Abstract

This paper presents a two-shot common-path phase-shifting interferometer that consists of a 4f optical system with two windows in the input plane and a Ronchi grating in the Fourier plane, and generates two adjacent interferograms using only diffraction orders 0 and +1 and 0 and 1. Four phase-shifted interferograms can be obtained in two shots by modulating two linear polarizers with angle difference of π/4 and translating the grating with only an unknown phase shift. An algorithm similar to the standard four-step algorithm is used to retrieve the phase of a specimen, and it requires no knowledge of the phase shift introduced by translation of the grating. The validity and repeatability of the proposed method is proved through simulations and experiments.

© 2014 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]

2013

2012

D. G. Abdelsalam, B. Yao, P. Gao, J. Min, and R. Guo, “Single-shot parallel four-step phase shifting using on-axis Fizeau interferometry,” Appl. Opt. 51, 4891–4895 (2012).
[CrossRef]

B. Hao, M. Shan, M. Diao, Z. Zhong, and H. Ma, “Common-path interferometer with a tri-window,” Opt. Lett. 37, 3213–3215 (2012).
[CrossRef]

X. Lu, J. Chen, S. Liu, Z. Ma, Z. Zhang, and L. Zhong, “3D profile reconstruction of biological sample by in-line image-plane phase-shifting digital microscopic holography,” Opt. Lasers Eng. 50, 1431–1435 (2012).
[CrossRef]

W. Jin, Y. Wang, N. Ren, M. Bu, X. Shang, Y. Xu, and Y. Chen, “Simulation of simultaneous measurement for red blood cell thickness and refractive index,” Opt. Lasers Eng. 50, 154–158 (2012).
[CrossRef]

2011

2009

2008

2006

2004

J. E. Millerd, N. J. Brock, J. B. Hayes, and J. C. Wyant, “Instantaneous phase-shift, point-diffraction interferometer,” Proc. SPIE 5531, 264–272 (2004).
[CrossRef]

2003

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

2000

A. Hettwer, J. Kranz, and J. Schwider, “Three channel phase-shifting interferometer using polarization-optics and a diffraction grating,” Opt. Eng. 39, 960–966 (2000).
[CrossRef]

1999

1997

1992

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

1991

1986

1984

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 234361 (1984).
[CrossRef]

1974

Abdelsalam, D. G.

Awatsuji, Y.

Brangaccio, D. J.

Brock, N. J.

J. E. Millerd, N. J. Brock, J. B. Hayes, and J. C. Wyant, “Instantaneous phase-shift, point-diffraction interferometer,” Proc. SPIE 5531, 264–272 (2004).
[CrossRef]

Bruning, J. H.

Bu, M.

W. Jin, Y. Wang, N. Ren, M. Bu, X. Shang, Y. Xu, and Y. Chen, “Simulation of simultaneous measurement for red blood cell thickness and refractive index,” Opt. Lasers Eng. 50, 154–158 (2012).
[CrossRef]

Cai, L. Z.

Chen, J.

X. Lu, J. Chen, S. Liu, Z. Ma, Z. Zhang, and L. Zhong, “3D profile reconstruction of biological sample by in-line image-plane phase-shifting digital microscopic holography,” Opt. Lasers Eng. 50, 1431–1435 (2012).
[CrossRef]

Chen, Y.

W. Jin, Y. Wang, N. Ren, M. Bu, X. Shang, Y. Xu, and Y. Chen, “Simulation of simultaneous measurement for red blood cell thickness and refractive index,” Opt. Lasers Eng. 50, 154–158 (2012).
[CrossRef]

Cuche, E.

Depeursinge, C.

Diao, M.

Dong, G. Y.

Encarnacion-Gutierrez, M.

C. Meneses-Fabian, G. Rodriguez-Zurita, M. Encarnacion-Gutierrez, and N. I. Toto-Arellano, “Phase-shifting interferometry with four interferograms using linear polarization modulation and a Ronchi grating displaced by only a small unknown amount,” Opt. Commun. 282, 3063–3068 (2009).
[CrossRef]

Gallagher, J. E.

Gao, P.

García, J.

Guo, R.

Hao, B.

Harder, I.

Hayes, J. B.

J. E. Millerd, N. J. Brock, J. B. Hayes, and J. C. Wyant, “Instantaneous phase-shift, point-diffraction interferometer,” Proc. SPIE 5531, 264–272 (2004).
[CrossRef]

Herriott, D. R.

Hettwer, A.

A. Hettwer, J. Kranz, and J. Schwider, “Three channel phase-shifting interferometer using polarization-optics and a diffraction grating,” Opt. Eng. 39, 960–966 (2000).
[CrossRef]

Hui, W. K.

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

Javidi, B.

Jin, W.

W. Jin, Y. Wang, N. Ren, M. Bu, X. Shang, Y. Xu, and Y. Chen, “Simulation of simultaneous measurement for red blood cell thickness and refractive index,” Opt. Lasers Eng. 50, 154–158 (2012).
[CrossRef]

Kaneko, A.

Katz, B.

Kelner, R.

Kiire, T.

Koliopoulos, C. L.

