Abstract

Combining spatial carrier-frequency phase-shifting (SCPS) technique and Fourier transform method, from one-frame spatial carrier-frequency interferogram (SCFI), a novel phase retrieval method is proposed and applied to dynamic phase measurement. First, using the SCPS technique, four-frame phase-shifting sub-interferograms can be constructed from one-frame SCFI. Second, using Fourier transform method, the accurate phase-shifts of four sub-interferograms can be extracted rapidly, so there is no requirement of calibration for the carrier-frequency in advance compared to most existing SCPS methods. Third, the wrapped phase can be retrieved with the least-squares algorithm through using the above phase-shifts. Finally, the phase variations of a water droplet evaporation and a Jurkat cell apoptosis induced by a drug are presented with the proposed method. Both the simulation and experimental results demonstrate that in addition to maintaining high accuracy of the SCPS method, the proposed method reveals more rapid processing speed of phase retrieval, and this will greatly facilitate its application in dynamic phase measurement.

© 2016 Optical Society of America

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References

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2015 (2)

P. Sun, L. Zhong, C. Luo, W. Niu, and X. Lu, “Visual measurement of the evaporation process of a sessile droplet by dual-channel simultaneous phase-shifting interferometry,” Sci. Rep. 5, 12053 (2015).
[Crossref] [PubMed]

D. Zhang, Y. Feng, Q. Zhang, S. Xin, X. Lu, S. Liu, and L. Zhong, “Raman spectrum reveals the cell cycle arrest of Triptolide-induced leukemic T-lymphocytes apoptosis,” Spec. Acta Part A Mol. Bio 141, 216–222 (2015).

2012 (3)

2011 (5)

2010 (1)

2008 (1)

2005 (1)

D. Malacara, M. Servín, and Z. Malacara, “Interferogram analysis for optical testing,” Opt. Eng. 5, 461–462 (2005).

2004 (2)

Z. Wang and B. Han, “Advanced iterative algorithm for phase extraction of randomly phase-shifted interferograms,” Opt. Lett. 29(14), 1671–1673 (2004).
[Crossref] [PubMed]

C. Quan, C. Tay, and Y. Huang, “3-D deformation measurement using fringe projection and digital image correlation,” Optik (Stuttg.) 115(4), 164–168 (2004).
[Crossref]

2001 (2)

2000 (1)

A. Hettwer, J. Kranz, J. Schwider, 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]

1997 (1)

1995 (2)

M. Servin and F. J. Cuevas, “A novel technique for spatial phase-shifting interferometry,” J. Mod. Opt. 42(9), 1853–1862 (1995).
[Crossref]

M. Pirga and M. Kujawinska, “Two directional spatial-carrier phase-shifting method for analysis of crossed and closed fringe patterns,” Opt. Eng. 34(8), 2459–2466 (1995).
[Crossref]

1983 (1)

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Proc. SPIE 429, 16–21 (1983).
[Crossref]

1982 (1)

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. A 72(1), 156–160 (1982).
[Crossref]

1972 (1)

Awatsuji, Y.

Belenguer, T.

Bokor, J.

Carazo, J. M.

Creath, K.

K. Creath and G. Goldstein, “Dynamic phase imaging and processing of moving biological organisms,” Proc. SPIE 8227, 822710 (2012).

Cuevas, F. J.

M. Servin and F. J. Cuevas, “A novel technique for spatial phase-shifting interferometry,” J. Mod. Opt. 42(9), 1853–1862 (1995).
[Crossref]

Debnath, S. K.

Du, Y.

Estrada, J. C.

Feng, G.

Feng, Y.

D. Zhang, Y. Feng, Q. Zhang, S. Xin, X. Lu, S. Liu, and L. Zhong, “Raman spectrum reveals the cell cycle arrest of Triptolide-induced leukemic T-lymphocytes apoptosis,” Spec. Acta Part A Mol. Bio 141, 216–222 (2015).

Goldberg, K. A.

Goldstein, G.

K. Creath and G. Goldstein, “Dynamic phase imaging and processing of moving biological organisms,” Proc. SPIE 8227, 822710 (2012).

Han, B.

Heppner, J.

Hettwer, A.

A. Hettwer, J. Kranz, J. Schwider, 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]

A. Hettwer, J. Kranz, J. Schwider, 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]

Huang, Y.

