Abstract

A simple noniterative algorithm for retrieval of the unknown phase shifts in phase-shifting holography is proposed. In this algorithm, the phase shift value between two phase-shifting holograms can be calculated through a simple analytical formula that is derived according to the fact that there exist some points whose intensity difference between two phase-shifting holograms is equal to zero. Both the simulated and experimental results demonstrated the feasibility of this so-called zero difference algorithm over a wide range of phase shifts.

© 2014 Optical Society of America

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  1. T. Tahara, Y. Ito, Y. Lee, P. Xia, J. Inoue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, Opt. Lett. 38, 2789 (2013).
    [CrossRef]
  2. H. Huang, Y. Ren, Y. Yan, N. Ahmed, Y. Yue, A. Bozovich, B. I. Erkmen, K. Birnbaum, S. Dolinar, M. Tur, and A. E. Willner, Opt. Lett. 38, 2348 (2013).
    [CrossRef]
  3. C. Meneses-Fabian, R. Kantun-Montiel, G.-P. Lemus-Alonso, and U. Rivera-Ortega, Opt. Lett. 38, 1850 (2013).
    [CrossRef]
  4. J. Wang, Y. Song, Z. Li, and A. He, Opt. Lett. 38, 1116 (2013).
    [CrossRef]
  5. L. I. Muravsky, A. B. Kmet’, and T. I. Voronyak, Opt. Lasers Eng. 50, 1508 (2012).
    [CrossRef]
  6. M. Shan, B. Hao, Z. Zhong, M. Diao, and Y. Zhang, Opt. Express 21, 2126 (2013).
    [CrossRef]
  7. T. Kakue, S. Itoh, P. Xia, T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, Opt. Express 20, 20286 (2012).
    [CrossRef]
  8. M. Imbe and T. Nomura, Appl. Opt. 52, 4097 (2013).
    [CrossRef]
  9. S. Nakadate, S. Sawada, T. Kiire, M. Shibuya, and T. Yatagai, Appl. Opt. 52, A433 (2013).
    [CrossRef]
  10. K. A. Goldberg and J. Bokor, Appl. Opt. 40, 2886 (2001).
    [CrossRef]
  11. Z. Wang and B. Han, Opt. Lett. 29, 1671 (2004).
    [CrossRef]
  12. J. Xu, W. Jin, L. Chai, and Q. Xu, Opt. Express 19, 20483 (2011).
    [CrossRef]
  13. S. Zhang, Opt. Commun. 268, 231 (2006).
    [CrossRef]
  14. X. F. Xu, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Meng, G. Y. Dong, X. X. Shen, and H. Zhang, Appl. Phys. Lett. 90, 121124 (2007).
    [CrossRef]
  15. X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, W. J. Sun, H. Zhang, X. C. Cheng, G. Y. Dong, and X. X. Shen, Opt. Lett. 33, 776 (2008).
    [CrossRef]
  16. P. Gao, B. Yao, N. Lindlein, K. Mantel, I. Harder, and E. Geist, Opt. Lett. 34, 3553 (2009).
    [CrossRef]
  17. Q. Hao, Q. Zhu, and Y. Hu, Opt. Lett. 34, 1288 (2009).
    [CrossRef]
  18. J. Xu, Q. Xu, L. Chai, Y. Li, and H. Wang, Opt. Express 18, 20620 (2010).
    [CrossRef]
  19. J. Vargas, J. A. Quiroga, and T. Belenguer, Opt. Lett. 36, 1326 (2011).
    [CrossRef]
  20. J. Vargas, J. Antonio Quiroga, C. O. S. Sorzano, J. C. Estrada, and J. M. Carazo, Opt. Lett. 37, 443 (2012).
    [CrossRef]
  21. J. Deng, H. Wang, F. Zhang, D. Zhang, L. Zhong, and X. Lu, Opt. Lett. 37, 4669 (2012).
    [CrossRef]
  22. H. Guo and Z. Zhang, Appl. Opt. 52, 6572 (2013).
    [CrossRef]
  23. X. Xu, G. Lu, G. Han, F. Gao, Z. Jiao, and D. Li, Appl. Opt. 52, 4864 (2013).
    [CrossRef]
  24. J. Deng, H. Wang, D. Zhang, L. Zhong, J. Fan, and X. Lu, Opt. Lett. 38, 1506 (2013).
    [CrossRef]
  25. C. S. Guo, L. Zhang, H. T. Wang, J. Liao, and Y. Y. Zhu, Opt. Lett. 27, 1687 (2002).
    [CrossRef]

