Abstract

The complex modulation characteristics of a light field through an amplitude-phase double-layer spatial light modulator are analyzed based on the wave-optic numerical model, and the structural conditions for the optimal double-layer complex modulation structure are investigated. The relationships of interlayer distance, pixel size, and complex light modulation performance are analyzed. The main finding of this study is that the optimal interlayer distance for the double-layer structure can be found at the Talbot effect condition. For validating the practical usefulness of our findings, a high quality reconstruction of the complex computer-generated holograms and the robustness of the angular tolerance of the complex modulation at the Talbot interlayer distance are numerically demonstrated.

© 2017 Optical Society of America

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References

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  1. J. Hong, Y. Kim, H.-J. Choi, J. Hahn, J.-H. Park, H. Kim, S.-W. Min, N. Chen, and B. Lee, “Three-dimensional display technologies of recent interest: principles, status, and issues [Invited],” Appl. Opt. 50(34), H87–H115 (2011).
    [Crossref] [PubMed]
  2. H. Kim, C.-Y. Hwang, K.-S. Kim, J. Roh, W. Moon, S. Kim, B.-R. Lee, S. Oh, and J. Hahn, “Anamorphic optical transformation of an amplitude spatial light modulator to a complex spatial light modulator with square pixels [invited],” Appl. Opt. 53(27), G139–G146 (2014).
    [Crossref] [PubMed]
  3. S. Choi, J. Roh, H. Song, G. Sung, J. An, W. Seo, K. Won, J. Ungnapatanin, M. Jung, Y. Yoon, H.-S. Lee, C.-H. Oh, J. Hahn, and H. Kim, “Modulation efficiency of double-phase hologram complex light modulation macro-pixels,” Opt. Express 22(18), 21460–21470 (2014).
    [Crossref] [PubMed]
  4. H. Song, G. Sung, S. Choi, K. Won, H.-S. Lee, and H. Kim, “Optimal synthesis of double-phase computer generated holograms using a phase-only spatial light modulator with grating filter,” Opt. Express 20(28), 29844–29853 (2012).
    [Crossref] [PubMed]
  5. S. Reichelt, R. Häussler, G. Fütterer, N. Leister, H. Kato, N. Usukura, and Y. Kanbayashi, “Full-range, complex spatial light modulator for real-time holography,” Opt. Lett. 37(11), 1955–1957 (2012).
    [Crossref] [PubMed]
  6. J.-P. Liu, W.-Y. Hsieh, T.-C. Poon, and P. Tsang, “Complex Fresnel hologram display using a single SLM,” Appl. Opt. 50(34), H128–H135 (2011).
    [Crossref] [PubMed]
  7. E. Ulusoy, L. Onural, and H. M. Ozaktas, “Full-complex amplitude modulation with binary spatial light modulators,” J. Opt. Soc. Am. A 28(11), 2310–2321 (2011).
    [Crossref] [PubMed]
  8. P. Zhou and J. H. Burge, “Analysis of wavefront propagation using the Talbot effect,” Appl. Opt. 49(28), 5351–5359 (2010).
    [Crossref] [PubMed]
  9. D. Im, E. Moon, Y. Park, D. Lee, J. Hahn, and H. Kim, “Phase-regularized polygon computer-generated holograms,” Opt. Lett. 39(12), 3642–3645 (2014).
    [Crossref] [PubMed]
  10. J. An, G. Sung, S. Kim, H. Song, J. Seo, H. Kim, W. Seo, C.-S. Choi, E. Moon, H. Kim, H.-S. Lee, and U. Chung, “Binocular holographic display with pupil space division method,” SID Symposium Digest of Technical Papers46, 522–525 (2015).
    [Crossref]
  11. Y. Lim, K. Hong, H. Kim, H.-E. Kim, E.-Y. Chang, S. Lee, T. Kim, J. Nam, H.-G. Choo, J. Kim, and J. Hahn, “360-degree tabletop electronic holographic display,” Opt. Express 24(22), 24999–25009 (2016).
    [Crossref] [PubMed]

2016 (1)

2014 (3)

2012 (2)

2011 (3)

2010 (1)

An, J.

