Abstract

A novel numerical iterative approach is proposed to effectively eliminate the zero-order term and to improve the signal-to-noise ratio of the reconstructed image in off-axis digital holography. The iterations are conducted in the spatial domain, resulting in considerable reduction in the computational time and avoiding the subjectivity involved in selecting a filter window in spectral domain. These advantages promote the application of this approach in real-time detection processes. The feasibility of this approach is confirmed by mathematical deductions and numerical simulations, and the robustness of the proposed approach is tested by means of an experimentally obtained hologram.

© 2013 Optical Society of America

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References

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2013 (1)

2012 (2)

2011 (1)

2010 (2)

2009 (4)

2004 (1)

2003 (2)

2002 (1)

C. Liu, Y. Li, X. Cheng, Z. Liu, F. Bo, and J. Zhu, “Elimination of zero-order diffraction in digital holography,” Opt. Eng.41(10), 2434–2437 (2002).
[CrossRef]

2001 (1)

1999 (1)

1997 (1)

1965 (1)

Ali, P. T. S.

Arfire, C.

Bergoënd, I.

Bo, F.

C. Liu, Y. Li, X. Cheng, Z. Liu, F. Bo, and J. Zhu, “Elimination of zero-order diffraction in digital holography,” Opt. Eng.41(10), 2434–2437 (2002).
[CrossRef]

Cai, L. Z.

Carazo, J. M.

Cheng, X.

C. Liu, Y. Li, X. Cheng, Z. Liu, F. Bo, and J. Zhu, “Elimination of zero-order diffraction in digital holography,” Opt. Eng.41(10), 2434–2437 (2002).
[CrossRef]

Demoli, N.

Depeursinge, C.

Devaney, A. J.

Dong, Y.

Dong, Y. C.

Estrada, J. C.

Guo, P.

Haines, K. A.

Huang, M.

Jin, H.

Joseph, J.

Kanka, M.

Kato, J.

Kawai, H.

Khare, K.

Kreuzer, H. J.

Kühn, J.

Leith, E. N.

Li, Y.

L. Ma, H. Wang, Y. Li, and H. Jin, “Partition calculation for zero-order and conjugate image removal in digital in-line holography,” Opt. Express20(2), 1805–1815 (2012).
[CrossRef] [PubMed]

C. Liu, Y. Li, X. Cheng, Z. Liu, F. Bo, and J. Zhu, “Elimination of zero-order diffraction in digital holography,” Opt. Eng.41(10), 2434–2437 (2002).
[CrossRef]

Liu, C.

C. Liu, Y. Li, X. Cheng, Z. Liu, F. Bo, and J. Zhu, “Elimination of zero-order diffraction in digital holography,” Opt. Eng.41(10), 2434–2437 (2002).
[CrossRef]

Liu, J. P.

Liu, Q.

Liu, Z.

C. Liu, Y. Li, X. Cheng, Z. Liu, F. Bo, and J. Zhu, “Elimination of zero-order diffraction in digital holography,” Opt. Eng.41(10), 2434–2437 (2002).
[CrossRef]

Lu, M. F.

Ma, L.

Mestrovic, J.

Mizuno, J.

Ohta, S.

Ohzu, H.

Pavillon, N.

Poon, T. C.

Quiroga, J. A.

Riesenberg, R.

Rinehart, M. T.

Seelamantula, C. S.

Shaked, N. T.

Sorzano, C. O. S.

Sovic, I.

Takaki, Y.

Unser, M.

Upatnieks, J.

Vargas, J.

Wang, H.

Wax, A.

Wu, J.

Wu, Y. N.

Yamaguchi, I.

Yang, X. L.

Zhang, T.

Zheng, M.

Zhu, J.

C. Liu, Y. Li, X. Cheng, Z. Liu, F. Bo, and J. Zhu, “Elimination of zero-order diffraction in digital holography,” Opt. Eng.41(10), 2434–2437 (2002).
[CrossRef]

Zhu, Y.

Appl. Opt. (5)

J. Opt. Soc. Am. (1)

Opt. Eng. (1)

C. Liu, Y. Li, X. Cheng, Z. Liu, F. Bo, and J. Zhu, “Elimination of zero-order diffraction in digital holography,” Opt. Eng.41(10), 2434–2437 (2002).
[CrossRef]

Opt. Express (4)

Opt. Lett. (7)

Other (3)

http://en.wikipedia.org/wiki/Cosine_similarity

F.B. Soulard, A. Purvis, R. McWilliam, J.J. Cowling, G.L. Williams, J.J.Toriz-Garcia, N.L. Seed, and P.A. Ivey, “Iterative zero-order suppression from an off-axis hologram based on the 2D Hilbert transform”, Biomedical Optics and 3-D Imaging, OSA Technical Digest (Optical Society of America), paper DSu3C.4.(2012).

J. W. Goodman, Introduction to Fourier Optics 2nd edition (McGraw Hill, New York, 1996).

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Figures (7)

Fig. 1
Fig. 1

Simulation of iterative approach. (a) digital hologram; (b) Fourier spectrum of hologram; (c) reconstructed image intensity using proposed approach; (d) Fourier spectrum after eliminating zero-order term.

Fig. 2
Fig. 2

Relationships between CF and A2, where solid line denotes use of |ψO|+ and dashed line, that of |ψO|-.

Fig. 3
Fig. 3

Correlation factor verses iteration steps for different A2.