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

Koyama, T.

Kranz, J.

A. Hettwer, J. Kranz, and J. Schwider, “Three channel phase-shifting interferometer using polarization-optics and a diffraction grating,” Opt. Eng. 39, 960–966 (2000).
[CrossRef]

Kries, T.

Kubota, T.

Lin, D.

Liu, J. P.

Liu, S.

X. Lu, J. Chen, S. Liu, Z. Ma, Z. Zhang, and L. Zhong, “3D profile reconstruction of biological sample by in-line image-plane phase-shifting digital microscopic holography,” Opt. Lasers Eng. 50, 1431–1435 (2012).
[CrossRef]

Lu, X.

X. Lu, J. Chen, S. Liu, Z. Ma, Z. Zhang, and L. Zhong, “3D profile reconstruction of biological sample by in-line image-plane phase-shifting digital microscopic holography,” Opt. Lasers Eng. 50, 1431–1435 (2012).
[CrossRef]

Ma, H.

Ma, Z.

X. Lu, J. Chen, S. Liu, Z. Ma, Z. Zhang, and L. Zhong, “3D profile reconstruction of biological sample by in-line image-plane phase-shifting digital microscopic holography,” Opt. Lasers Eng. 50, 1431–1435 (2012).
[CrossRef]

Mantel, K.

Marquet, P.

Matoba, O.

Meneses-Fabian, C.

Meng, X. F.

Micó, V.

Millerd, J. E.

J. E. Millerd, N. J. Brock, J. B. Hayes, and J. C. Wyant, “Instantaneous phase-shift, point-diffraction interferometer,” Proc. SPIE 5531, 264–272 (2004).
[CrossRef]

Min, J.

Moore, R.

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 234361 (1984).
[CrossRef]

Nakadate, S.

Nercissian, V.

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 interferometry,” Opt. Eng. 42, 367–372 (2003).
[CrossRef]

Nishio, K.

Poon, T. C.

Ren, N.

W. Jin, Y. Wang, N. Ren, M. Bu, X. Shang, Y. Xu, and Y. Chen, “Simulation of simultaneous measurement for red blood cell thickness and refractive index,” Opt. Lasers Eng. 50, 154–158 (2012).
[CrossRef]

Rinehart, M. T.

Rivenson, Y.

Robledo-Sánchez, C.

Rodriguez-Zurita, G.

Rosen, J.

Rosenfeld, D. P.

Schreiber, H.

H. Schreiber and J. H. Bruning, in Optical Shop Testing, D. Malacara, ed. (Wiley, 2007), Chap. 14, p. 547.

Schwider, J.

A. Hettwer, J. Kranz, and J. Schwider, “Three channel phase-shifting interferometer using polarization-optics and a diffraction grating,” Opt. Eng. 39, 960–966 (2000).
[CrossRef]

Shaked, N. T.

Shan, M.

Shang, X.

W. Jin, Y. Wang, N. Ren, M. Bu, X. Shang, Y. Xu, and Y. Chen, “Simulation of simultaneous measurement for red blood cell thickness and refractive index,” Opt. Lasers Eng. 50, 154–158 (2012).
[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 interferometry,” Opt. Eng. 42, 367–372 (2003).
[CrossRef]

Smythe, R.

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 234361 (1984).
[CrossRef]

Tahara, T.

Toto-Arellano, N. I.

Ura, S.

Vázquez-Castillo, J. F.

Venkatakrishnan, K.

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

Wan, D.

Wang, Y.

W. Jin, Y. Wang, N. Ren, M. Bu, X. Shang, Y. Xu, and Y. Chen, “Simulation of simultaneous measurement for red blood cell thickness and refractive index,” Opt. Lasers Eng. 50, 154–158 (2012).
[CrossRef]

Wang, Y. R.

Wax, A.

White, A. D.

Wyant, J. C.

J. E. Millerd, N. J. Brock, J. B. Hayes, and J. C. Wyant, “Instantaneous phase-shift, point-diffraction interferometer,” Proc. SPIE 5531, 264–272 (2004).
[CrossRef]

Xu, X. F.

Xu, Y.

W. Jin, Y. Wang, N. Ren, M. Bu, X. Shang, Y. Xu, and Y. Chen, “Simulation of simultaneous measurement for red blood cell thickness and refractive index,” Opt. Lasers Eng. 50, 154–158 (2012).
[CrossRef]

Yamaguchi, I.

Yang, X. L.

Yao, B.

Yatagai, T.

Ye, T.

Zalevsky, Z.

Zhang, T.

Zhang, Y.

M. Shan, B. Hao, Z. Zhong, M. Diao, and Y. Zhang, “Parallel two-step spatial carrier phase-shifting common-path interferometer with a Ronchi grating outside the Fourier plane,” Opt. Express 21, 2126–2132 (2013).
[CrossRef]

B. Hao, M. Shan, Z. Zhong, M. Diao, and Y. Zhang, “Common-path interferometer with four simultaneous phase-shifted interferograms using Ronchi grating and cube beamsplitter,” Opt. Lasers Eng. 51, 1278–1282 (2013).
[CrossRef]

Zhang, Z.