S. Choi, J. Roh, H. Song, G. Sung, J. An, W. Seo, K. Won, J. Ungnapatanin, M. Jung, Y. Yoon, H.-S. Lee, C.-H. Oh, J. Hahn, and H. Kim, “Modulation efficiency of double-phase hologram complex light modulation macro-pixels,” Opt. Express 22(18), 21460–21470 (2014).
[Crossref] [PubMed]

J. An, G. Sung, S. Kim, H. Song, J. Seo, H. Kim, W. Seo, C.-S. Choi, E. Moon, H. Kim, H.-S. Lee, and U. Chung, “Binocular holographic display with pupil space division method,” SID Symposium Digest of Technical Papers46, 522–525 (2015).
[Crossref]

Burge, J. H.

Chang, E.-Y.

Chen, N.

Choi, C.-S.

J. An, G. Sung, S. Kim, H. Song, J. Seo, H. Kim, W. Seo, C.-S. Choi, E. Moon, H. Kim, H.-S. Lee, and U. Chung, “Binocular holographic display with pupil space division method,” SID Symposium Digest of Technical Papers46, 522–525 (2015).
[Crossref]

Choi, H.-J.

Choi, S.

Choo, H.-G.

Chung, U.

J. An, G. Sung, S. Kim, H. Song, J. Seo, H. Kim, W. Seo, C.-S. Choi, E. Moon, H. Kim, H.-S. Lee, and U. Chung, “Binocular holographic display with pupil space division method,” SID Symposium Digest of Technical Papers46, 522–525 (2015).
[Crossref]

Fütterer, G.

Hahn, J.

Häussler, R.

Hong, J.

Hong, K.

Hsieh, W.-Y.

Hwang, C.-Y.

Im, D.

Jung, M.

Kanbayashi, Y.

Kato, H.

Kim, H.

Y. Lim, K. Hong, H. Kim, H.-E. Kim, E.-Y. Chang, S. Lee, T. Kim, J. Nam, H.-G. Choo, J. Kim, and J. Hahn, “360-degree tabletop electronic holographic display,” Opt. Express 24(22), 24999–25009 (2016).
[Crossref] [PubMed]

D. Im, E. Moon, Y. Park, D. Lee, J. Hahn, and H. Kim, “Phase-regularized polygon computer-generated holograms,” Opt. Lett. 39(12), 3642–3645 (2014).
[Crossref] [PubMed]

S. Choi, J. Roh, H. Song, G. Sung, J. An, W. Seo, K. Won, J. Ungnapatanin, M. Jung, Y. Yoon, H.-S. Lee, C.-H. Oh, J. Hahn, and H. Kim, “Modulation efficiency of double-phase hologram complex light modulation macro-pixels,” Opt. Express 22(18), 21460–21470 (2014).
[Crossref] [PubMed]

H. Kim, C.-Y. Hwang, K.-S. Kim, J. Roh, W. Moon, S. Kim, B.-R. Lee, S. Oh, and J. Hahn, “Anamorphic optical transformation of an amplitude spatial light modulator to a complex spatial light modulator with square pixels [invited],” Appl. Opt. 53(27), G139–G146 (2014).
[Crossref] [PubMed]

H. Song, G. Sung, S. Choi, K. Won, H.-S. Lee, and H. Kim, “Optimal synthesis of double-phase computer generated holograms using a phase-only spatial light modulator with grating filter,” Opt. Express 20(28), 29844–29853 (2012).
[Crossref] [PubMed]

J. Hong, Y. Kim, H.-J. Choi, J. Hahn, J.-H. Park, H. Kim, S.-W. Min, N. Chen, and B. Lee, “Three-dimensional display technologies of recent interest: principles, status, and issues [Invited],” Appl. Opt. 50(34), H87–H115 (2011).
[Crossref] [PubMed]

J. An, G. Sung, S. Kim, H. Song, J. Seo, H. Kim, W. Seo, C.-S. Choi, E. Moon, H. Kim, H.-S. Lee, and U. Chung, “Binocular holographic display with pupil space division method,” SID Symposium Digest of Technical Papers46, 522–525 (2015).
[Crossref]

J. An, G. Sung, S. Kim, H. Song, J. Seo, H. Kim, W. Seo, C.-S. Choi, E. Moon, H. Kim, H.-S. Lee, and U. Chung, “Binocular holographic display with pupil space division method,” SID Symposium Digest of Technical Papers46, 522–525 (2015).
[Crossref]

Kim, H.-E.

Kim, J.

Kim, K.-S.

Kim, S.

