

Y. Lee, Y. Ito, T. Tahara, J. Inoue, P. Xia, Y. Awatsuji, K. Nishio, S. Ura, and O. Matoba, in, Proceedings of the 2013 IEEE/SICE International Symposium on System Integration (IEEE, 2013), pp. 592–597.

Inuiya, M.

Ito, T.

Ito, Y.

Y. Lee, Y. Ito, T. Tahara, J. Inoue, P. Xia, Y. Awatsuji, K. Nishio, S. Ura, and O. Matoba, in, Proceedings of the 2013 IEEE/SICE International Symposium on System Integration (IEEE, 2013), pp. 592–597.

Itoh, K.

Javidi, B.

Kakue, T.

Kaneko, A.

Kato, J.

I. Yamaguchi, J. Kato, and S. Ohta, Opt. Rev. 8, 85 (2001).
[CrossRef]

Kim, M. K.

Kim, N.

A. Phan, J. Park, and N. Kim, Jpn. J. Appl. Phys. 50, 092503 (2011).

Koyama, T.

Kubota, T.

Kühn, J.

Lawrence, R. W.

J. W. Goodman and R. W. Lawrence, Appl. Phys. Lett. 11, 77 (1967).
[CrossRef]

Lee, B.

Lee, S.

Lee, Y.

Y. Lee, Y. Ito, T. Tahara, J. Inoue, P. Xia, Y. Awatsuji, K. Nishio, S. Ura, and O. Matoba, in, Proceedings of the 2013 IEEE/SICE International Symposium on System Integration (IEEE, 2013), pp. 592–597.

Lim, Y.

Maeda, A.

Makowski, M.

Marquet, P.

Matoba, O.

Montfort, F.

Murata, S.

S. Murata, D. Harada, and Y. Tanaka, Jpn. J. Appl. Phys. 48, 09LB01 (2009).

Nishio, K.

Ohta, S.

I. Yamaguchi, J. Kato, and S. Ohta, Opt. Rev. 8, 85 (2001).
[CrossRef]

Ohtsuka, Y.

Oikawa, M.

Oka, K.

Okada, N.

Osten, W.

Park, J.

A. Phan, J. Park, and N. Kim, Jpn. J. Appl. Phys. 50, 092503 (2011).

Pedrini, G.

Phan, A.

A. Phan, J. Park, and N. Kim, Jpn. J. Appl. Phys. 50, 092503 (2011).

Romero, L. A.

Santoyo, F. M.

Sasada, M.

Y. Awatsuji, M. Sasada, and T. Kubota, Appl. Phys. Lett. 85, 1069 (2004).
[CrossRef]

Saucedo, A. T.

Shimobaba, T.

Tahara, T.

Tajahuerce, E.

Tanaka, Y.

S. Murata, D. Harada, and Y. Tanaka, Jpn. J. Appl. Phys. 48, 09LB01 (2009).

Ura, S.

Werner, C. L.

R. M. Goldstein, H. A. Zebker, and C. L. Werner, Radio Sci. 23, 713 (1988).
[CrossRef]

Xia, P.

T. Tahara, A. Maeda, Y. Awatsuji, T. Kakue, P. Xia, K. Nishio, S. Ura, T. Kubota, and O. Matoba, Opt. Lett. 37, 4002 (2012).
[CrossRef]

Y. Lee, Y. Ito, T. Tahara, J. Inoue, P. Xia, Y. Awatsuji, K. Nishio, S. Ura, and O. Matoba, in, Proceedings of the 2013 IEEE/SICE International Symposium on System Integration (IEEE, 2013), pp. 592–597.

Yamaguchi, I.

Yamashita, K.

Yokota, M.

Yonesaka, R.

Zebker, H. A.

R. M. Goldstein, H. A. Zebker, and C. L. Werner, Radio Sci. 23, 713 (1988).
[CrossRef]

Zhang, T.

Appl. Opt. (8)

Appl. Phys. Lett. (2)

J. W. Goodman and R. W. Lawrence, Appl. Phys. Lett. 11, 77 (1967).
[CrossRef]

Y. Awatsuji, M. Sasada, and T. Kubota, Appl. Phys. Lett. 85, 1069 (2004).
[CrossRef]

J. Opt. Soc. Am. A (1)

Jpn. J. Appl. Phys. (2)

S. Murata, D. Harada, and Y. Tanaka, Jpn. J. Appl. Phys. 48, 09LB01 (2009).

A. Phan, J. Park, and N. Kim, Jpn. J. Appl. Phys. 50, 092503 (2011).

Opt. Express (4)

Opt. Lett. (5)

Opt. Rev. (1)

I. Yamaguchi, J. Kato, and S. Ohta, Opt. Rev. 8, 85 (2001).
[CrossRef]

Radio Sci. (1)

R. M. Goldstein, H. A. Zebker, and C. L. Werner, Radio Sci. 23, 713 (1988).
[CrossRef]

Other (1)

Y. Lee, Y. Ito, T. Tahara, J. Inoue, P. Xia, Y. Awatsuji, K. Nishio, S. Ura, and O. Matoba, in, Proceedings of the 2013 IEEE/SICE International Symposium on System Integration (IEEE, 2013), pp. 592–597.

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Figures (6)

Fig. 1.
Fig. 1.

Schematic of an example of the proposed method based on parallel four-step phase-shifting interferometry.

Fig. 2.
Fig. 2.

Schematics of an example of the optical setup of the proposed method.

Fig. 3.
Fig. 3.

Schematic of the image reconstruction algorithm of the proposed method.

Fig. 4.
Fig. 4.

Object. (a) Photograph of the object surface. (b) Enlarged photograph of (a). (c) AFM measurement result of the object.

Fig. 5.
Fig. 5.

Experimental results. Phase distribution at (a) λ1=473nm and (b) λ2=532nm. (c) Unwrapped image calculated from (a) and (b). (d) 3D rendering of the height distribution of the object. (e) Enlarged image of the portion of (d) corresponding to Fig. 4(c).

Fig. 6.
Fig. 6.

Space bandwidths. Proposed method using (a) parallel two-step phase-shifting interferometry and (b) angular multiplexing technique.

Equations (5)

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

ϕ1=(4π/λ1)h(x,y),
ϕ2=(4π/λ2)h(x,y),
h(x,y)=λe4π(ϕ1ϕ2),
λe=λ1λ2/|λ1λ2|,
Δhmax(x,y)=λe2=λ1λ22|λ1λ2|.

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