Abstract

A new method is presented using a tri-window common-path interferometer (TriWCPI) for quantitative phase measurement. The prior method obtains the phase shift introduced by the Ronchi grating and the intensity value of the incident light with interferograms acquired offline without any objects. As a consequence, an improved recovery algorithm is established using the phase shift, the intensity value of the incident light, and the interferograms for a phase object acquired by camera in a single shot. The phase of an object then can be reconstructed from the improved algorithm. Because the calculation of phase shift and intensity value can be performed offline only once after the TriWCPI is built, the real-time ability and stability of the TriWCPI remains in this method. But the method avoids the normalization process and thus improves phase-retrieval precision. Experiments are demonstrated to prove the precision, real-time ability, and stability of the proposed method.

© 2014 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  5. 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]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. P. Gao, B. Yao, J. Min, R. Guo, J. Zheng, and T. Ye, “Parallel two-step phase-shifting microscopic interferometry based on a cube beamsplitter,” Opt. Commun. 284, 4136–4140 (2011).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  24. Z. Zhong, B. Hao, M. Shan, Y. Wang, M. Diao, and Y. Zhang, “Two-shot common-path phase-shifting interferometer with a four-step algorithm and an unknown phase shift,” Appl. Opt. 53, 2067–2072 (2014).
    [CrossRef]
  25. 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]
  26. H. Schreiber and J. H. Bruning, in Optical Shop Testing, D. Malacara, ed. (Wiley, 2007), Chap. 14, p. 547.
  27. 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]

2014 (1)

2013 (4)

2012 (4)

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]

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]

2011 (2)

P. Gao, B. Yao, I. Harder, J. Min, R. Guo, J. Zheng, and T. Ye, “Parallel two-step phase-shifting digital holograph microscopy based on a grating pair,” J. Opt. Soc. Am. A 28, 434–440 (2011).
[CrossRef]

P. Gao, B. Yao, J. Min, R. Guo, J. Zheng, and T. Ye, “Parallel two-step phase-shifting microscopic interferometry based on a cube beamsplitter,” Opt. Commun. 284, 4136–4140 (2011).
[CrossRef]

2010 (2)

2009 (1)

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]

2008 (4)

2004 (1)

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 (1)

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]

1999 (1)

1992 (1)

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

1991 (1)

1984 (2)

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

O. Y. Kwon, “Multichannel phase-shifted interferometer,” Opt. Lett. 9, 59–61 (1984).
[CrossRef]

1974 (1)

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]

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.

Dan, D.

Depeursinge, C.

Diao, M.

Ehlers, M. D.

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.

Guo, R.

Han, J.

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.

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]

Ito, K.

Ito, Y.

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]

Kakue, T.

Kaneko, A.

Koliopoulos, C. L.

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

Koyama, T.

Kubota, T.

Kwon, O. Y.

Lei, M.

Lin, D.

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]

Marquet, P.

Matoba, O.

Meneses-Fabian, C.

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]

Moritani, Y.

Newpher, T. M.

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.

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]

Robledo-Sánchez, C.

Rodriguez-Zurita, G.

Rosenfeld, D. P.

Schreiber, H.

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

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]

Shimozato, Y.

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.

Vazquez-Castillo, J. F.

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.

Z. Zhong, B. Hao, M. Shan, Y. Wang, M. Diao, and Y. Zhang, “Two-shot common-path phase-shifting interferometer with a four-step algorithm and an unknown phase shift,” Appl. Opt. 53, 2067–2072 (2014).
[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]

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]

Xia, P.

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]

Yan, S.

Yang, Y.

Yao, B.

Ye, T.

Yu, X.

Zhang, Y.

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.

P. Gao, B. Yao, J. Min, R. Guo, J. Zheng, and T. Ye, “Parallel two-step phase-shifting microscopic interferometry based on a cube beamsplitter,” Opt. Commun. 284, 4136–4140 (2011).
[CrossRef]

P. Gao, B. Yao, I. Harder, J. Min, R. Guo, J. Zheng, and T. Ye, “Parallel two-step phase-shifting digital holograph microscopy based on a grating pair,” J. Opt. Soc. Am. A 28, 434–440 (2011).
[CrossRef]

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.