H. Kim, C.-Y. Hwang, K.-S. Kim, J. Roh, W. Moon, S. Kim, B.-R. Lee, S. Oh, and J. Hahn, “Anamorphic optical transformation of an amplitude spatial light modulator to a complex spatial light modulator with square pixels [invited],” Appl. Opt. 53(27), G139–G146 (2014).
[Crossref] [PubMed]

J. An, G. Sung, S. Kim, H. Song, J. Seo, H. Kim, W. Seo, C.-S. Choi, E. Moon, H. Kim, H.-S. Lee, and U. Chung, “Binocular holographic display with pupil space division method,” SID Symposium Digest of Technical Papers46, 522–525 (2015).
[Crossref]

Kim, T.

Kim, Y.

Lee, B.

Lee, B.-R.

Lee, D.

Lee, H.-S.

Lee, S.

Leister, N.

Lim, Y.

Liu, J.-P.

Min, S.-W.

Moon, E.

D. Im, E. Moon, Y. Park, D. Lee, J. Hahn, and H. Kim, “Phase-regularized polygon computer-generated holograms,” Opt. Lett. 39(12), 3642–3645 (2014).
[Crossref] [PubMed]

J. An, G. Sung, S. Kim, H. Song, J. Seo, H. Kim, W. Seo, C.-S. Choi, E. Moon, H. Kim, H.-S. Lee, and U. Chung, “Binocular holographic display with pupil space division method,” SID Symposium Digest of Technical Papers46, 522–525 (2015).
[Crossref]

Moon, W.

Nam, J.

Oh, C.-H.

Oh, S.

Onural, L.

Ozaktas, H. M.

Park, J.-H.

Park, Y.

Poon, T.-C.

Reichelt, S.

Roh, J.

Seo, J.

J. An, G. Sung, S. Kim, H. Song, J. Seo, H. Kim, W. Seo, C.-S. Choi, E. Moon, H. Kim, H.-S. Lee, and U. Chung, “Binocular holographic display with pupil space division method,” SID Symposium Digest of Technical Papers46, 522–525 (2015).
[Crossref]

Seo, W.

S. Choi, J. Roh, H. Song, G. Sung, J. An, W. Seo, K. Won, J. Ungnapatanin, M. Jung, Y. Yoon, H.-S. Lee, C.-H. Oh, J. Hahn, and H. Kim, “Modulation efficiency of double-phase hologram complex light modulation macro-pixels,” Opt. Express 22(18), 21460–21470 (2014).
[Crossref] [PubMed]

J. An, G. Sung, S. Kim, H. Song, J. Seo, H. Kim, W. Seo, C.-S. Choi, E. Moon, H. Kim, H.-S. Lee, and U. Chung, “Binocular holographic display with pupil space division method,” SID Symposium Digest of Technical Papers46, 522–525 (2015).
[Crossref]

Song, H.

Sung, G.

Tsang, P.

Ulusoy, E.

Ungnapatanin, J.

Usukura, N.

Won, K.

Yoon, Y.

Zhou, P.

Appl. Opt. (4)

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

Opt. Express (3)

Opt. Lett. (2)

Other (1)

J. An, G. Sung, S. Kim, H. Song, J. Seo, H. Kim, W. Seo, C.-S. Choi, E. Moon, H. Kim, H.-S. Lee, and U. Chung, “Binocular holographic display with pupil space division method,” SID Symposium Digest of Technical Papers46, 522–525 (2015).
[Crossref]

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Figures (6)

Fig. 1
Fig. 1 Numerical model of the holographic 3D display system with an amplitude-phase double-layer complex spatial light modulator
Fig. 2
Fig. 2 Numerical model of an oblique observation of the amplitude-phase double-layer BM patterned complex spatial light modulator
Fig. 3
Fig. 3 Oblique observation of the double-layer SLM with finite interlayer distance; (a) observation simulation results of the double layer without BM patterning and (b) with BM patterning. The upper left and upper right figures of (a) and (b) are the optical field distributions at the virtual SLM plane and the eye lens plane, G( x 1 , y 1 ) and W( u,v ) , respectively. The lower left and right figures are the observation images for the focus adjusted to the rear ( f eye = f A ) and front ( f eye = f ϕ ) layers.
Fig. 4
Fig. 4 Talbot effect analysis results. (a) E 1 ( d ) measure and (b) E 2 ( d ) and DE( d ) measures with a comparison of E 1 ( d ) for pixel size 10μm, and (c) the observation image at the retina plane F( x 2 , y 2 ;d ) in the selected positions indicated in (a).
Fig. 5
Fig. 5 Magnified view of the complex field distributions at the virtual SLM plane, for the spatial shifts of the eye; (a) h=16.7mm and (b) h=10.6mm .
Fig. 6
Fig. 6 DE( d ) measures at the first three Talbot interlayer distances with change in the observation angle.

