Abstract

A parallel two-step spatial carrier phase-shifting common-path interferometer with a Ronchi grating placed outside the Fourier plane is proposed in this paper for quantitative phase imaging. Two phase-shifted interferograms with spatial carrier can be captured simultaneously using the proposed interferometer. The dc term can be eliminated by subtracting the two phase-shifted interferograms, and the phase of a specimen can be reconstructed through Fourier transform. The validity and stability of the interferometer proposed are experimentally demonstrated via the measurement of a phase plate.

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References

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2012 (1)

2011 (3)

2009 (2)

N. T. Shaked, Y. Zhu, M. T. Rinehart, and A. Wax, “Two-step-only phase-shifting interferometry with optimized detector bandwidth for microscopy of live cells,” Opt. Express17(18), 15585–15591 (2009).
[CrossRef] [PubMed]

C. Meneses-Fabian, G. Rodriguez-Zurita, M.-C. 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(15), 3063–3068 (2009).
[CrossRef]

2008 (1)

2006 (2)

2004 (1)

2000 (1)

A. Hettwer, J. Kranz, and J. Schwider, “Three channel phase-shifting interferometer using polarization-optics and a diffraction grating,” Opt. Eng.39(4), 960–966 (2000).
[CrossRef]

1999 (1)

1997 (1)

1991 (1)

1982 (1)

Awatsuji, Y.

Blu, T.

Cai, L. Z.

Cuche, E.

Dasari, R. R.

Depeursinge, C.

Diao, M.

Dong, G. Y.

Encarnacion-Gutierrez, M.-C.

C. Meneses-Fabian, G. Rodriguez-Zurita, M.-C. 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(15), 3063–3068 (2009).
[CrossRef]

Feld, M. S.

Gao, P.

Guo, R.

Hao, B.

Harder, I.

Hettwer, A.

A. Hettwer, J. Kranz, and J. Schwider, “Three channel phase-shifting interferometer using polarization-optics and a diffraction grating,” Opt. Eng.39(4), 960–966 (2000).
[CrossRef]

Ikeda, T.

Ina, H.

Kaneko, A.

Kobayashi, S.

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(4), 960–966 (2000).
[CrossRef]

Kubota, T.

Liebling, M.

Lin, D. T.

Ma, H.

Mantel, K.

Marquet, P.

Matoba, O.

Meneses-Fabian, C.

C. Meneses-Fabian and G. Rodriguez-Zurita, “Carrier fringes in the two-aperture common-path interferometer,” Opt. Lett.36(5), 642–644 (2011).
[CrossRef] [PubMed]

C. Meneses-Fabian, G. Rodriguez-Zurita, M.-C. 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(15), 3063–3068 (2009).
[CrossRef]

Meng, X. F.

Min, J.

Nercissian, V.

Nishio, K.

Popescu, G.

Rinehart, M. T.

Rodriguez-Zurita, G.

C. Meneses-Fabian and G. Rodriguez-Zurita, “Carrier fringes in the two-aperture common-path interferometer,” Opt. Lett.36(5), 642–644 (2011).
[CrossRef] [PubMed]

C. Meneses-Fabian, G. Rodriguez-Zurita, M.-C. 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(15), 3063–3068 (2009).
[CrossRef]

Schwider, J.

A. Hettwer, J. Kranz, and J. Schwider, “Three channel phase-shifting interferometer using polarization-optics and a diffraction grating,” Opt. Eng.39(4), 960–966 (2000).
[CrossRef]

Shaked, N. T.

Shan, M.

Shen, X. X.

Tahara, T.

Takeda, M.

Toto-Arellano, N. I.

C. Meneses-Fabian, G. Rodriguez-Zurita, M.-C. 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(15), 3063–3068 (2009).
[CrossRef]

Unser, M.

Ura, S.

Wan, D. S.

Wang, Y. R.

Wax, A.

Xu, X. F.

Yamaguchi, I.

Yang, X. L.

Yao, B.

Ye, T.

Zhang, T.

Zheng, J.

Zhong, Z.

Zhu, Y.

Appl. Opt. (3)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

C. Meneses-Fabian, G. Rodriguez-Zurita, M.-C. 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(15), 3063–3068 (2009).
[CrossRef]

Opt. Eng. (1)

A. Hettwer, J. Kranz, and J. Schwider, “Three channel phase-shifting interferometer using polarization-optics and a diffraction grating,” Opt. Eng.39(4), 960–966 (2000).
[CrossRef]

Opt. Express (2)

Opt. Lett. (5)

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Figures (5)

Fig. 1
Fig. 1

(a) Experimental setup for two-step spatial carrier phase-shifting common-path interferometer; (b) Polarization state of beams in the input aperture; (c) Polarization state of polarizing filter array(PLA). At the right side of grating G, the blue, red and green beams indicate the diffraction orders +1, 0 and −1, respectively; P, Polarizer; CE, Collimator & expander; QWR, QWL, Quarter wave plates; Ap, Aperture; S, Specimen; G, Ronchi grating; L1, L2, Lenses.

Fig. 2
Fig. 2

Schematic for diffraction of grating. Orders +1, 0 and −1 are indicated with blue, red and green; Δf, displacement of grating; Δx, distance between adjacent orders in the Fourier plane; θ, diffraction angle of ±1st orders.

Fig. 3
Fig. 3

Experimental results without specimen: (a) 2D intensity distribution recorded in the image plane and (b) 1D profile of (a) along the red line; (c) 2D and (d) 1D spectrum distribution recorded in the Fourier plane.

Fig. 4
Fig. 4

Experimental results for a phase plate: (a) interferograms with phase shift π; (b) reconstructed OPD distribution using the method reported in Ref. [14]; (c) reconstructed OPD distribution using the proposed method; (d) profile along the dash line marked in (b).

Fig. 5
Fig. 5

Stability and repeatability of the proposed method. Hti denotes the ith measurement and RMS denotes the standard deviate.

Equations (9)

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f 0 =Δx/λf.
sinθ= λ d =tanθ= Δx Δf .
f 0 = Δf fd .
I 1 ( x,y )=a( x,y )+c( x,y )exp( i2π f 0 x )+c*( x,y )exp( i2π f 0 x ),
I 2 ( x,y )=a( x,y )+c( x,y )exp( iα )exp( i2π f 0 x )+c*( x,y )exp( iα )exp( i2π f 0 x )
c( x,y )=Aexp[ iφ( x,y ) ],
Rr=exp( i2π f 0 x )=exp( i2π Δf fd x ).
c ( x,y )=c( x,y )[ 1exp( iα ) ]=IFT{ FT{ Rr( I 1 I 2 ) }LF },
φ( x,y )= Im[ c ( x,y ) ] Re[ c ( x,y ) ] φ C ,

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