Abstract

A phase derivative (PD) method is proposed for reconstruction of off-axis holograms. In this method, a phase distribution of the tested object wave constrained within 0 to pi radian is firstly worked out by a simple analytical formula; then it is corrected to its right range from –pi to pi according to the sign characteristics of its first-order derivative. A theoretical analysis indicates that this PD method is particularly suitable for reconstruction of slightly off-axis holograms because it only requires the spatial frequency of the reference beam larger than spatial frequency of the tested object wave in principle. In addition, because the PD method belongs to a pure local method with no need of any integral operation or phase shifting algorithm in process of the phase retrieval, it could have some advantages in reducing computer load and memory requirements to the image processing system. Some experimental results are given to demonstrate the feasibility of the method.

© 2014 Optical Society of America

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References

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2014 (8)

A. Anand and B. Javidi, “Digital holographic microscopy for automated 3D cell identification: an overview,” Chin. Opt. Lett. 12(6), 060012 (2014).
[Crossref]

K. W. Seo, H. J. Byeon, and S. J. Lee, “Measuring the light scattering and orientation of a spheroidal particle using in-line holography,” Opt. Lett. 39(13), 3915–3918 (2014).
[Crossref] [PubMed]

E. Hack and P. Zolliker, “Terahertz holography for imaging amplitude and phase objects,” Opt. Express 22(13), 16079–16086 (2014).
[Crossref] [PubMed]

E. Stoykova, H. Kang, and J. Park, “Twin-image problem in digital holography-a survey,” Chin. Opt. Lett. 12(6), 060013 (2014).
[Crossref]

E. Sánchez-Ortiga, A. Doblas, G. Saavedra, M. Martínez-Corral, and J. Garcia-Sucerquia, “Off-axis digital holographic microscopy: practical design parameters for operating at diffraction limit,” Appl. Opt. 53(10), 2058–2066 (2014).
[Crossref] [PubMed]

I. Frenklach, P. Girshovitz, and N. T. Shaked, “Off-axis interferometric phase microscopy with tripled imaging area,” Opt. Lett. 39(6), 1525–1528 (2014).
[Crossref] [PubMed]

P. Girshovitz and N. T. Shaked, “Real-time quantitative phase reconstruction in off-axis digital holography using multiplexing,” Opt. Lett. 39(8), 2262–2265 (2014).
[Crossref] [PubMed]

C. S. Guo, Y. Y. Xie, and B. Sha, “Diffraction algorithm suitable for both near and far field with shifted destination window and oblique illumination,” Opt. Lett. 39(8), 2338–2341 (2014).
[Crossref] [PubMed]

2013 (4)

2012 (2)

2011 (2)

2009 (1)

2008 (1)

2007 (1)

Anand, A.

Byeon, H. J.

Cai, L. Z.

Chegal, W.

Cheng, X. C.

Dan, D.

Deng, J.

Doblas, A.

Dong, G. Y.

Duan, T.

Fan, J.

Frenklach, I.

Gao, P.

Garcia-Sucerquia, J.

Girshovitz, P.

Gu, Y.

Guo, C. S.

Guo, R.

Hack, E.

Han, J.

Hernández-Montes, M. S.

Hong, J.

Huang, M.

Javidi, B.

Jin, M.

Kang, H.

Kim, D.

Kim, M. K.

Lai, J.

Lee, J.

Lee, S. J.

Lei, M.

Li, Z.

Lu, X.

Ma, B.

Magnusson, R.

Martínez-Corral, M.

Meng, X. F.

Min, J.

Nomura, T.

Park, J.

Rinehart, M. T.

Saavedra, G.

Sánchez-Ortiga, E.

Santoyo, F. M.

Seo, K. W.

Sha, B.

Shaked, N. T.

Shen, X. X.

Solís, S. M.

Stoykova, E.

Sun, W. J.

Wang, H.

Wang, S.

Wang, Y. R.

Wax, A.

