Abstract

Formulas of partially spatial coherent light are derived and its corresponding design algorithm is proposed for generating computer-generated holograms based on partially spatial coherent light. The partially coherent light is divided into two terms: spatially absolute coherent part and incoherent part. The former is propagated by angular spectrum method, while the latter is based on the optical transfer function. The related formulas are derived where the coherent function (degree of coherence) is related. A modified iterative algorithm is further developed for optimizing the phase distributions. Numerical simulations and optical experiments are both performed to verify the proposed algorithm. The results obtained by the proposed method and the traditional method are compared, and it is clear that the speckle contrasts in optical experiments are improved more than 46%, and the image quality is obviously improved. This method could also provide new applications for three-dimensional holographic display, beam shaping, and other wave-front modulation techniques.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]

2017 (2)

2016 (1)

2015 (5)

2014 (2)

2013 (4)

2012 (1)

2011 (1)

2010 (1)

2009 (2)

2008 (3)

2006 (1)

2005 (1)

C. Slinger, C. Cameron, and M. Stanley, “Computer-generated holography as a generic display technology,” Computer 38(8), 46–53 (2005).
[Crossref]

2003 (1)

1993 (1)

M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2(1), 28–34 (1993).
[Crossref]

1992 (1)

A. D. Stein, Z. Wang, and J. J. S. Leigh, “Computer-generated holograms: a simplified ray-tracing approach,” Comput. Phys. 6(4), 389–392 (1992).
[Crossref]

1988 (1)

1972 (1)

R. W. Gerchberg, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35(2), 237–246 (1972).

1957 (1)

Ahrenberg, L.

Benzie, P.

Bi, Y.

Cameron, C.

C. Slinger, C. Cameron, and M. Stanley, “Computer-generated holography as a generic display technology,” Computer 38(8), 46–53 (2005).
[Crossref]

Cao, A.

Cao, L.

Chang, C.

Chen, D. C.

Chen, Y. G.

Chong, T. C.

Deng, Q.

Ding, Y. C.

Dong, J. W.

Frère, C.

Fukuoka, T.

Gao, C.

Garcia-Sucerquia, J.

Gerchberg, R. W.

R. W. Gerchberg, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35(2), 237–246 (1972).

Haouat, M.

Huai, Y.

Ito, T.

Jia, J.

Jia, S.

Jiang, S. J.

Jiang, W.

Jin, G.

Jin, Y.

Kellou, A.

Kelly, D. P.

Kim, E. S.

Kim, J.

Kim, S.

Kim, S. C.

Kong, D.

Lee, B.

Lee, S.

Lee, W.

Leigh, J. J. S.

A. D. Stein, Z. Wang, and J. J. S. Leigh, “Computer-generated holograms: a simplified ray-tracing approach,” Comput. Phys. 6(4), 389–392 (1992).
[Crossref]

Leseberg, D.

Li, F.

Li, G.

Li, H.

Li, X.

Liang, X.

Liu, J.

Liu, S.

Lucente, M.

M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2(1), 28–34 (1993).
[Crossref]

Magnor, M.

Makowski, M.

Masuda, N.

Matsushima, K.

Mori, Y.

Morio, J.

Nakayama, H.

Nie, S.

Nomura, T.

Pan, Y.

Pang, H.

Pang, X. N.

Picart, P.

Qi, Y.

Qiu, Y.

Réfrégier, P.

Ryle, J. P.

Schimmel, H.

Shimobaba, T.

Slinger, C.

C. Slinger, C. Cameron, and M. Stanley, “Computer-generated holography as a generic display technology,” Computer 38(8), 46–53 (2005).
[Crossref]

Solanki, S.

Stanley, M.

C. Slinger, C. Cameron, and M. Stanley, “Computer-generated holography as a generic display technology,” Computer 38(8), 46–53 (2005).
[Crossref]

Stein, A. D.

A. D. Stein, Z. Wang, and J. J. S. Leigh, “Computer-generated holograms: a simplified ray-tracing approach,” Comput. Phys. 6(4), 389–392 (1992).
[Crossref]

Stern, A.

Sun, M.

Sun, Z.

Tan, C.

Tanjung, R. B.

Thompson, B. J.

Wang, H.

Wang, J.

Wang, Y.

Wang, Z.

A. D. Stein, Z. Wang, and J. J. S. Leigh, “Computer-generated holograms: a simplified ray-tracing approach,” Comput. Phys. 6(4), 389–392 (1992).
[Crossref]

Watson, J.

Wolf, E.

Wu, J.

Wu, K.

Wu, Y.

Wyrowski, F.

Xia, J.

Xu, X.

Xue, G.

Yoon, J. H.

Zhang, B.

Zhang, H.

Zhao, Q.

Zhao, Y.

Zhou, P.

