Abstract

A parallel two-step polarizing phase shifting interferometer based on a Double Cyclic Shear Interferometer (DCSI) is proposed in this paper for quantitative phase imaging. The system has the advantage of retrieving the derivative phase data map directly. Due to its configuration, it presents better stability against external configurations than other types of interferometers. The DCSI generates two π-shifted interferograms, which are recorded by the CCD camera in a single-shot. The separation between parallel interferograms can be varied in the two axes for convenience. To obtain the optical phase data map, a parallel phase shift between interferograms is obtained by rotating a half wave plate retarder. We analyzed the cases of four patterns with shifts of π/2 captured in two shots; the optical phase was processed by a four-step algorithm. Related experimental results obtained for microscopic transparent samples are presented.

© 2013 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  4. H. J. Okoomian, “A two-beam polarization technique to measure optical phase,” Appl. Opt. 8(11), 2363–2365 (1969).
    [Crossref] [PubMed]
  5. T. Nomura, S. Murata, E. Nitanai, and T. Numata, “Phase-shifting digital holography with a phase difference between orthogonal polarizations,” Appl. Opt. 45(20), 4873–4877 (2006).
    [Crossref] [PubMed]
  6. P. Gao, B. Yao, J. Min, R. Guo, J. Zheng, T. Ye, I. Harder, V. Nercissian, and K. Mantel, “Parallel two-step phase-shifting point-diffraction interferometry for microscopy based on a pair of cube beamsplitters,” Opt. Express 19(3), 1930–1935 (2011).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  10. T. Kiire, S. Nakadate, and M. Shibuya, “Simultaneous formation of four fringes by using a polarization quadrature phase-shifting interferometer with wave plates and a diffraction grating,” Appl. Opt. 47(26), 4787–4792 (2008).
    [Crossref] [PubMed]
  11. N. I. Toto-Arellano, G. Rodriguez-Zurita, C. Meneses-Fabian, and J. F. Vázquez-Castillo, “A single-shot phase-shifting radial-shearing interferometer,” J. Opt. A, Pure Appl. Opt. 11(4), 045704 (2009).
    [Crossref]
  12. J. Min, B. Yao, P. Gao, R. Guo, J. Zheng, and T. Ye, “Parallel phase-shifting interferometry based on Michelson-like architecture,” Appl. Opt. 49(34), 6612–6616 (2010).
    [Crossref] [PubMed]
  13. A.-H. Phan, M. L. Piao, J.-H. Park, and N. Kim, “Error analysis in parallel two-step phase-shifting method,” Appl. Opt. 52(11), 2385–2393 (2013).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  16. N.-I. Toto-Arellano, A. Martínez-García, G. Rodríguez-Zurita, J. A. Rayas-Álvarez, and A. Montes-Perez, “Slope measurement of a phase object using a polarizing phase-shifting high-frequency Ronchi grating interferometer,” Appl. Opt. 49(33), 6402–6408 (2010).
    [Crossref] [PubMed]
  17. D. Malacara, M. Servin, and Z. Malacara, “Phase detection algorithms,” in Interferogram Analysis for Optical Testing, D. Malacara ed. (Taylor & Francis Group, 2005).
  18. P. Ferraro, S. De Nicola, A. Finizio, G. Coppola, S. Grilli, C. Magro, and G. Pierattini, “Compensation of the inherent wave front curvature in digital holographic coherent microscopy for quantitative phase-contrast imaging,” Appl. Opt. 42(11), 1938–1946 (2003).
    [Crossref] [PubMed]
  19. W. Steinchen and L. Yang, “Phase-Shifting Shearography” in Digital Shearography: Theory and application of digital speckle pattern shearing interferometer, SPIE Press, (PM100, Washington, 2003).
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2013 (2)

2011 (2)