Appl. Opt. (8)

J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt. 13, 2693–2703 (1974).
[CrossRef]

D. Lin and D. Wan, “Profile measurement of an aspheric cylindrical surface from retroreflection,” Appl. Opt. 30, 3200–3204 (1991).
[CrossRef]

E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38, 6994–7001 (1999).
[CrossRef]

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, D183–D189 (2008).
[CrossRef]

N. T. Shaked, T. M. Newpher, M. D. Ehlers, and A. Wax, “Parallel on-axis holographic phase microscopy of biological cells and unicellular microorganism dynamics,” Appl. Opt. 49, 2872–2878 (2010).
[CrossRef]

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]

R. Guo, B. Yao, P. Gao, J. Min, J. Han, X. Yu, M. Lei, S. Yan, Y. Yang, D. Dan, and T. Ye, “Parallel on-axis phase-shifting holographic phase microscopy based on reflective point-diffraction interferometer with long-term stability,” Appl. Opt. 52, 3484–3489 (2013).
[CrossRef]

Z. Zhong, B. Hao, M. Shan, Y. Wang, M. Diao, and Y. Zhang, “Two-shot common-path phase-shifting interferometer with a four-step algorithm and an unknown phase shift,” Appl. Opt. 53, 2067–2072 (2014).
[CrossRef]

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

Opt. Commun. (2)

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]

P. Gao, B. Yao, J. Min, R. Guo, J. Zheng, and T. Ye, “Parallel two-step phase-shifting microscopic interferometry based on a cube beamsplitter,” Opt. Commun. 284, 4136–4140 (2011).
[CrossRef]

Opt. Eng. (2)

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]

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

Opt. Express (4)

Opt. Lasers Eng. (3)

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. (4)

Proc. SPIE (2)

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 (1)

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

Supplementary Material (2)

» Media 1: AVI (389 KB)     
» Media 2: AVI (347 KB)     

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Figures (8)

Fig. 1.
Fig. 1.

Experimental setup for TriWCPI: NF, neutral attenuation filter; CE, beam collimator and expander; Ap, aperture; S, object; G, Ronchi grating, L1 and L2, lenses.

Fig. 2.
Fig. 2.

Intensity variance of three interferograms with u0.

Fig. 3.
Fig. 3.

Interferogram acquired (a) without and (b) with an object.

Fig. 4.
Fig. 4.

(a) and (c) Value of cos(θ0) and A2 solved from three interferograms separated from Fig. 3(a), respectively. (b) and (d) 1D distribution of (a) and (c) along the blue dashed line.

Fig. 5.
Fig. 5.

Experimental results of a plano–convex cylinder lens. Phase distribution retrieved using (a) the proposed method, (b) normalization method, and (c) least-squares algorithm. (d) Difference map of (a) and (c). (e) Difference map of (b) and (c).

Fig. 6.
Fig. 6.

Experimental results of a piece of PMMA tube. (a) Interferograms recorded with an object. (b) Wrapped and (c) unwrapped phase of the object.

Fig. 7.
Fig. 7.

Experimental results of an alcohol drop. (a) Three phase-shifted interferograms (Media 1). (b) Retrieved phase (unit: rad) during the evaporation (Media 2).

Fig. 8.
Fig. 8.

Stability and repeatability test of the proposed method. Stability is defined as the phase variance of a random selected point. Repeatability is defined as the RMS of a difference between ith and (i1)th measurement; σ denotes the standard deviation.

Equations (17)

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

I+=14A2+14sinc2(12)A2+12sinc(12)A2cos[φ(x,y)θ0],
I0=14A2+cos2(θ0)sinc2(12)A2+cos(θ0)sinc(12)A2cos[φ(x,y)],
I=14A2+14sinc2(12)A2+12sinc(12)A2cos[φ(x,y)+θ0],
φ(x,y)=arctan[(II+)cot(θ0)2I0(I+I+)(2cos2(θ0)12)sinc2(12)A2].
Ibg+=14A2+14sinc2(12)A2+12cos(θ0)sinc(12)A2,
Ibg0=14A2+cos2(θ0)sinc2(12)A2+cos(θ0)sinc(12)A2,
Ibg=14A2+14sinc2(12)A2+12cos(θ0)sinc(12)A2.
Ibg++IbgIbg0=12+12sinc2(12)+sinc(12)cos(θ0)14+sinc2(12)cos2(θ0)+sinc(12)cos(θ0),
Ibg++IbgIbg0A2=14+(12cos2(θ0))sinc2(12).
acos2(θ0)+bcos(θ0)+c=0,
a=Csinc2(12)b=(C1)sinc(12)c=14C1212sinc2(12).
cos(θ0)=1C±1+2Csinc2(12)2Csinc(12).
[1412sinc2(12)]A2<Ibg++IbgIbg0<[14+12sinc2(12)]A2.
C=Ibg++IbgIbg0>1,
1+2Csinc2(12)>1.
cos(θ0)=1C+1+2Csinc2(12)2Csinc(12).
A2=Ibg++IbgIbg014+(12cos2(θ0))sinc2(12).

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