Appl. Opt. (10)

P. Zhou, Y. Bi, M. Sun, H. Wang, F. Li, and Y. Qi, “Image quality enhancement and computation acceleration of 3D holographic display using a symmetrical 3D GS algorithm,” Appl. Opt. 53(27), G209–G213 (2014).
[Crossref] [PubMed]

S. C. Kim and E. S. Kim, “Effective generation of digital holograms of three-dimensional objects using a novel look-up table method,” Appl. Opt. 47(19), D55–D62 (2008).
[Crossref] [PubMed]

J. Jia, Y. Wang, J. Liu, X. Li, Y. Pan, Z. Sun, B. Zhang, Q. Zhao, and W. Jiang, “Reducing the memory usage for effective computer-generated hologram calculation using compressed look-up table in full-color holographic display,” Appl. Opt. 52(7), 1404–1412 (2013).
[Crossref] [PubMed]

S. C. Kim and E. S. Kim, “Fast computation of hologram patterns of a 3D object using run-length encoding and novel look-up table methods,” Appl. Opt. 48(6), 1030–1041 (2009).
[Crossref] [PubMed]

S. C. Kim, J. H. Yoon, and E. S. Kim, “Fast generation of three-dimensional video holograms by combined use of data compression and lookup table techniques,” Appl. Opt. 47(32), 5986–5995 (2008).
[Crossref] [PubMed]

Y. Pan, Y. Wang, J. Liu, X. Li, and J. Jia, “Fast polygon-based method for calculating computer-generated holograms in three-dimensional display,” Appl. Opt. 52(1), A290–A299 (2013).
[Crossref] [PubMed]

L. Ahrenberg, P. Benzie, M. Magnor, and J. Watson, “Computer generated holograms from three dimensional meshes using an analytic light transport model,” Appl. Opt. 47(10), 1567–1574 (2008).
[Crossref] [PubMed]

D. Leseberg and C. Frère, “Computer-generated holograms of 3-D objects composed of tilted planar segments,” Appl. Opt. 27(14), 3020–3024 (1988).
[Crossref] [PubMed]

Y. Wu, J. P. Ryle, S. Liu, D. P. Kelly, and A. Stern, “Experimental evaluation of inline free-space holography systems,” Appl. Opt. 54(13), 3991–4000 (2015).
[Crossref]

Y. Mori, T. Fukuoka, and T. Nomura, “Speckle reduction in holographic projection by random pixel separation with time multiplexing,” Appl. Opt. 53(35), 8182–8188 (2014).
[Crossref] [PubMed]

Comput. Phys. (1)

A. D. Stein, Z. Wang, and J. J. S. Leigh, “Computer-generated holograms: a simplified ray-tracing approach,” Comput. Phys. 6(4), 389–392 (1992).
[Crossref]

Computer (1)

C. Slinger, C. Cameron, and M. Stanley, “Computer-generated holography as a generic display technology,” Computer 38(8), 46–53 (2005).
[Crossref]

J. Electron. Imaging (1)

M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2(1), 28–34 (1993).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Opt. Express (12)

Y. Zhao, L. Cao, H. Zhang, D. Kong, and G. Jin, “Accurate calculation of computer-generated holograms using angular-spectrum layer-oriented method,” Opt. Express 23(20), 25440–25449 (2015).
[Crossref] [PubMed]

C. Gao, J. Liu, X. Li, G. Xue, J. Jia, and Y. Wang, “Accurate compressed look up table method for CGH in 3D holographic display,” Opt. Express 23(26), 33194–33204 (2015).
[Crossref] [PubMed]

G. Li, Y. Qiu, and H. Li, “Coherence theory of a laser beam passing through a moving diffuser,” Opt. Express 21(11), 13032–13039 (2013).
[Crossref] [PubMed]

T. Shimobaba, H. Nakayama, N. Masuda, and T. Ito, “Rapid calculation algorithm of Fresnel computer-generated-hologram using look-up table and wavefront-recording plane methods for three-dimensional display,” Opt. Express 18(19), 19504–19509 (2010).
[Crossref] [PubMed]

Y. Pan, X. Xu, S. Solanki, X. Liang, R. B. Tanjung, C. Tan, and T. C. Chong, “Fast CGH computation using S-LUT on GPU,” Opt. Express 17(21), 18543–18555 (2009).
[Crossref] [PubMed]

W. Lee, S. Lee, J. Kim, S. Kim, and B. Lee, “A numerical analysis of the effect of partially-coherent light in photovoltaic devices considering coherence length,” Opt. Express 20(S6), A941–A953 (2012).
[Crossref]

K. Wu, Y. Huai, S. Jia, and Y. Jin, “Coupled simulation of chemical lasers based on intracavity partially coherent light model and 3D CFD model,” Opt. Express 19(27), 26295–26307 (2011).
[Crossref] [PubMed]

T. Shimobaba and T. Ito, “Random phase-free computer-generated hologram,” Opt. Express 23(7), 9549–9554 (2015).
[Crossref] [PubMed]

H. Pang, J. Wang, A. Cao, and Q. Deng, “High-accuracy method for holographic image projection with suppressed speckle noise,” Opt. Express 24(20), 22766–22776 (2016).
[Crossref] [PubMed]

M. Makowski, “Minimized speckle noise in lens-less holographic projection by pixel separation,” Opt. Express 21(24), 29205–29216 (2013).
[Crossref] [PubMed]