Xie, Y. Y.

Xu, X. F.

Xue, L.

Yan, S.

Yang, Y.

Yao, B.

Ye, T.

Zhang, D.

Zhang, H.

Zheng, J.

Zhong, L.

Zhu, Y.

Zolliker, P.

Appl. Opt. (3)

Biomed. Opt. Express (2)

Chin. Opt. Lett. (2)

Opt. Express (4)

Opt. Lett. (8)

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, “Simple direct extraction of unknown phase shift and wavefront reconstruction in generalized phase-shifting interferometry: algorithm and experiments,” Opt. Lett. 33(8), 776–778 (2008).
[Crossref] [PubMed]

J. Deng, H. Wang, D. Zhang, L. Zhong, J. Fan, and X. Lu, “Phase shift extraction algorithm based on Euclidean matrix norm,” Opt. Lett. 38(9), 1506–1508 (2013).
[Crossref] [PubMed]

P. Girshovitz and N. T. Shaked, “Real-time quantitative phase reconstruction in off-axis digital holography using multiplexing,” Opt. Lett. 39(8), 2262–2265 (2014).
[Crossref] [PubMed]

C. S. Guo, Y. Y. Xie, and B. Sha, “Diffraction algorithm suitable for both near and far field with shifted destination window and oblique illumination,” Opt. Lett. 39(8), 2338–2341 (2014).
[Crossref] [PubMed]

J. Hong and M. K. Kim, “Single-shot self-interference incoherent digital holography using off-axis configuration,” Opt. Lett. 38(23), 5196–5199 (2013).
[Crossref] [PubMed]

I. Frenklach, P. Girshovitz, and N. T. Shaked, “Off-axis interferometric phase microscopy with tripled imaging area,” Opt. Lett. 39(6), 1525–1528 (2014).
[Crossref] [PubMed]

T. Nomura and B. Javidi, “Object recognition by use of polarimetric phase-shifting digital holography,” Opt. Lett. 32(15), 2146–2148 (2007).
[Crossref] [PubMed]

K. W. Seo, H. J. Byeon, and S. J. Lee, “Measuring the light scattering and orientation of a spheroidal particle using in-line holography,” Opt. Lett. 39(13), 3915–3918 (2014).
[Crossref] [PubMed]

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Figures (3)

Fig. 1
Fig. 1 (a) Part of the phase distribution of the object wave along x axis. (b) Corresponding relative phase φor. (c) Absolute phase Φ calculated according to Eq. (2). (d) Derivative of the phase Φ. (e) Retrieved relative phase according to Eq. (7). (f) Retrieved object phase after the reference phase is compensated.
Fig. 2
Fig. 2 Off-axis holographic recording setup used in our experiments mainly composed by the source S, the grating G, the lenses L1 and L2, the optical chopper OC, the beam splitters BS1 and BS2, the reflectors M1 and M2 and the image sensor IS.
Fig. 3
Fig. 3 (a)-(c) Intensities of I, Io and Ir respectively recorded in experiments. (d) Absolute phase Φ calculated by Eq. (2). (e) Sign distribution of the derivative of Φ. (f) Retrieved relative phase of the object wave according to Eq. (7). (g) Retrieved phase distribution of the object wave. (h) Image of the object through digital diffraction of the retrieved complex amplitude. (i) Image reconstructed by a single off-axis hologram based on the Fourier transform method.

Equations (7)

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

I= | A o exp(i φ 0 )+ A r exp(i φ r ) | 2 = I o + I r +2 I o I r cos( φ or ),
Φ= cos 1 ( I I o I r 2 I o I r )=| φ or |.
φ or x = φ o x φ r x = φ o x q.
q> φ o / x .
φ or / x <0 (for any phase of φ o ).
Φ x ={ φ or / x <0, (if φ or >0) φ or / x >0, (if φ or <0) .
φ or ={ Φ, (if Φ / x <0) Φ, (if Φ / x >0) .

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