P. Gao, B. Yao, J. Min, R. Guo, J. Zheng, T. Ye, I. Harder, V. Nercissian, and K. Mantel, “Parallel two-step phase-shifting point-diffraction interferometry for microscopy based on a pair of cube beamsplitters,” Opt. Express 19(3), 1930–1935 (2011).
[Crossref] [PubMed]

N. I. Toto-Arellano, D. I. Serrano-García, A. Martínez García, G. Rodríguez Zurita, and A. Montes-Pérez, “4D profile of phase objects through the use of a simultaneous phase shifting quasi-common path interferometer,” J. Opt. 13(11), 115502 (2011).
[Crossref]

2010 (2)

2009 (1)

N. I. Toto-Arellano, G. Rodriguez-Zurita, C. Meneses-Fabian, and J. F. Vázquez-Castillo, “A single-shot phase-shifting radial-shearing interferometer,” J. Opt. A, Pure Appl. Opt. 11(4), 045704 (2009).
[Crossref]

2008 (2)

2006 (2)

2003 (2)

1984 (1)

R. S. Sirohi, “Speckle shearing interferometry,” J. Opt. 33, 95–113 (1984).

1975 (1)

1974 (1)

1969 (1)

Awatsuji, Y.

Cai, L. Z.

Coppola, G.

De Nicola, S.

Diao, M.

Dong, G. Y.

Ferraro, P.

Finizio, A.

Gao, P.

Grilli, S.

Guo, R.

Hao, B.

Harder, I.

Kaneko, A.

Kiire, T.

Kim, N.

Koyama, T.

Kubota, T.

Magro, C.

Mantel, K.

Martínez García, A.

N. I. Toto-Arellano, D. I. Serrano-García, A. Martínez García, G. Rodríguez Zurita, and A. Montes-Pérez, “4D profile of phase objects through the use of a simultaneous phase shifting quasi-common path interferometer,” J. Opt. 13(11), 115502 (2011).
[Crossref]

Martínez-García, A.

Matoba, O.

Meneses-Fabian, C.

N. I. Toto-Arellano, G. Rodriguez-Zurita, C. Meneses-Fabian, and J. F. Vázquez-Castillo, “A single-shot phase-shifting radial-shearing interferometer,” J. Opt. A, Pure Appl. Opt. 11(4), 045704 (2009).
[Crossref]

Meng, X. F.

Min, J.

Montes-Perez, A.

Montes-Pérez, A.

N. I. Toto-Arellano, D. I. Serrano-García, A. Martínez García, G. Rodríguez Zurita, and A. Montes-Pérez, “4D profile of phase objects through the use of a simultaneous phase shifting quasi-common path interferometer,” J. Opt. 13(11), 115502 (2011).
[Crossref]

Murata, S.

Nakadate, S.

Nercissian, V.

Nishio, K.

Nitanai, E.

Nomura, T.

Numata, T.

Okoomian, H. J.

Park, J.-H.

Phan, A.-H.

Piao, M. L.

Pierattini, G.

Rayas-Álvarez, J. A.

Rodríguez Zurita, G.

N. I. Toto-Arellano, D. I. Serrano-García, A. Martínez García, G. Rodríguez Zurita, and A. Montes-Pérez, “4D profile of phase objects through the use of a simultaneous phase shifting quasi-common path interferometer,” J. Opt. 13(11), 115502 (2011).
[Crossref]

Rodriguez-Zurita, G.

N. I. Toto-Arellano, G. Rodriguez-Zurita, C. Meneses-Fabian, and J. F. Vázquez-Castillo, “A single-shot phase-shifting radial-shearing interferometer,” J. Opt. A, Pure Appl. Opt. 11(4), 045704 (2009).
[Crossref]

Rodríguez-Zurita, G.

Serrano-García, D. I.

N. I. Toto-Arellano, D. I. Serrano-García, A. Martínez García, G. Rodríguez Zurita, and A. Montes-Pérez, “4D profile of phase objects through the use of a simultaneous phase shifting quasi-common path interferometer,” J. Opt. 13(11), 115502 (2011).
[Crossref]

Shan, M.

