Abstract

In dual-wavelength interferometry (DWI), by combing the advantage of the shorter synthetic-wavelength and the immune algorithm of phase ambiguity, we propose an improved phase retrieval method with both high accuracy and large measurement range, which is a pair of contradiction in the reported DWI method. First, we calculate the height of measured object at longer synthetic-wavelength through using the wrapped phases of two single-wavelengths. Second, by combining the immune algorithm of phase ambiguity and the height of measured object at longer synthetic-wavelength, we can perform the phase unwrapping of the larger one of the two single-wavelengths, then achieve accurate height at single-wavelength named as the transition height. Finally, we perform phase unwrapping of shorter synthetic-wavelength through using the immune algorithm of phase ambiguity and the transition height, and then the height at shorter synthetic-wavelength can be achieved. Compared with the reported method, in addition to maintaining the advantage of high accuracy, the proposed method does not need the additional wavelength, so the corresponding measurement procedures is greatly simplified. Simulation and experimental results demonstrate the performance of proposed method.

© 2017 Optical Society of America

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References

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    [Crossref] [PubMed]
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  24. J. Di, J. Zhang, T. Xi, C. Ma, and J. Zhao, “Improvement of measurement accuracy in digital holographic microscopy by using dual-wavelength technique,” J. Micro. Nanolithogr. MEMS MOEMS 14(4), 041313 (2015).
    [Crossref]

2016 (2)

2015 (2)

W. Zhang, X. Lu, C. Luo, L. Zhong, and J. Vargas, “Principal component analysis based simultaneous dual-wavelength phase-shifting interferometry,” Opt. Commun. 341, 276–283 (2015).
[Crossref]

J. Di, J. Zhang, T. Xi, C. Ma, and J. Zhao, “Improvement of measurement accuracy in digital holographic microscopy by using dual-wavelength technique,” J. Micro. Nanolithogr. MEMS MOEMS 14(4), 041313 (2015).
[Crossref]

2014 (3)

2013 (1)

J. Di, W. Qu, B. Wu, X. Chen, J. Zhao, and A. Asundi, “Dual wavelength digital holography for improving the measurement accuracy,” Proc. SPIE 8769(19), 9149–9427 (2013).

2012 (1)

2011 (4)

2008 (2)

G. Popescu, Y. Park, W. Choi, R. R. Dasari, M. S. Feld, and K. Badizadegan, “Imaging red blood cell dynamics by quantitative phase microscopy,” Blood Cells Mol. Dis. 41(1), 10–16 (2008).
[Crossref] [PubMed]

C. J. Mann, P. R. Bingham, V. C. Paquit, and K. W. Tobin, “Quantitative phase imaging by three-wavelength digital holography,” Opt. Express 16(13), 9753–9764 (2008).
[Crossref] [PubMed]

2006 (1)

2004 (1)

2003 (2)

2001 (1)

1998 (1)

1991 (1)

1987 (1)

1984 (1)

Abdelsalam, D. G.

Abdulhalim, I.

Asundi, A.

J. Di, W. Qu, B. Wu, X. Chen, J. Zhao, and A. Asundi, “Dual wavelength digital holography for improving the measurement accuracy,” Proc. SPIE 8769(19), 9149–9427 (2013).

Badizadegan, K.

G. Popescu, Y. Park, W. Choi, R. R. Dasari, M. S. Feld, and K. Badizadegan, “Imaging red blood cell dynamics by quantitative phase microscopy,” Blood Cells Mol. Dis. 41(1), 10–16 (2008).
[Crossref] [PubMed]

Banaszak Holl, M. M.

Belenguer, T.

Bingham, P. R.

Bokor, J.

Chen, X.

J. Di, W. Qu, B. Wu, X. Chen, J. Zhao, and A. Asundi, “Dual wavelength digital holography for improving the measurement accuracy,” Proc. SPIE 8769(19), 9149–9427 (2013).

Chen, Z.

Choi, W.

G. Popescu, Y. Park, W. Choi, R. R. Dasari, M. S. Feld, and K. Badizadegan, “Imaging red blood cell dynamics by quantitative phase microscopy,” Blood Cells Mol. Dis. 41(1), 10–16 (2008).
[Crossref] [PubMed]

Creath, K.

