Abstract

In this Letter, the character of Euclidean matrix norm (EMN) of the intensity difference between phase-shifting interferograms, which changes in sinusoidal form with the phase shifts, is presented. Based on this character, an EMN phase shift extraction algorithm is proposed. Both the simulation calculation and experimental research show that the phase shifts with high precision can be determined with the proposed EMN algorithm easily. Importantly, the proposed EMN algorithm will supply a powerful tool for the rapid calibration of the phase shifts.

© 2013 Optical Society of America

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References

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  1. D. Malacara, M. Servín, and Z. Malacara, Interferogram analysis for optical testing (CRC, 2005).
  2. P. Gao, B. Yao, N. Lindlein, K. Mantel, I. Harder, and E. Geist, Opt. Lett. 34, 3553 (2009).
    [CrossRef]
  3. Z. Wang and B. Han, Opt. Lett. 29, 1671 (2004).
    [CrossRef]
  4. K. A. Goldberg and J. Bokor, Appl. Opt. 40, 2886 (2001).
    [CrossRef]
  5. Q. Hao, Q. Zhu, and Y. Hu, Opt. Lett. 34, 1288 (2009).
    [CrossRef]
  6. J. Xu, Q. Xu, L. Chai, Y. Li, and H. Wang, Opt. Express 18, 20620 (2010).
    [CrossRef]
  7. J. Vargas, J. A. Quiroga, and T. Belenguer, Opt. Lett. 36, 1326 (2011).
    [CrossRef]
  8. J. Vargas, J. A. Quiroga, and T. Belenguer, Opt. Lett. 36, 2215 (2011).
    [CrossRef]
  9. J. Deng, H. Wang, F. Zhang, D. Zhang, L. Zhong, and X. Lu, Opt. Lett. 37, 4669 (2012).
    [CrossRef]

2012 (1)

2011 (2)

2010 (1)

2009 (2)

2004 (1)

2001 (1)

Belenguer, T.

Bokor, J.

Chai, L.

Deng, J.

Gao, P.

Geist, E.

Goldberg, K. A.

Han, B.

Hao, Q.

Harder, I.

Hu, Y.

Li, Y.

Lindlein, N.

Lu, X.

Malacara, D.

D. Malacara, M. Servín, and Z. Malacara, Interferogram analysis for optical testing (CRC, 2005).

Malacara, Z.

D. Malacara, M. Servín, and Z. Malacara, Interferogram analysis for optical testing (CRC, 2005).

Mantel, K.

Quiroga, J. A.

Servín, M.

D. Malacara, M. Servín, and Z. Malacara, Interferogram analysis for optical testing (CRC, 2005).

Vargas, J.

Wang, H.

Wang, Z.

Xu, J.

Xu, Q.

Yao, B.

Zhang, D.

Zhang, F.

Zhong, L.

Zhu, Q.

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Figures (2)

Fig. 1.
Fig. 1.

Simulation results. (a) One of the simulation fringe patterns, (b) the EMN of the intensity difference between phase-shifting fringe patterns changes with the phase shifts, (c) the phase shifts obtained with the EMN algorithm, and (d) the phase shift errors between the proposed EMN algorithm and the theoretical value.

Fig. 2.
Fig. 2.

Experimental results. (a) One of the experimental phase-shifting interferograms, (b) the EMN of the intensity difference between phase-shifting interferograms changes with the phase shifts, (c) the phase shifts obtained with EMN algorithm, and (d) the phase shift errors between the proposed EMN algorithm and the EVI algorithm.

Tables (1)

Tables Icon

Table 1. Processing Times, RMSEs and MAXEs Obtained by the EMN, AIA, PCA, and ACA Methods with Real Interferograms

Equations (10)

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PQ2=(m=1Mn=1N[pmnqmn]2)1/2,
Ik=[ikmn],
ikmn=amn+bmncos[φmn+θk],
dk=I1Ik2=[m=1Mn=1N(i1mnikmn)2]1/2.
i1mnikmn=2bmnsin(θk/2)sin(φmn+θk/2).
dk=2sin(θk/2)[m=1Mn=1Nbmn2m=1Mn=1Nbmn2cos(2φmn+θk)]1/2.
m=1Mn=1Nbmn2cos(2φmn+θk)m=1Mn=1Nbmn2.
dk2(m=1Mn=1Nbmn2)1/2sin(θk/2).
dmax2(m=1Mn=1Nbmn2)1/2.
θk=2arcsin(dk/dmax).

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