2013 (10)

2012 (4)

2011 (2)

2010 (1)

2009 (2)

2008 (1)

2007 (1)

X. F. Xu, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Meng, G. Y. Dong, X. X. Shen, and H. Zhang, Appl. Phys. Lett. 90, 121124 (2007).
[CrossRef]

2006 (1)

S. Zhang, Opt. Commun. 268, 231 (2006).
[CrossRef]

2004 (1)

2002 (1)

2001 (1)

Ahmed, N.

Antonio Quiroga, J.

Awatsuji, Y.

Belenguer, T.

Birnbaum, K.

Bokor, J.

Bozovich, A.

Cai, L. Z.

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, W. J. Sun, H. Zhang, X. C. Cheng, G. Y. Dong, and X. X. Shen, Opt. Lett. 33, 776 (2008).
[CrossRef]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Meng, G. Y. Dong, X. X. Shen, and H. Zhang, Appl. Phys. Lett. 90, 121124 (2007).
[CrossRef]

Carazo, J. M.

Chai, L.

Cheng, X. C.

Deng, J.

Diao, M.

Dolinar, S.

Dong, G. Y.

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, W. J. Sun, H. Zhang, X. C. Cheng, G. Y. Dong, and X. X. Shen, Opt. Lett. 33, 776 (2008).
[CrossRef]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Meng, G. Y. Dong, X. X. Shen, and H. Zhang, Appl. Phys. Lett. 90, 121124 (2007).
[CrossRef]

Erkmen, B. I.

Estrada, J. C.

Fan, J.

Gao, F.

Gao, P.

Geist, E.

Goldberg, K. A.

Guo, C. S.

Guo, H.

Han, B.

Han, G.

Hao, B.

Hao, Q.

Harder, I.

He, A.

Hu, Y.

Huang, H.

Imbe, M.

Inoue, J.

Ito, Y.

Itoh, S.

Jiao, Z.

Jin, W.

Kakue, T.

Kantun-Montiel, R.

Kiire, T.

Kmet’, A. B.

L. I. Muravsky, A. B. Kmet’, and T. I. Voronyak, Opt. Lasers Eng. 50, 1508 (2012).
[CrossRef]

Kubota, T.

Lee, Y.

Lemus-Alonso, G.-P.

Li, D.

Li, Y.

Li, Z.

Liao, J.

Lindlein, N.

Lu, G.

Lu, X.

Mantel, K.

Matoba, O.

Meneses-Fabian, C.

Meng, X. F.

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, W. J. Sun, H. Zhang, X. C. Cheng, G. Y. Dong, and X. X. Shen, Opt. Lett. 33, 776 (2008).
[CrossRef]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Meng, G. Y. Dong, X. X. Shen, and H. Zhang, Appl. Phys. Lett. 90, 121124 (2007).
[CrossRef]

Muravsky, L. I.

L. I. Muravsky, A. B. Kmet’, and T. I. Voronyak, Opt. Lasers Eng. 50, 1508 (2012).
[CrossRef]

Nakadate, S.

Nishio, K.

Nomura, T.

Quiroga, J. A.

Ren, Y.

Rivera-Ortega, U.

Sawada, S.

Shan, M.

Shen, X. X.

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, W. J. Sun, H. Zhang, X. C. Cheng, G. Y. Dong, and X. X. Shen, Opt. Lett. 33, 776 (2008).
[CrossRef]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Meng, G. Y. Dong, X. X. Shen, and H. Zhang, Appl. Phys. Lett. 90, 121124 (2007).
[CrossRef]

Shibuya, M.

Song, Y.

Sorzano, C. O. S.

Sun, W. J.

Tahara, T.

Tur, M.

Ura, S.