Shen, X. X.

Shibuya, M.

Sirohi, R. S.

R. S. Sirohi, “Speckle shearing interferometry,” J. Opt. 33, 95–113 (1984).

Tahara, T.

Toto-Arellano, N. I.

N. I. Toto-Arellano, D. I. Serrano-García, A. Martínez García, G. Rodríguez Zurita, and A. Montes-Pérez, “4D profile of phase objects through the use of a simultaneous phase shifting quasi-common path interferometer,” J. Opt. 13(11), 115502 (2011).
[Crossref]

N. I. Toto-Arellano, G. Rodriguez-Zurita, C. Meneses-Fabian, and J. F. Vázquez-Castillo, “A single-shot phase-shifting radial-shearing interferometer,” J. Opt. A, Pure Appl. Opt. 11(4), 045704 (2009).
[Crossref]

Toto-Arellano, N.-I.

Ura, S.

Vázquez-Castillo, J. F.

N. I. Toto-Arellano, G. Rodriguez-Zurita, C. Meneses-Fabian, and J. F. Vázquez-Castillo, “A single-shot phase-shifting radial-shearing interferometer,” J. Opt. A, Pure Appl. Opt. 11(4), 045704 (2009).
[Crossref]

Wang, Y. R.

Wyant, J. C.

Xu, X. F.

Yang, X. L.

Yao, B.

Ye, T.

Zhang, Y.

Zheng, J.

Zhong, Z.

Appl. Opt. (10)

J. C. Wyant, “White Light Extended Source Shearing Interferometer,” Appl. Opt. 13(1), 200–202 (1974).
[Crossref] [PubMed]

J. C. Wyant, “Use of an ac heterodyne lateral shear interferometer with real-time wavefront correction systems,” Appl. Opt. 14(11), 2622–2626 (1975).
[Crossref] [PubMed]

P. Ferraro, S. De Nicola, A. Finizio, G. Coppola, S. Grilli, C. Magro, and G. Pierattini, “Compensation of the inherent wave front curvature in digital holographic coherent microscopy for quantitative phase-contrast imaging,” Appl. Opt. 42(11), 1938–1946 (2003).
[Crossref] [PubMed]

T. Nomura, S. Murata, E. Nitanai, and T. Numata, “Phase-shifting digital holography with a phase difference between orthogonal polarizations,” Appl. Opt. 45(20), 4873–4877 (2006).
[Crossref] [PubMed]

Y. Awatsuji, T. Tahara, A. Kaneko, T. Koyama, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel two-step phase-shifting digital holography,” Appl. Opt. 47(19), D183–D189 (2008).
[Crossref] [PubMed]

H. J. Okoomian, “A two-beam polarization technique to measure optical phase,” Appl. Opt. 8(11), 2363–2365 (1969).
[Crossref] [PubMed]

T. Kiire, S. Nakadate, and M. Shibuya, “Simultaneous formation of four fringes by using a polarization quadrature phase-shifting interferometer with wave plates and a diffraction grating,” Appl. Opt. 47(26), 4787–4792 (2008).
[Crossref] [PubMed]

N.-I. Toto-Arellano, A. Martínez-García, G. Rodríguez-Zurita, J. A. Rayas-Álvarez, and A. Montes-Perez, “Slope measurement of a phase object using a polarizing phase-shifting high-frequency Ronchi grating interferometer,” Appl. Opt. 49(33), 6402–6408 (2010).
[Crossref] [PubMed]

J. Min, B. Yao, P. Gao, R. Guo, J. Zheng, and T. Ye, “Parallel phase-shifting interferometry based on Michelson-like architecture,” Appl. Opt. 49(34), 6612–6616 (2010).
[Crossref] [PubMed]