Dakoff, A.

Dasari, R. R.

G. Popescu, Y. Park, W. Choi, R. R. Dasari, M. S. Feld, and K. Badizadegan, “Imaging red blood cell dynamics by quantitative phase microscopy,” Blood Cells Mol. Dis. 41(1), 10–16 (2008).
[Crossref] [PubMed]

Di, J.

J. Di, J. Zhang, T. Xi, C. Ma, and J. Zhao, “Improvement of measurement accuracy in digital holographic microscopy by using dual-wavelength technique,” J. Micro. Nanolithogr. MEMS MOEMS 14(4), 041313 (2015).
[Crossref]

J. Di, W. Qu, B. Wu, X. Chen, J. Zhao, and A. Asundi, “Dual wavelength digital holography for improving the measurement accuracy,” Proc. SPIE 8769(19), 9149–9427 (2013).

Fei, L.

Feld, M. S.

G. Popescu, Y. Park, W. Choi, R. R. Dasari, M. S. Feld, and K. Badizadegan, “Imaging red blood cell dynamics by quantitative phase microscopy,” Blood Cells Mol. Dis. 41(1), 10–16 (2008).
[Crossref] [PubMed]

Gaskill, J. D.

Gass, J.

Goldberg, K. A.

Han, B.

Huang, L.

Ishii, Y.

Khmaladze, A.

Kim, D.

Kim, M. K.

Lam, P. S.

Li, D.

Lu, X.

Luo, C.

W. Zhang, X. Lu, C. Luo, L. Zhong, and J. Vargas, “Principal component analysis based simultaneous dual-wavelength phase-shifting interferometry,” Opt. Commun. 341, 276–283 (2015).
[Crossref]

Ma, C.

J. Di, J. Zhang, T. Xi, C. Ma, and J. Zhao, “Improvement of measurement accuracy in digital holographic microscopy by using dual-wavelength technique,” J. Micro. Nanolithogr. MEMS MOEMS 14(4), 041313 (2015).
[Crossref]

Magnusson, R.

Mann, C. J.

Matz, R. L.

Onodera, R.

Paquit, V. C.

Park, Y.

G. Popescu, Y. Park, W. Choi, R. R. Dasari, M. S. Feld, and K. Badizadegan, “Imaging red blood cell dynamics by quantitative phase microscopy,” Blood Cells Mol. Dis. 41(1), 10–16 (2008).
[Crossref] [PubMed]

Parshall, D.

Pförtner, A.

Popescu, G.

G. Popescu, Y. Park, W. Choi, R. R. Dasari, M. S. Feld, and K. Badizadegan, “Imaging red blood cell dynamics by quantitative phase microscopy,” Blood Cells Mol. Dis. 41(1), 10–16 (2008).
[Crossref] [PubMed]

Qiu, X.

Qu, W.

J. Di, W. Qu, B. Wu, X. Chen, J. Zhao, and A. Asundi, “Dual wavelength digital holography for improving the measurement accuracy,” Proc. SPIE 8769(19), 9149–9427 (2013).

Quiroga, J. A.

Safrani, A.

Schwider, J.

Shaked, N. T.

Tian, J.

Tobin, K. W.

Vargas, J.

W. Zhang, X. Lu, C. Luo, L. Zhong, and J. Vargas, “Principal component analysis based simultaneous dual-wavelength phase-shifting interferometry,” Opt. Commun. 341, 276–283 (2015).
[Crossref]

J. Vargas, J. A. Quiroga, and T. Belenguer, “Analysis of the principal component algorithm in phase-shifting interferometry,” Opt. Lett. 36(12), 2215–2217 (2011).
[Crossref] [PubMed]

Wang, H.

Wang, T.

Wang, Z.

Wu, B.

J. Di, W. Qu, B. Wu, X. Chen, J. Zhao, and A. Asundi, “Dual wavelength digital holography for improving the measurement accuracy,” Proc. SPIE 8769(19), 9149–9427 (2013).

Wyant, J. C.

Xi, T.