C. Chang, Y. Qi, J. Wu, J. Xia, and S. Nie, “Speckle reduced lensless holographic projection from phase-only computer-generated hologram,” Opt. Express 25(6), 6568–6580 (2017).
[Crossref] [PubMed]

X. N. Pang, D. C. Chen, Y. C. Ding, Y. G. Chen, S. J. Jiang, and J. W. Dong, “Image quality improvement of polygon computer generated holography,” Opt. Express 23(15), 19066–19073 (2015).
[Crossref] [PubMed]

Opt. Lett. (1)

Optik (Stuttg.) (1)

R. W. Gerchberg, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35(2), 237–246 (1972).

Other (1)

M. Born and E. Wolf, Principles of Optics (Cambridge, 2011).

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Figures (9)

Fig. 1
Fig. 1 The schematic of hologram recording and reconstruction under partially spatial coherent light illumination. (a) the recording process; (b) the reconstruction process.
Fig. 2
Fig. 2 Flow chart of CGH with partially spatial coherent light.
Fig. 3
Fig. 3 The numerical simulation results. (a) and (b) are reconstructed images when γ = 1; (c) and (d) are reconstructed images when γ = 0.98; (e) and (f) are PSNR and SC of binary and gray images as γ increases, respectively.
Fig. 4
Fig. 4 The numerical simulation results with iteration algorithm when γ = 0.98. (a) and (b) are reconstructed images when iteration n = 1; (c) and (d) are reconstructed images when iteration n = 10; (e) and (f) are PSNR and SC of binary and gray images as iterations increase, respectively.
Fig. 5
Fig. 5 The numerical simulation results. (a) and (b) are the reconstructed images using ASM; (c) and (d) are the reconstructed images using proposed method.
Fig. 6
Fig. 6 Schematic view of the optical experimental setup.
Fig. 7
Fig. 7 Reconstructed results with coherent light. (a) is the original binary image; (b) is result by ASM (γ = 1); (c) and (d) are results by proposed method with γ = 0.98, γ = 0.92 respectively.
Fig. 8
Fig. 8 Reconstructed results with coherent light. (a) the original gray image; (b) image by ASM (γ = 1); (c), (d) are results by proposed method with γ = 0.98, γ = 0.92 respectively.
Fig. 9
Fig. 9 Reconstructed results for (a) conventional (ASM) CGH and (b) proposed method CGH with both partially coherent illumination of same degree of coherent (γ = 0.98).

Tables (4)

Tables Icon

Table 1 SC and PSNR of the simulated reconstructed images

Tables Icon

Table 2 SC and PSNR of reconstructed binary image

Tables Icon

Table 3 SC and PSNR of reconstructed gray image

Tables Icon

Table 4 SC and PSNR of reconstructed images for conventional and proposed CGH with same partially coherent illumination.

Equations (19)

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

I= I ( 1 ) ( Q )+ I ( 2 ) ( Q )+2 I ( 1 ) ( Q ) I ( 2 ) ( Q ) | γ 12 |cos( φ 1 φ 2 ),
E= 1 2 1| γ 12 ( τ ) | I ( 1 ) ( Q )+ I ( 2 ) ( Q ) e i φ in + | γ 12 ( τ ) | I ( 1 ) ( Q ) I (2) (Q) e i φ co ,
E i = 1 2 1| γ 12 ( τ ) | I ( 1 ) ( Q )+ I ( 2 ) ( Q ) e i φ in ,
E c = | γ 12 ( τ ) | I ( 1 ) ( Q ) I (2) (Q) e i φ co ,
S( α,β )= D 2 tri( λdα D )( λdβ D ),| λdα D |1,| λdβ D |1,
I i ( ξ,η )= I ˜ i ( α,β )S( α,β )exp[ i2π( ξα+ηβ ) ]dαdβ ,
a 0 ( α,β )= A 0 ( ξ,η )exp[ i2π( ξα+ηβ ) ]dαdβ .
A c ( ξ,η )= a 0 ( α,β )exp[ ikd 1 λ 2 ( α 2 + β 2 ) ]exp[ i2π( ξα+ηβ ) ]dαdβ .
I 0 ( ξ,η ) OTF I i ( ξ,η ).
A 0 ( ξ,η )= I 0 ( ξ,η ) exp( i φ r ),
A 0 ( ξ,η ) ASM A c ( ξ,η ).
I c ( ξ,η )= | A c ( ξ,η ) | 2 ,
φ c ( ξ,η )=angle[ A c ( ξ,η ) ].
A( ξ,η )=exp{ i[ ( 1γ ) I i ( ξ,η )+γ I c ( ξ,η ) ] }exp[ i φ c ( ξ,η ) ],
| A( ξ,η ) | 2 OT F 1 I i ' ( ξ,η ),
A( ξ,η ) ASM E c ( ξ,η ).
I= I i ' + | E c | 2 ,
SC= 1 N i=1 N ( p i I ¯ ) 2 I ¯ ,
PSNR=10lg( ( 2 n 1 ) 2 MSE ),

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