A.-H. Phan, M. L. Piao, J.-H. Park, and N. Kim, “Error analysis in parallel two-step phase-shifting method,” Appl. Opt. 52(11), 2385–2393 (2013).
[Crossref] [PubMed]

J. Opt. (2)

R. S. Sirohi, “Speckle shearing interferometry,” J. Opt. 33, 95–113 (1984).

N. I. Toto-Arellano, D. I. Serrano-García, A. Martínez García, G. Rodríguez Zurita, and A. Montes-Pérez, “4D profile of phase objects through the use of a simultaneous phase shifting quasi-common path interferometer,” J. Opt. 13(11), 115502 (2011).
[Crossref]

J. Opt. A, Pure Appl. Opt. (1)

N. I. Toto-Arellano, G. Rodriguez-Zurita, C. Meneses-Fabian, and J. F. Vázquez-Castillo, “A single-shot phase-shifting radial-shearing interferometer,” J. Opt. A, Pure Appl. Opt. 11(4), 045704 (2009).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Optics & Photonics News (1)

J. C. Wyant, “Dynamic Interferometry,” Optics & Photonics News 14(4), 36–41 (2003).
[Crossref]

Other (3)

D. Malacara, M. Servin, and Z. Malacara, “Phase detection algorithms,” in Interferogram Analysis for Optical Testing, D. Malacara ed. (Taylor & Francis Group, 2005).

W. Steinchen and L. Yang, “Phase-Shifting Shearography” in Digital Shearography: Theory and application of digital speckle pattern shearing interferometer, SPIE Press, (PM100, Washington, 2003).

M. V. Mantravadi, “Lateral shearing interferometers,” in Optical Shop Testing, D. Malacara ed.,(John Wiley & Sons, Inc., Hoboken, New Jersey 2007).

Supplementary Material (1)

» Media 1: MP4 (2659 KB)     

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Figures (5)

Fig. 1
Fig. 1 Two step parallel phase-shifting interferometer (a) Optical setup scheme of the cyclic shear interferometer. (b) Coupled cyclic shear interferometer used to generate parallel interferograms. Qi: Quarter wave plates. Hi: Half wave plates. M: Mirrors. PBSi: Polarizing beam splitters. Δxi: Adjustable mirrors. xi: beam separation. bi: Split beams.
Fig. 2
Fig. 2 Double Cyclic Shear Interferometer. (a) Four beams generated for the DCSI. (b) Interference patterns generated for the system with shear in the x-y direction. (c) Interference patterns generated for the system with shear in the x-direction. (d) Phase step: interference patterns generated for the system with shear in the y-direction. a: beam transversal section. bi: Split beams. x0: beam separation. x1: Interferograms separation. (Media 1)
Fig. 3
Fig. 3 Out of plane deformation generated by acetate. (a) Four shearograms generated for the DCSI. (b) 3D Slope in y-direction.
Fig. 4
Fig. 4 Oil film on a microscopy slide (a) Four shearograms generated for the DCSI. (b) 3D Slope in x-direction.
Fig. 5
Fig. 5 Radial patterns combined with a water bubble of approximately 0.5 mm in radius. (a) Four shearograms generated for the DCIS. (b) Radial slope. (c) Deformation introduced by the water bubble.

Equations (5)

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

I 1 (x,y)= A 0 + A 1 cos[ 4χ ϕ(x,y) x ], I 2 (x,y)= A 0 A 1 cos[ 4χ ϕ(x,y) x ]
I 3 (x,y)= A 0 + A 1 sin[ 4χ ϕ(x,y) x ], I 4 (x,y)= A 0 A 1 sin[ 4χ ϕ(x,y) x ]
ϕ(x,y) x = tan 1 [ I 3 (x,y) I 4 (x,y) I 1 (x,y) I 2 (x,y) ]
ϕ(x,y) x = 4π λ w(x,y) x x 0
ϕ(r) r = 4π λ w(r) r r 0

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