Y. Huang, F. Janabi-Sharifi, Y. Liu, and Y. Y. Hung, “Dynamic phase measurement in shearography by clustering method and Fourier filtering,” Opt. Express 19(2), 606–615 (2011).
[Crossref] [PubMed]

C. Quan, C. Tay, and Y. Huang, “3-D deformation measurement using fringe projection and digital image correlation,” Optik (Stuttg.) 115(4), 164–168 (2004).
[Crossref]

Hung, Y. Y.

Ichioka, Y.

Ina, H.

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. A 72(1), 156–160 (1982).
[Crossref]

Inuiya, M.

Janabi-Sharifi, F.

Kakue, T.

Kobayashi, S.

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. A 72(1), 156–160 (1982).
[Crossref]

Kranz, J.

A. Hettwer, J. Kranz, J. Schwider, 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]

A. Hettwer, J. Kranz, J. Schwider, 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.

Kujawinska, M.

M. Pirga and M. Kujawinska, “Two directional spatial-carrier phase-shifting method for analysis of crossed and closed fringe patterns,” Opt. Eng. 34(8), 2459–2466 (1995).
[Crossref]

Li, H.

Liu, S.

D. Zhang, Y. Feng, Q. Zhang, S. Xin, X. Lu, S. Liu, and L. Zhong, “Raman spectrum reveals the cell cycle arrest of Triptolide-induced leukemic T-lymphocytes apoptosis,” Spec. Acta Part A Mol. Bio 141, 216–222 (2015).

Liu, Y.

Lu, X.

P. Sun, L. Zhong, C. Luo, W. Niu, and X. Lu, “Visual measurement of the evaporation process of a sessile droplet by dual-channel simultaneous phase-shifting interferometry,” Sci. Rep. 5, 12053 (2015).
[Crossref] [PubMed]

D. Zhang, Y. Feng, Q. Zhang, S. Xin, X. Lu, S. Liu, and L. Zhong, “Raman spectrum reveals the cell cycle arrest of Triptolide-induced leukemic T-lymphocytes apoptosis,” Spec. Acta Part A Mol. Bio 141, 216–222 (2015).

Luo, C.

P. Sun, L. Zhong, C. Luo, W. Niu, and X. Lu, “Visual measurement of the evaporation process of a sessile droplet by dual-channel simultaneous phase-shifting interferometry,” Sci. Rep. 5, 12053 (2015).
[Crossref] [PubMed]

Malacara, D.

D. Malacara, M. Servín, and Z. Malacara, “Interferogram analysis for optical testing,” Opt. Eng. 5, 461–462 (2005).

Malacara, Z.

D. Malacara, M. Servín, and Z. Malacara, “Interferogram analysis for optical testing,” Opt. Eng. 5, 461–462 (2005).

Massig, J. H.

Matoba, O.

Moore, R.

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Proc. SPIE 429, 16–21 (1983).
[Crossref]

Nishio, K.

Niu, W.

P. Sun, L. Zhong, C. Luo, W. Niu, and X. Lu, “Visual measurement of the evaporation process of a sessile droplet by dual-channel simultaneous phase-shifting interferometry,” Sci. Rep. 5, 12053 (2015).
[Crossref] [PubMed]

Oliver, J.

Park, Y.

Peng, H.

Pirga, M.

M. Pirga and M. Kujawinska, “Two directional spatial-carrier phase-shifting method for analysis of crossed and closed fringe patterns,” Opt. Eng. 34(8), 2459–2466 (1995).
[Crossref]

Quan, C.

C. Quan, C. Tay, and Y. Huang, “3-D deformation measurement using fringe projection and digital image correlation,” Optik (Stuttg.) 115(4), 164–168 (2004).
[Crossref]

Quiroga, J. A.

Schwider, J.

A. Hettwer, J. Kranz, J. Schwider, 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]

A. Hettwer, J. Kranz, J. Schwider, 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]

Servin, M.

M. Servin and F. J. Cuevas, “A novel technique for spatial phase-shifting interferometry,” J. Mod. Opt. 42(9), 1853–1862 (1995).
[Crossref]

Servín, M.

J. Vargas, J. A. Quiroga, T. Belenguer, M. Servín, and J. C. Estrada, “Two-step self-tuning phase-shifting interferometry,” Opt. Express 19(2), 638–648 (2011).
[Crossref] [PubMed]

D. Malacara, M. Servín, and Z. Malacara, “Interferogram analysis for optical testing,” Opt. Eng. 5, 461–462 (2005).

Smythe, R.

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Proc. SPIE 429, 16–21 (1983).
[Crossref]

Sorzano, C. O. S.

Sun, P.