Vargas, J.

Voronyak, T. I.

L. I. Muravsky, A. B. Kmet’, and T. I. Voronyak, Opt. Lasers Eng. 50, 1508 (2012).
[CrossRef]

Wang, H.

Wang, H. T.

Wang, J.

Wang, Y. R.

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, W. J. Sun, H. Zhang, X. C. Cheng, G. Y. Dong, and X. X. Shen, Opt. Lett. 33, 776 (2008).
[CrossRef]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Meng, G. Y. Dong, X. X. Shen, and H. Zhang, Appl. Phys. Lett. 90, 121124 (2007).
[CrossRef]

Wang, Z.

Willner, A. E.

Xia, P.

Xu, J.

Xu, Q.

Xu, X.

Xu, X. F.

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, W. J. Sun, H. Zhang, X. C. Cheng, G. Y. Dong, and X. X. Shen, Opt. Lett. 33, 776 (2008).
[CrossRef]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Meng, G. Y. Dong, X. X. Shen, and H. Zhang, Appl. Phys. Lett. 90, 121124 (2007).
[CrossRef]

Yan, Y.

Yang, X. L.

X. F. Xu, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Meng, G. Y. Dong, X. X. Shen, and H. Zhang, Appl. Phys. Lett. 90, 121124 (2007).
[CrossRef]

Yao, B.

Yatagai, T.

Yue, Y.

Zhang, D.

Zhang, F.

Zhang, H.

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, W. J. Sun, H. Zhang, X. C. Cheng, G. Y. Dong, and X. X. Shen, Opt. Lett. 33, 776 (2008).
[CrossRef]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Meng, G. Y. Dong, X. X. Shen, and H. Zhang, Appl. Phys. Lett. 90, 121124 (2007).
[CrossRef]

Zhang, L.

Zhang, S.

S. Zhang, Opt. Commun. 268, 231 (2006).
[CrossRef]

Zhang, Y.

Zhang, Z.

Zhong, L.

Zhong, Z.

Zhu, Q.

Zhu, Y. Y.

Appl. Opt. (5)

Appl. Phys. Lett. (1)

X. F. Xu, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Meng, G. Y. Dong, X. X. Shen, and H. Zhang, Appl. Phys. Lett. 90, 121124 (2007).
[CrossRef]

Opt. Commun. (1)

S. Zhang, Opt. Commun. 268, 231 (2006).
[CrossRef]

Opt. Express (4)

Opt. Lasers Eng. (1)

L. I. Muravsky, A. B. Kmet’, and T. I. Voronyak, Opt. Lasers Eng. 50, 1508 (2012).
[CrossRef]

Opt. Lett. (13)

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Figures (2)

Fig. 1.
Fig. 1.

Experimental results. (a) and (b) are the holograms recorded by the CCD sensor before and after tilting the glass plate about 4 degrees; (c) and (d) are the recorded intensities of the object wave and the reference wave on the recording plane, respectively; (e) is the image directly reconstructed by the hologram shown in (a); and (f) is the final image reconstructed by the retrieved complex amplitude, based on the ZD algorithm.

Fig. 2.
Fig. 2.

RMS errors of the extracted phase shifts, based on our ZD method when the phase shift value changes from 0.1 to 3.1 rad; the curves marked by squares, circles, regular triangles, and inverted triangles represent the simulated results when the quantization of the imaging sensor is taken as 8, 10, 12, and 16 bits, respectively.

Equations (8)

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

I1=Io+Ir+2IrIocos(φor),
I2=Io+Ir+2IrIocos(φorδ),
Aoexp(iφor)=I1Ao2Ar2exp(jδ)(I2Ao2Ar2)Ar[1exp(j2δ)].
I1I2=4IrIosin(φorδ/2)sin(δ/2).
IrIosin(φorδ/2)sin(δ/2)=0,
φor=δ/2,(atI1=I2).
δ2=cos1(I1(0)Io(0)Ir(0)2Io(0)Ir(0)),
δ2Nn=1Ncos1(I1,n(ε)Io,n(ε)Ir,n(ε)2Io,n(ε)Ir,n(ε)).

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