J. Di, J. Zhang, T. Xi, C. Ma, and J. Zhao, “Improvement of measurement accuracy in digital holographic microscopy by using dual-wavelength technique,” J. Micro. Nanolithogr. MEMS MOEMS 14(4), 041313 (2015).
[Crossref]

Xiong, J.

Zhang, C.

Zhang, J.

J. Di, J. Zhang, T. Xi, C. Ma, and J. Zhao, “Improvement of measurement accuracy in digital holographic microscopy by using dual-wavelength technique,” J. Micro. Nanolithogr. MEMS MOEMS 14(4), 041313 (2015).
[Crossref]

Zhang, W.

Zhao, H.

Zhao, J.

J. Di, J. Zhang, T. Xi, C. Ma, and J. Zhao, “Improvement of measurement accuracy in digital holographic microscopy by using dual-wavelength technique,” J. Micro. Nanolithogr. MEMS MOEMS 14(4), 041313 (2015).
[Crossref]

J. Di, W. Qu, B. Wu, X. Chen, J. Zhao, and A. Asundi, “Dual wavelength digital holography for improving the measurement accuracy,” Proc. SPIE 8769(19), 9149–9427 (2013).

Zhong, L.

Zhou, Y.

Appl. Opt. (9)

P. S. Lam, J. D. Gaskill, and J. C. Wyant, “Two-wavelength holographic interferometer,” Appl. Opt. 23(18), 3079–3081 (1984).
[Crossref] [PubMed]

K. Creath, “Step height measurement using two-wavelength phase-shifting interferometry,” Appl. Opt. 26(14), 2810–2816 (1987).
[Crossref] [PubMed]

R. Onodera and Y. Ishii, “Two-wavelength interferometry that uses a fourier-transform method,” Appl. Opt. 37(34), 7988–7994 (1998).
[Crossref] [PubMed]

K. A. Goldberg and J. Bokor, “Fourier-transform method of phase-shift determination,” Appl. Opt. 40(17), 2886–2894 (2001).
[Crossref] [PubMed]

A. Pförtner and J. Schwider, “Red-green-blue interferometer for the metrology of discontinuous structures,” Appl. Opt. 42(4), 667–673 (2003).
[Crossref] [PubMed]

D. Parshall and M. K. Kim, “Digital holographic microscopy with dual-wavelength phase unwrapping,” Appl. Opt. 45(3), 451–459 (2006).
[Crossref] [PubMed]

D. G. Abdelsalam, R. Magnusson, and D. Kim, “Single-shot, dual-wavelength digital holography based on polarizing separation,” Appl. Opt. 50(19), 3360–3368 (2011).
[Crossref] [PubMed]

D. G. Abdelsalam and D. Kim, “Two-wavelength in-line phase-shifting interferometry based on polarizing separation for accurate surface profiling,” Appl. Opt. 50(33), 6153–6161 (2011).
[Crossref] [PubMed]

L. Huang, X. Lu, Y. Zhou, J. Tian, and L. Zhong, “Dual-wavelength interferometry based on the spatial carrier-frequency phase-shifting method,” Appl. Opt. 55(9), 2363–2369 (2016).
[Crossref] [PubMed]

Blood Cells Mol. Dis. (1)

G. Popescu, Y. Park, W. Choi, R. R. Dasari, M. S. Feld, and K. Badizadegan, “Imaging red blood cell dynamics by quantitative phase microscopy,” Blood Cells Mol. Dis. 41(1), 10–16 (2008).
[Crossref] [PubMed]

J. Micro. Nanolithogr. MEMS MOEMS (1)

J. Di, J. Zhang, T. Xi, C. Ma, and J. Zhao, “Improvement of measurement accuracy in digital holographic microscopy by using dual-wavelength technique,” J. Micro. Nanolithogr. MEMS MOEMS 14(4), 041313 (2015).
[Crossref]

Opt. Commun. (1)

W. Zhang, X. Lu, C. Luo, L. Zhong, and J. Vargas, “Principal component analysis based simultaneous dual-wavelength phase-shifting interferometry,” Opt. Commun. 341, 276–283 (2015).
[Crossref]

Opt. Express (3)

Opt. Lett. (8)

Proc. SPIE (1)

J. Di, W. Qu, B. Wu, X. Chen, J. Zhao, and A. Asundi, “Dual wavelength digital holography for improving the measurement accuracy,” Proc. SPIE 8769(19), 9149–9427 (2013).

