Abstract

In this paper, we present a new scheme for parallel phase-shifting interferometry that employs a Michelson-like architecture and a simple polarization unit to generate two phase-shifting interferograms with phase shift of π/2 at a single camera exposure. The parallel phase-shifting unit is built with simple optical components, and the distance between the parallel interferograms can be adjusted conveniently. Phase reconstruction is performed by using an algorithm developed for two-step phase-shifting inter ferometry. The practicability of the proposed configuration and the reconstruction method is demonstrated by experiments.

© 2010 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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2010 (1)

L. Chen, S. Yeh, A. Tapilouw, and J. Chang, “3-D surface profilometry using simultaneous phase-shifting interferometry,” Opt. Commun. 283, 3376–3382 (2010).
[CrossRef]

2009 (1)

2008 (5)

2006 (1)

2004 (2)

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85, 1069–1071(2004).
[CrossRef]

2003 (2)

2002 (2)

J. A. Ferrari, E. M. Frins, and C. D. Perciante, “A new scheme for phase-shifting ESPI using polarized light,” Opt. Commun. 202, 233–237 (2002).
[CrossRef]

K. Chang, A. Hsu, and J. Chern, “Comment on ‘Phase-shifting shearing interferometer’,” Opt. Lett. 27, 509–510 (2002).
[CrossRef]

2001 (1)

1997 (1)

1996 (1)

1992 (1)

C. L. Koliopoulos, “Simultaneous phase shift interferometer,” Proc. SPIE 1531, 119–127 (1992).
[CrossRef]

1985 (1)

1984 (1)

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 361–364 (1984).

1974 (1)

Awatsuji, Y.

Brangaccio, D. J.

Brock, N.

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Bruning, J. H.

Burton, D. R.

Cai, L. Z.

Chang, J.

L. Chen, S. Yeh, A. Tapilouw, and J. Chang, “3-D surface profilometry using simultaneous phase-shifting interferometry,” Opt. Commun. 283, 3376–3382 (2010).
[CrossRef]

Chang, K.

Chen, L.

L. Chen, S. Yeh, A. Tapilouw, and J. Chang, “3-D surface profilometry using simultaneous phase-shifting interferometry,” Opt. Commun. 283, 3376–3382 (2010).
[CrossRef]

Chern, J.

Clegg, D. B.

Coppola, G.

De Nicola, S.

Dong, G. Y.

Ferrari, J. A.

J. A. Ferrari, E. M. Frins, and C. D. Perciante, “A new scheme for phase-shifting ESPI using polarized light,” Opt. Commun. 202, 233–237 (2002).
[CrossRef]

Ferraro, P.

Finizio, A.

Frins, E. M.

J. A. Ferrari, E. M. Frins, and C. D. Perciante, “A new scheme for phase-shifting ESPI using polarized light,” Opt. Commun. 202, 233–237 (2002).
[CrossRef]

Gallagher, J. E.

Grilli, S.

Hayes, J.

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Herraez, M. A.

Herriott, D. R.

Hsu, A.

Hui, W. K.

N. R. Sivakumar, W. K. Hui, K. Venkatakrishnan, and B. K. A. Ngoi, “Large surface profile measurement with instantaneous phase-shifting intferometry,” Opt. Eng. 42, 367–372 (2003).
[CrossRef]

Kaneko, A.

Kato, J.

Kiire, T.

Koliopoulos, C. L.

C. L. Koliopoulos, “Simultaneous phase shift interferometer,” Proc. SPIE 1531, 119–127 (1992).
[CrossRef]

Koyama, T.

Kubota, T.

Lalor, M. J.

Liu, J.-P.

Magro, C.

Matoba, O.

Meneses-Fabian, C.

Meng, X. F.

Millerd, J.

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Mizuno, J.

Moore, R.

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 361–364 (1984).

Nakadate, S.

Ngoi, B. K. A.

N. R. Sivakumar, W. K. Hui, K. Venkatakrishnan, and B. K. A. Ngoi, “Large surface profile measurement with instantaneous phase-shifting intferometry,” Opt. Eng. 42, 367–372 (2003).
[CrossRef]

Nishio, K.

North-Morris, M.

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Novak, M.

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Ohta, S.

Perciante, C. D.

J. A. Ferrari, E. M. Frins, and C. D. Perciante, “A new scheme for phase-shifting ESPI using polarized light,” Opt. Commun. 202, 233–237 (2002).
[CrossRef]

Pierattini, G.

Poon, T.-C.

Robledo-Sánchez, C.

Rodriguez-Zurita, G.

Rosenfeld, D. P.

Saito, H.

Sasada, M.

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85, 1069–1071(2004).
[CrossRef]

Schreiber, H.

H. Schreiber and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, 3rd ed., D.Malacara, ed. (Wiley, 2007), pp. 547–666.
[CrossRef]

Shen, X. X.

Shibuya, M.

Sivakumar, N. R.