P. Sun, L. Zhong, C. Luo, W. Niu, and X. Lu, “Visual measurement of the evaporation process of a sessile droplet by dual-channel simultaneous phase-shifting interferometry,” Sci. Rep. 5, 12053 (2015).
[Crossref] [PubMed]

Tahara, T.

Takeda, M.

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. A 72(1), 156–160 (1982).
[Crossref]

Tay, C.

C. Quan, C. Tay, and Y. Huang, “3-D deformation measurement using fringe projection and digital image correlation,” Optik (Stuttg.) 115(4), 164–168 (2004).
[Crossref]

Ura, S.

Van Der Weide, D.

Vargas, J.

Wang, Z.

Xin, S.

D. Zhang, Y. Feng, Q. Zhang, S. Xin, X. Lu, S. Liu, and L. Zhong, “Raman spectrum reveals the cell cycle arrest of Triptolide-induced leukemic T-lymphocytes apoptosis,” Spec. Acta Part A Mol. Bio 141, 216–222 (2015).

Xu, J.

Xu, Q.

Yamaguchi, I.

Yonesaka, R.

Zhang, D.

D. Zhang, Y. Feng, Q. Zhang, S. Xin, X. Lu, S. Liu, and L. Zhong, “Raman spectrum reveals the cell cycle arrest of Triptolide-induced leukemic T-lymphocytes apoptosis,” Spec. Acta Part A Mol. Bio 141, 216–222 (2015).

Zhang, Q.

D. Zhang, Y. Feng, Q. Zhang, S. Xin, X. Lu, S. Liu, and L. Zhong, “Raman spectrum reveals the cell cycle arrest of Triptolide-induced leukemic T-lymphocytes apoptosis,” Spec. Acta Part A Mol. Bio 141, 216–222 (2015).

Zhang, S.

Zhang, T.

Zhong, L.

P. Sun, L. Zhong, C. Luo, W. Niu, and X. Lu, “Visual measurement of the evaporation process of a sessile droplet by dual-channel simultaneous phase-shifting interferometry,” Sci. Rep. 5, 12053 (2015).
[Crossref] [PubMed]

D. Zhang, Y. Feng, Q. Zhang, S. Xin, X. Lu, S. Liu, and L. Zhong, “Raman spectrum reveals the cell cycle arrest of Triptolide-induced leukemic T-lymphocytes apoptosis,” Spec. Acta Part A Mol. Bio 141, 216–222 (2015).

Zhou, S.

Appl. Opt. (4)

J. Mod. Opt. (1)

M. Servin and F. J. Cuevas, “A novel technique for spatial phase-shifting interferometry,” J. Mod. Opt. 42(9), 1853–1862 (1995).
[Crossref]

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

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. A 72(1), 156–160 (1982).
[Crossref]

Opt. Eng. (3)

M. Pirga and M. Kujawinska, “Two directional spatial-carrier phase-shifting method for analysis of crossed and closed fringe patterns,” Opt. Eng. 34(8), 2459–2466 (1995).
[Crossref]

A. Hettwer, J. Kranz, J. Schwider, 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]

D. Malacara, M. Servín, and Z. Malacara, “Interferogram analysis for optical testing,” Opt. Eng. 5, 461–462 (2005).

Opt. Express (4)

Opt. Lett. (6)

Optik (Stuttg.) (1)

C. Quan, C. Tay, and Y. Huang, “3-D deformation measurement using fringe projection and digital image correlation,” Optik (Stuttg.) 115(4), 164–168 (2004).
[Crossref]

Proc. SPIE (2)

K. Creath and G. Goldstein, “Dynamic phase imaging and processing of moving biological organisms,” Proc. SPIE 8227, 822710 (2012).

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Proc. SPIE 429, 16–21 (1983).
[Crossref]

Sci. Rep. (1)

P. Sun, L. Zhong, C. Luo, W. Niu, and X. Lu, “Visual measurement of the evaporation process of a sessile droplet by dual-channel simultaneous phase-shifting interferometry,” Sci. Rep. 5, 12053 (2015).
[Crossref] [PubMed]

Spec. Acta Part A Mol. Bio (1)

D. Zhang, Y. Feng, Q. Zhang, S. Xin, X. Lu, S. Liu, and L. Zhong, “Raman spectrum reveals the cell cycle arrest of Triptolide-induced leukemic T-lymphocytes apoptosis,” Spec. Acta Part A Mol. Bio 141, 216–222 (2015).

