Abstract

A method for fast reconstruction of off-axis digital holograms based on digital multiplexing algorithm is proposed. Instead of the existed angular multiplexing (AM), the new method utilizes a spatial multiplexing (SM) algorithm, in which four off-axis holograms recorded in sequence are synthesized into one SM function through multiplying each hologram with a tilted plane wave and then adding them up. In comparison with the conventional methods, the SM algorithm simplifies two-dimensional (2-D) Fourier transforms (FTs) of four N*N arrays into a 1.25-D FTs of one N*N arrays. Experimental results demonstrate that, using the SM algorithm, the computational efficiency can be improved and the reconstructed wavefronts keep the same quality as those retrieved based on the existed AM method. This algorithm may be useful in design of a fast preview system of dynamic wavefront imaging in digital holography.

© 2014 Optical Society of America

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References

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2014 (11)

C. S. Guo, B. Sha, Y. Y. Xie, and X. J. Zhang, “Zero difference algorithm for phase shift extraction in blind phase-shifting holography,” Opt. Lett. 39(4), 813–816 (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]

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]

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. A. Trujillo and J. Garcia-Sucerquia, “Automatic method for focusing biological specimens in digital lensless holographic microscopy,” Opt. Lett. 39(9), 2569–2572 (2014).
[Crossref] [PubMed]

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

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

X. Chen, J. Zhao, J. Wang, J. Di, B. Wu, and J. Liu, “Measurement and reconstruction of three-dimensional configurations of specimen with tiny scattering based on digital holographic tomography,” Appl. Opt. 53(18), 4044–4048 (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]

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]

L. Rong, T. Latychevskaia, D. Y. Wang, X. Zhou, H. C. Huang, Z. Y. Li, and Y. X. Wang, “Terahertz in-line digital holography of dragonfly hindwing: amplitude and phase reconstruction at enhanced resolution by extrapolation,” Opt. Express 22(14), 17236–17245 (2014).
[Crossref] [PubMed]

2013 (6)

2012 (1)

2011 (1)

2010 (1)

2008 (1)

2007 (1)

Allano, D.

Anand, A.

Brunel, M.

Byeon, H. J.

Cai, L. Z.

Chegal, W.

Chen, X.

Cheng, X. C.

Coëtmellec, S.

Deng, J.

Denis, L.

Di, J.

Ding, H.

Do, M.

Doblas, A.

Dong, G. Y.

Fan, J.

Fournier, C.

Fréchou, D.

Frenklach, I.

Garcia-Sucerquia, J.

Girshovitz, P.

Guo, C. S.

Hack, E.

Hernández-Montes, M. S.

Hong, J.

Huang, H. C.

Ichihashi, Y.

Ito, T.

Javidi, B.

Jin, M.

Kang, H.

Kim, D.

Kim, M. K.

Latychevskaia, T.

Lebrun, D.

Lee, J.

Lee, S. J.

Li, Z. Y.

Liu, J.

Lu, X.

Magnusson, R.

Martínez-Corral, M.

Masuda, N.

Méès, L.

Meng, X. F.

Nomura, T.

Park, J.

Patel, S.

Pham, H.

Popescu, G.

Rong, L.

Saavedra, G.

Sánchez-Ortiga, E.

Santoyo, F. M.

Seifi, M.

Seo, K. W.

Sha, B.

Shaked, N. T.

Shen, X. X.

Shimobaba, T.

Sobh, N.

Solís, S. M.

Stoykova, E.

Sun, W. J.

Takada, N.

Trujillo, C. A.

Wang, D. Y.

Wang, H.

Wang, J.

Wang, Y. R.

Wang, Y. X.

Wu, B.

Xie, Y. Y.

Xu, X. F.

Zhang, D.

Zhang, H.

Zhang, X. J.

Zhao, J.

Zhong, L.

Zhou, X.

Zolliker, P.

Appl. Opt. (2)

Biomed. Opt. Express (2)

Chin. Opt. Lett. (2)

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

Opt. Express (6)

Opt. Lett. (9)

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]

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]

C. S. Guo, B. Sha, Y. Y. Xie, and X. J. Zhang, “Zero difference algorithm for phase shift extraction in blind phase-shifting holography,” Opt. Lett. 39(4), 813–816 (2014).
[Crossref] [PubMed]

C. A. Trujillo and J. Garcia-Sucerquia, “Automatic method for focusing biological specimens in digital lensless holographic microscopy,” Opt. Lett. 39(9), 2569–2572 (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]

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]

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 (4)

Fig. 1
Fig. 1 Spatial frequencies of the holograms described in (a) Eq. (1), (b) Eq. (2) and (c) Eq. (3), respectively.
Fig. 2
Fig. 2 Flowchart of the digital spatial multiplexing algorithm for fast reconstruction of off-axis holograms.
Fig. 3
Fig. 3 (a)-(d) are four off-axis holograms experimentally recorded in sequence, (e) shows the result obtained by 1-D FFTs of all the horizontal rows of the SM function array, and (f) gives the desired spatial frequencies calculated from further 1-D FFTs of the columns marked by the dashed lines in (e).
Fig. 4
Fig. 4 (a)-(d) are the phase distributions reconstructed by using the SM algorithm, (e) is the unwrapped phase profiles along the dashed line shown in Fig. 4(a) reconstructed, respectively, by using the SM algorithm (red dashed line) and the AM algorithm (black line).

Equations (3)

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H t = R 0 2 + O t 2 + R 0 O t exp ( i φ t i 2 π ξ 0 x ) + R 0 O t exp ( i 2 π ξ 0 x i φ t ) ,
H = H t + 90 { H t + 1 } ,
H = H t exp ( i 3 π B 4 y ) + H t + 1 exp ( i π B 4 y ) + H t + 2 exp ( i π B 4 y ) + H t + 3 exp ( i 3 π B 4 y ) ,

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