Equations (27)

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A( x 1 , y 1 )=| CGH( x 1 , y 1 ) |,
ϕ( x 1 , y 1 )=Arg[ CGH( x 1 , y 1 ) ].
G( x 1 , y 1 )={ [ M( x 1 , y 1 )A( x 1 , y 1 ) ] h gap ( x 1 , y 1 ) }×{ M( x 1 , y 1 )exp[ jϕ( x 1 , y 1 ) ] },
M(x,y)= m,n rect( xma f B a )rect( yna f B a ) ,
G opt ( x 1 , y 1 )=M( x 1 , y 1 )×A( x 1 , y 1 )exp[ jϕ( x 1 , y 1 ) ].
F( x 2 , y 2 )=CdFr{ G( x 1 , y 1 ); D 1 , d eye , f eye , R eye }and,
G( x 1 , y 1 )=ICdFr{ F( x 2 , y 2 ); D 1 , d eye , f eye },
W( u,v )=Fr T 1 { G( x 1 , y 1 ) }and,
F( x 2 , y 2 )=Fr T 2 { t( u,v )W( u,v ) }.
W( u,v )= e jkF jλ D 1 G( x 1 , y 1 ) e j 2π λ D 1 ( x 1 u+ y 1 v ) d x 1 d y 1 .
F( x 2 , y 2 )= e j π λ d eye ( x 2 2 + y 2 2 ) jλ d eye t( u,v )W( u,v ) e j 2π λ d eye ( u x 2 +v y 2 ) dudv ,
t( u,v )= e j π λ ( 1 D 1 + 1 d eye 1 f eye )( u 2 + v 2 ) circ( [ u 2 + v 2 ]/ ρ 2 ),
( Δu,Δv )=( λ D 1 /( NΔ x 1 ),λ D 1 /( NΔ y 1 ) ).
( Δ x 2 ,Δ y 2 )=( Δ x 1 d eye / D 1 ,Δ y 1 d eye / D 1 ).
IFr T 1 { t( uh,v )W( uh,v ) }=G( x 1 , y 1 )exp( j2πh x 1 λ d 1 )and,
Fr T 2 { t( uh,v )W( uh,v ) }=F( x 2 , y 2 )exp( j2π h λ d 2 x 2 ).
G A ( x 1 , y 1 )=ICdFr{ M( x 2 D 1 / d eye , y 2 D 1 / d eye )A( x 2 D 1 / d eye , y 2 D 1 / d eye ); D 1 , d eye , f eye }.
G( x 1 , y 1 )= G A ( x 1 , y 1 )×exp( jϕ( x 1 , y 1 ) )×M( x 1 , y 1 )
G( x 1 , y 1 ;d )=Trcas{ M( x 1 , y 1 )A( x 1 , y 1 ),M( x 1 , y 1 )exp( jϕ( x 1 , y 1 ) );d,M } { [ M( x 1 , y 1 )A( x 1 , y 1 ) ] h gap ( x 1 , y 1 ) }×{ M( x 1 , y 1 )exp[ jϕ( x 1 , y 1 ) ] }.
CGH( x 1 , y 1 )=ICdFr{ I( x 2 , y 2 ); D 1 , d eye , f eye },
f eye =1/[ 1/( D 1 z center )+1/ d eye ].
E 1 ( d )= | G ref ( x 1 , y 1 ) || G( x 1 , y 1 ;d ) | 2 .
F ref ( x 2 , y 2 )=CdFr{ G ref ( x 1 , y 1 ); D 1 , d eye , f c , R eye }.
F( x 2 , y 2 ;d )=CdFr{ G( x 1 , y 1 ;d ); D 1 , d eye , f c , R eye }.
E 2 ( d )= | F ref ( x 2 , y 2 ) || F( x 2 , y 2 ;d ) | 2 .
DE( d )= Γ( x 2 , y 2 ) | F( x 2 , y 2 ;d ) | 2 d x 2 d y 2 Γ( x 2 , y 2 ) | F ref ( x 2 , y 2 ) | 2 d x 2 d y 2 × | F ref ( x 2 , y 2 ) | 2 d x 2 d y 2 | F( x 2 , y 2 ;d ) | 2 d x 2 d y 2 ,
z T,m =γ2 a 2 /λ,

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