Fig. 4
Fig. 4

Simulation results for sample with higher bandwidth. (a) Digital hologram; (b) spectrum of digital hologram in (a); (c) spectrum processed using proposed approach; (d) original object intensity of school badge of Nankai University; (e) reconstructed image from + 1-order spectrum of (b); (f) reconstructed image from + 1-order spectrum of (c).

Fig. 5
Fig. 5

Phase profile reconstruction. (a) Sinusoidal phase; (b) amplitude information; (c) phase reconstructed using standard approach; (d) phase reconstructed using iterative approach; (e) tomographic phase profile of dashed lines in Fig. 5(a) using standard and iterative approaches.

Fig. 6
Fig. 6

Schematic diagram of experimental configuration. (SPF: spatial filter; BS: beam splitter; M: mirror; S: sample; MO: microscope objective)

Fig. 7
Fig. 7

Output comparison before and after iterative approach processing. (a) Fourier spectrum of directly obtained hologram; (b) Fourier spectrum processed using iterative approach; (c) reconstructed image using spectrum filtering; (d) reconstructed image using iterative approach.

Equations (16)

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I H =( ψ O + ψ R ) ( ψ O + ψ R ) * = | ψ R | 2 + | ψ O | 2 + ψ O ψ R + ψ O ψ R ,
( I H | ψ R | 2 ) 2 =( | ψ O | 2 + ψ O ψ R + ψ O ψ R )( | ψ O | 2 + ψ O ψ R + ψ O ψ R ) = | ψ O | 4 +2 | ψ R | 2 | ψ O | 2 +2 | ψ O | 2 ψ R ψ O +2 | ψ O | 2 ψ R ψ O + ( ψ R ψ O ) 2 + ( ψ R ψ O ) 2
( I H | ψ R | 2 ) 2 = | ψ O | 2 0 | ψ O | 2 +2 | ψ R | 2 | ψ O | 2 0 +2 | ψ O | 2 0 ψ R ψ O +2 | ψ O | 2 0 ψ R ψ O + ( ψ R ψ O ) 2 + ( ψ R ψ O ) 2
( I H + | ψ R | 2 ) | ψ O | 2 0 =(2 | ψ R | 2 + | ψ O | 2 + ψ O ψ R + ψ O ψ R ) | ψ O | 2 0 = | ψ O | 2 | ψ O | 2 0 +2 | ψ R | 2 | ψ O | 2 0 + | ψ O | 2 0 ψ O ψ R + | ψ O | 2 0 ψ O ψ R
{ ( I H | ψ R | 2 ) 2 }(u,v)=( | ψ O | 2 0 ) G O (u,v) G * O (u,v)+2 R 2 ( | ψ O | 2 0 )δ(u,v) +2( | ψ O | 2 0 ) G O Rδ(u u 0 ,v v 0 )+2( | ψ O | 2 0 ) G O * Rδ(u+ u 0 ,v+ v 0 ) + R 2 G O G O δ(u2 u 0 ,v2 v 0 )+ R 2 G O * G O * δ(u+2 u 0 ,v+2 v 0 )
{( I H + | ψ R | 2 ) | ψ O | 2 0 }(u,v)=( | ψ O | 2 0 ) G O (u,v) G * O (u,v)+2 R 2 ( | ψ O | 2 0 )δ(u,v) +( | ψ O | 2 0 ) G O Rδ(u u 0 ,v v 0 )+( | ψ O | 2 0 ) G O * Rδ(u+ u 0 ,v+ v 0 )
{ ( I H | ψ R | 2 ) 2 }(u,v)rect( ua/2 b , va/2 b ) =[( | ψ O | 2 0 ) G O (u,v) G * O (u,v)+2 R 2 ( | ψ O | 2 0 )δ(u,v)]rect( ua/2 b , va/2 b ) +2( | ψ O | 2 0 ) G O Rδ(u u 0 ,v v 0 )+ R 2 G O G O δ(u2 u 0 ,v2 v 0 )
{( I H + | ψ R | 2 ) | ψ O | 2 0 }(u,v)rect( ua/2 b , va/2 b ) =[( | ψ O | 2 0 ) G O (u,v) G * O (u,v)+2 R 2 ( | ψ O | 2 0 )δ(u,v)]rect( ua/2 b , va/2 b ) +( | ψ O | 2 0 ) G O Rδ(u u 0 ,v v 0 )
J 1 =[ | ψ O | 2 0 | ψ O | 2 +2 | ψ R | 2 | ψ O | 2 0 ][ b 2 sinc(bx,by)exp(jπa(x+y)] +2 | ψ O | 2 0 ψ R ψ O + ( ψ R ψ O ) 2
J 2 =[ | ψ O | 2 0 | ψ O | 2 +2 | ψ R | 2 | ψ O | 2 0 ][ b 2 sinc(bx,by)exp(jπa(x+y)] + | ψ O | 2 0 ψ R ψ O
J 1 J 2 = | ψ O | 2 0 ψ R ψ O + ( ψ R ψ O ) 2
ψ R ψ O = | ψ O | 2 0 ± | ψ O | 4 0 +4( J 1 J 2 ) 2
| ψ O |=| | ψ O | 2 0 ± | ψ O | 4 0 +4( J 1 J 2 ) 2 ψ R |
A 2 = | ψ R 1 2 [max(| ψ O |)+min(| ψ O |)] | 2 ,
CF= [ I Re I Orig ] peak I Re ,
ψ O ψ R + ψ O ψ R = I H | ψ O | 2 | ψ R | 2 = I H ( | ψ O | k ) 2 | ψ R | 2

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