X. Lu, J. Chen, S. Liu, Z. Ma, Z. Zhang, and L. Zhong, “3D profile reconstruction of biological sample by in-line image-plane phase-shifting digital microscopic holography,” Opt. Lasers Eng. 50, 1431–1435 (2012).
[CrossRef]

Zheng, J.

Zhong, L.

X. Lu, J. Chen, S. Liu, Z. Ma, Z. Zhang, and L. Zhong, “3D profile reconstruction of biological sample by in-line image-plane phase-shifting digital microscopic holography,” Opt. Lasers Eng. 50, 1431–1435 (2012).
[CrossRef]

Zhong, Z.

Zhu, Y.

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Commun.

C. Meneses-Fabian, G. Rodriguez-Zurita, M. Encarnacion-Gutierrez, and N. I. Toto-Arellano, “Phase-shifting interferometry with four interferograms using linear polarization modulation and a Ronchi grating displaced by only a small unknown amount,” Opt. Commun. 282, 3063–3068 (2009).
[CrossRef]

Opt. Eng.

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

A. Hettwer, J. Kranz, and J. Schwider, “Three channel phase-shifting interferometer using polarization-optics and a diffraction grating,” Opt. Eng. 39, 960–966 (2000).
[CrossRef]

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 234361 (1984).
[CrossRef]

Opt. Express

Opt. Lasers Eng.

X. Lu, J. Chen, S. Liu, Z. Ma, Z. Zhang, and L. Zhong, “3D profile reconstruction of biological sample by in-line image-plane phase-shifting digital microscopic holography,” Opt. Lasers Eng. 50, 1431–1435 (2012).
[CrossRef]

W. Jin, Y. Wang, N. Ren, M. Bu, X. Shang, Y. Xu, and Y. Chen, “Simulation of simultaneous measurement for red blood cell thickness and refractive index,” Opt. Lasers Eng. 50, 154–158 (2012).
[CrossRef]

B. Hao, M. Shan, Z. Zhong, M. Diao, and Y. Zhang, “Common-path interferometer with four simultaneous phase-shifted interferograms using Ronchi grating and cube beamsplitter,” Opt. Lasers Eng. 51, 1278–1282 (2013).
[CrossRef]

Opt. Lett.

Proc. SPIE

J. E. Millerd, N. J. Brock, J. B. Hayes, and J. C. Wyant, “Instantaneous phase-shift, point-diffraction interferometer,” Proc. SPIE 5531, 264–272 (2004).
[CrossRef]

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

Other

H. Schreiber and J. H. Bruning, in Optical Shop Testing, D. Malacara, ed. (Wiley, 2007), Chap. 14, p. 547.

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Figures (9)

Fig. 1.
Fig. 1.

(a) Scheme of setup; (b) polarization state of P; (c) placement of quarter wave plates; and (d) polarization state of polarizing filter array. P, P1, and P2, linear polarizers; BE, beam expander; QWR and QWL, quarter wave plates; Ap, aperture; S, specimen; G, Ronchi grating.

Fig. 2.
Fig. 2.

Effect of the angle difference error of the two polarizers in front of the CCD camera on the RMSE of the retrieved phase.

Fig. 3.
Fig. 3.

Interferograms recorded in the (a) first and (b) second shot.

Fig. 4.
Fig. 4.

(a) Wrapped and (b) unwrapped phase of the reconstructed phase; (c) phase reconstruction error.

Fig. 5.
Fig. 5.

Interferograms acquired by a CCD camera in (a) the first shot, (b) the second shot, and (c) the result of subtraction of (a) and (b).

Fig. 6.
Fig. 6.

Experimental results of a plano–convex cylinder lens. (a) Wrapped, and (b) unwrapped OPD profile reconstructed with the method proposed in this paper; (c) unwrapped OPD profile reconstructed with the least squares method; and (d) error of (b) and (c).

Fig. 7.
Fig. 7.

Experimental results of a piece of PMMA tube. (a) and (b) Interferograms recorded in two shots; (c) Interferogram difference of (a) and (b); and (d) unwrapped phase of specimen.

Fig. 8.
Fig. 8.

Repeatability test of the proposed method.

Fig. 9.
Fig. 9.

Effect of the unknown phase shift.

Equations (8)

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

I1(x,y)=0.5(A02+A12)+A0A1cos[φ(x,y)θ02α1],
I2(x,y)=0.5(A02+A12)+A0A1cos[φ(x,y)θ02α2],
I3(x,y)=0.5(A02+A12)+A0A1cos[φ(x,y)θ0Δθ2α1],
I4(x,y)=0.5(A02+A12)+A0A1cos[φ(x,y)θ0Δθ2α2].
I3(x,y)I1(x,y)=2A0A1sinΔθ2sin[φ(x,y)],
I4(x,y)I2(x,y)=2A0A1sinΔθ2sin[φ(x,y)+2Δα],
I4(x,y)I2(x,y)=2A0A1sinΔθ2cos[φ(x,y)].
φ(x,y)=tan1[I3(x,y)I1(x,y)I4(x,y)I2(x,y)].

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