N. R. Sivakumar, W. K. Hui, K. Venkatakrishnan, and B. K. A. Ngoi, “Large surface profile measurement with instantaneous phase-shifting intferometry,” Opt. Eng. 42, 367–372 (2003).
[CrossRef]

Smythe, R.

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 361–364 (1984).

Tahara, T.

Tapilouw, A.

L. Chen, S. Yeh, A. Tapilouw, and J. Chang, “3-D surface profilometry using simultaneous phase-shifting interferometry,” Opt. Commun. 283, 3376–3382 (2010).
[CrossRef]

Toto-Arellano, N.

Ura, S.

Vazquez-Castillo, J.

Venkatakrishnan, K.

N. R. Sivakumar, W. K. Hui, K. Venkatakrishnan, and B. K. A. Ngoi, “Large surface profile measurement with instantaneous phase-shifting intferometry,” Opt. Eng. 42, 367–372 (2003).
[CrossRef]

Wang, Y. R.

White, A. D.

Wyant, J. C.

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Xu, X. F.

Yamaguchi, I.

Yang, X. L.

Yeh, S.

L. Chen, S. Yeh, A. Tapilouw, and J. Chang, “3-D surface profilometry using simultaneous phase-shifting interferometry,” Opt. Commun. 283, 3376–3382 (2010).
[CrossRef]

Zhang, T.

Appl. Opt. (7)

Appl. Phys. Lett. (1)

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85, 1069–1071(2004).
[CrossRef]

Opt. Commun. (2)

J. A. Ferrari, E. M. Frins, and C. D. Perciante, “A new scheme for phase-shifting ESPI using polarized light,” Opt. Commun. 202, 233–237 (2002).
[CrossRef]

L. Chen, S. Yeh, A. Tapilouw, and J. Chang, “3-D surface profilometry using simultaneous phase-shifting interferometry,” Opt. Commun. 283, 3376–3382 (2010).
[CrossRef]

Opt. Eng. (2)

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 361–364 (1984).

N. R. Sivakumar, W. K. Hui, K. Venkatakrishnan, and B. K. A. Ngoi, “Large surface profile measurement with instantaneous phase-shifting intferometry,” Opt. Eng. 42, 367–372 (2003).
[CrossRef]

Opt. Express (2)

Opt. Lett. (5)

Proc. SPIE (2)

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

C. L. Koliopoulos, “Simultaneous phase shift interferometer,” Proc. SPIE 1531, 119–127 (1992).
[CrossRef]

Other (1)

H. Schreiber and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, 3rd ed., D.Malacara, ed. (Wiley, 2007), pp. 547–666.
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Parallel two-step phase-shifting interferometry. (a) Schematic of parallel two-step phase-shifting interferometry, (b) obtained phase-shifting interferograms with phase shift π / 2 . O and R, object wave and reference wave; L 1 , L 2 , lenses; NPBS, nonpolarizing beam splitter; M 1 , M 2 , mirrors; QW, quarter-wave plate with its principal axis having the angle π / 4 with respect to the polarizations of O and R; the polarizations of O and R are linearly perpendicular. The polarizer array is comprised of two polarizers with their polarizations crossed at π / 4 angle.

Fig. 2
Fig. 2

Experimental setup for the parallel two-step phase-shifting interferomety. NF, variable neutral filter; P, linear polarizer; PBS, polarizing beam splitter; NPBS 1 , NPBS 2 , nonpolarizing beam splitters; M 1 M 4 , mirrors; BE 1 , BE 2 , beam expanders; MO, microscope objective; L 1 L 3 , lenses; QW, quarter-wave plate.

Fig. 3
Fig. 3

Measurement results of the quartz refractive microlens array: (a) two parallel phase-shifting interferograms acquired at a single camera exposure, (b) reconstructed pseudo-three-dimensional profile of the microlens array after removal of the background phase.

Equations (7)

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G r ( ξ , η ) = FT { O + R } exp ( i 2 π ξ sin α / λ ) , G t ( ξ , η ) = FT { O + R } exp ( i 2 π η sin β / λ ) ,
U r ( x , y ) = O ( x + f sin α , y ) + R ( x + f sin α , y ) , U t ( x , y ) = O ( x f sin β , y ) + R ( x f sin β , y ) ,
{ I 1 = I R + I S + 2 I R I S cos φ I 2 = I R + I S 2 I R I S sin φ ,
{ 2 I R I S cos φ = I 1 I R I S 2 I R I S sin φ = I 2 I R I S .
4 I R I S = ( I 1 I R I S ) 2 + ( I 2 I R I S ) 2 .
{ I S ( x , y ) = ( I 1 + I 2 ) ( I 1 + I 2 ) 2 2 ( I 1 I R ) 2 2 ( I 2 I R ) 2 2 φ ˜ ( x , y ) = arctan ( I 2 I S I R I 1 I S I R ) mod ( 2 π ) .
φ ˜ B = arctan ( I 2 I S I R I 1 I S I R ) mod ( 2 π ) .

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