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Figures (8)

Fig. 1
Fig. 1

Schematic of immune algorithm of phase ambiguity, in which h sub and h λ 1 denote the heights of measured sample at Λ sub and λ 1 , respectively; h λ 1 ' is the corresponding burring height.

Fig. 2
Fig. 2

Simulated result of a vortex phase plate through using the proposed method with the zero-mean Gaussian white noise with standard deviation σ=8 , one-frame interferogram of single-wavelength at (a) 532nm and (b) 632.8nm; (c)-(e) height maps of h sub , h λ1 and h add , respectively; (f) height map that achieved with the immune algorithm of phase ambiguity and φ add directly; (g) the difference maps between (c) and (d); (h) the difference maps between (e) and (d).

Fig. 3
Fig. 3

Height distributions of the 40 th row retrieved from Figs. 2(c)-2(e), respectively.

Fig. 4
Fig. 4

RMSEs of achieved height in different standard deviations of zero-mean Gaussian white noise.

Fig. 5
Fig. 5

Mach-Zehnder interferometer based dual-wavelength phase-shifting interferometry system, CLBE: collimating laser beam expander, ND: neutral density filter, BS1 and BS2:beam splitter, PZT: piezoelectric transducer, M1 and M2:mirror.

Fig. 6
Fig. 6

Experimental phase-shifting interferograms of a vortex phase plate of single-wavelength at (a) 532nm; (b) 632.8nm; (c),(d) the corresponding background of (a) and(b), respectively.

Fig. 7
Fig. 7

(a) Height map of h sub achieved with the wrapped phases of single-wavelength; (b) height map of h λ 1 achieved through combining the immune algorithm of phase ambiguity and h sub ; (c) height map of h add achieved through combining the immune algorithm of phase ambiguity and h λ 1 .

Fig. 8
Fig. 8

Height distribution curves of the 50 th row extracted from Fig. 7(a)-7(c), respectively.

Equations (19)

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h λ 1 (x,y)=[ n λ 1 (x,y)+ φ 1 (x,y) 2π ] λ 1 .
Λ sub = λ 1 λ 2 λ 1 λ 2 .
φ sub = φ 2 φ 1 .
h sub = φ sub Λ sub 2π .
h sub = h λ 1 +Δ.
r 1 =round( h sub λ 1 /2 λ 1 ).
h sub λ 1 /2= n λ 1 λ 1 + φ 1 2π λ 1 +Δ λ 1 /2.
λ 1 <Δ+ φ 1 2π λ 1 λ 1 /2< λ 1
r 1 ={ n λ 1 1 λ 1 /2<Δ+ φ 1 2π λ 1 <0 n λ 1 0<Δ+ φ 1 2π λ 1 < λ 1 n λ 1 +1 λ 1 <Δ+ φ 1 2π λ 1 <3 λ 1 /2 .
h λ 1 '=[ r 1 + φ 1 2π ] λ 1 .
D= h sub h λ 1 '={ Δ+ λ 1 r 1 = n λ 1 1 Δ r 1 = n λ 1 Δ λ 1 r 1 = n λ 1 +1 .
c 1 =round( D λ 1 )={ 1 r 1 = n λ 1 1 0 r 1 = n λ 1 1 r 1 = n λ 1 +1 .
h λ 1 =[ r 1 + c 1 + φ λ 1 (x,y) 2π ] λ 1 .
r 1 + c 1 ={ n λ 1 + m+1 2 (m=odd) n λ 1 + m+1 2 (m=odd) n λ 1 + m 2 (m=ever) n λ 1 + m 2 (m=ever) .
Λ add = λ 1 λ 2 λ 1 + λ 2 .
φ add = φ 1 + φ 2 .
h add (x,y)=[ n add (x,y)+ φ add (x,y) 2π ] Λ add .
φ add ={ φ add +2π φ add <0 φ add 2π φ add >2π .
h add =[ r add + c add + φ add (x,y) 2π ] Λ add .

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