Other (2)

K. Creath, “Dynamic phase imaging for in vitro process monitoring and cell tracking,” in Medicine & Biology Society IEEE Conference(Academic, 2011), 5977–5980.
[Crossref]

M. Kujawinska and J. Wojciak, “Spatial-carrier phase-shifting technique of fringe pattern analysis,” in International Society for Optics and Photonics(Academic, 1991), 61–67.

Supplementary Material (2)

NameDescription
» Visualization 1: MP4 (7209 KB)      The phase variation of a droplet evaporation process
» Visualization 2: MP4 (866 KB)      The phase variation of a Jurkat cell apoptosis treated with DNR

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Figures (5)

Fig. 1
Fig. 1 Simulation results. (a) one-frame SCFI; (b) the preset phase (reference phase); (c)the phase retrieved with the proposed method; (d)the difference of phase retrieval between (b) and (c).
Fig. 2
Fig. 2 Experimental setup for recording SCFI. ND: neutral density filter; BS1-BS2: beam splitter; M1-M2: mirror; MO1-MO2: micro-objective.
Fig. 3
Fig. 3 Experimental results. (a) one-frame SCFI of light-guide plate; the phases retrieved with (b) the proposed method; (c)TPS method; (d)the phase distributions of the 646th row in (b) and (c) and their difference.
Fig. 4
Fig. 4 Interferograms of a water droplet at different moments: (a) t = 0s, (b) t = 5s, (c) t = 10s and the corresponding phases (d-f) retrieved by the proposed method. The whole dynamic process of phase variation can be seen in Visualization 1.
Fig. 5
Fig. 5 Interferograms (a-c) of a Jurkat cell Jurkat cell treated with DNR at different moments after 37 hours 31 minutes (a) 0s, (b) 160s, (c) 240s and the corresponding phases (d-f) retrieved by the proposed method. The whole dynamic process of phase variation can be seen in Visualization 2.

Tables (2)

Tables Icon

Table 1 Phase-shift extracted by Fourier-transform method and its difference with the theoretical value.

Tables Icon

Table 2 RMSE, PVE and Processing time of phase retrieval with different methods.

Equations (15)

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I(x,y)=a(x,y)+b(x,y)cos[2π f 0x x+2π f 0y y+φ(x,y)],
I 1 ( x , y )=I(x,y)=a( x , y )+b( x , y )cos[2π( f 0x x + f 0y y )+φ( x , y )+ θ 1 ],
I 2 ( x , y )=I(x+1,y)=a( x , y )+b( x , y )cos[2π( f 0x x + f 0y y )+φ( x , y )+ θ 2 ],
I 3 ( x , y )=I(x,y+1)=a( x , y )+b( x , y )cos[2π( f 0x x + f 0y y )+φ( x , y )+ θ 3 ],
I 4 ( x , y )=I(x+1,y+1)=a( x , y )+b( x , y )cos[2π( f 0x x + f 0y y )+φ( x , y )+ θ 4 ],
I n (x,y)=a(x,y)+b(x,y)cos[2π( f 0x x+ f 0y y)+φ(x,y)+ θ n ],
I n (x,y)=a(x,y)+exp(i θ n )q(x,y)exp[i(2π f 0x x+2π f 0y y)] +exp(i θ n ) q * (x,y)exp[i(2π f 0x x+2π f 0y y)],
i n ( f x , f y )=A( f x , f y )+exp(i θ n )Q( f x f 0x , f y f 0y )+exp(i θ n ) Q * ( f x + f 0x , f y + f 0y ),
i n ( f 0x , f 0y )=A( f 0x , f 0y )+exp(i θ n )Q(0,0)+exp(i θ n ) Q * (2 f 0x ,2 f 0y ) exp(i θ n )Q(0,0),
θ n tan 1 [ i n ( f 0x , f 0y )],
I n (x,y)= a (x,y)+ b (x,y)cos θ n + c (x,y)sin θ n
S(x,y)= n=1 N [ I n e (x,y) I n (x,y)] 2 ,
S(x,y) a (x,y) =0, S(x,y) b (x,y) =0, S(x,y) c (x,y) =0,
[ a b c ]= | N n=1 N cos θ n n=1 N sin θ n n=1 N cos θ n n=1 N cos 2 θ n n=1 N sin θ n cos θ n n=1 N sin θ n n=1 N sin θ n cos θ n n=1 N sin 2 θ n | 1 | n=1 N I n e n=1 N I n e cos θ n n=1 N I n e sin θ n |
Φ(x,y)=arctan[ c (x,y) / b (x,y) ],

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