Abstract

We propose an optical system for synthesizing double-phase complex computer-generated holograms using a phase-only spatial light modulator and a phase grating filter. Two separated areas of the phase-only spatial light modulator are optically superposed by 4-f configuration with an optimally designed grating filter to synthesize arbitrary complex optical field distributions. The tolerances related to misalignment factors are analyzed, and the optimal synthesis method of double-phase computer-generated holograms is described.

©2012 Optical Society of America

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References

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  1. B. R. Brown and A. W. Lohmann, “Computer-generated binary holograms,” IBM J. Res. Develop. 13(2), 160–168 (1969).
    [Crossref]
  2. C. K. Hsueh and A. A. Sawchuk, “Computer-generated double-phase holograms,” Appl. Opt. 17(24), 3874–3883 (1978).
    [Crossref] [PubMed]
  3. L. G. Neto, D. Roberge, and Y. Sheng, “Full-range, continuous, complex modulation by the use of two coupled-mode liquid-crystal televisions,” Appl. Opt. 35(23), 4567–4576 (1996).
    [Crossref] [PubMed]
  4. C. Slinger, C. Cameron, and M. Stanley, “Computer-generated holography as a generic display technology,” IEEE. Computer 38(8), 46–53 (2005).
    [Crossref]
  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. 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]
  7. V. Arrizón, “Complex modulation with a twisted-nematic liquid-crystal spatial light modulator: double-pixel approach,” Opt. Lett. 28(15), 1359–1361 (2003).
    [Crossref] [PubMed]
  8. M. M. M. Makowski, A. S. A. Siemion, I. D. I. Ducin, K. K. K. Kakarenko, M. S. M. Sypek, A. M. S. A. M. Siemion, J. S. J. Suszek, D. W. D. Wojnowski, Z. J. Z. Jaroszewicz, and A. K. A. Kolodziejczyk, “Complex light modulation for lensless image projection,” Chin. Opt. Lett. 9(12), 120008 (2011).
    [Crossref]
  9. 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]
  10. H. Kim and B. Lee, “Analytic design of an anamorphic optical system for generation anisotropic partially coherent Gaussian Schell-model beams,” Opt. Commun. 260(2), 383–397 (2006).
    [Crossref]
  11. H. Kim, J. Hahn, and B. Lee, “Mathematical modeling of triangle-mesh-modeled three-dimensional surface objects for digital holography,” Appl. Opt. 47(19), D117–D127 (2008).
    [Crossref] [PubMed]

2012 (1)

2011 (3)

2008 (1)

2006 (1)

H. Kim and B. Lee, “Analytic design of an anamorphic optical system for generation anisotropic partially coherent Gaussian Schell-model beams,” Opt. Commun. 260(2), 383–397 (2006).
[Crossref]

2005 (1)

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

2003 (1)

1996 (1)

1978 (1)

1969 (1)

B. R. Brown and A. W. Lohmann, “Computer-generated binary holograms,” IBM J. Res. Develop. 13(2), 160–168 (1969).
[Crossref]

A. Kolodziejczyk, A. K.

A. M. Siemion, A. M. S.

A. Siemion, A. S.

Arrizón, V.

Brown, B. R.

B. R. Brown and A. W. Lohmann, “Computer-generated binary holograms,” IBM J. Res. Develop. 13(2), 160–168 (1969).
[Crossref]

Cameron, C.

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

D. Wojnowski, D. W.

Fütterer, G.

Hahn, J.

Häussler, R.

Hsieh, W.-Y.

Hsueh, C. K.

I. Ducin, I. D.

J. Suszek, J. S.

K. Kakarenko, K. K.

Kanbayashi, Y.

Kato, H.

Kim, H.

H. Kim, J. Hahn, and B. Lee, “Mathematical modeling of triangle-mesh-modeled three-dimensional surface objects for digital holography,” Appl. Opt. 47(19), D117–D127 (2008).
[Crossref] [PubMed]

H. Kim and B. Lee, “Analytic design of an anamorphic optical system for generation anisotropic partially coherent Gaussian Schell-model beams,” Opt. Commun. 260(2), 383–397 (2006).
[Crossref]

Lee, B.

H. Kim, J. Hahn, and B. Lee, “Mathematical modeling of triangle-mesh-modeled three-dimensional surface objects for digital holography,” Appl. Opt. 47(19), D117–D127 (2008).
[Crossref] [PubMed]

H. Kim and B. Lee, “Analytic design of an anamorphic optical system for generation anisotropic partially coherent Gaussian Schell-model beams,” Opt. Commun. 260(2), 383–397 (2006).
[Crossref]

Leister, N.

Liu, J.-P.

Lohmann, A. W.

B. R. Brown and A. W. Lohmann, “Computer-generated binary holograms,” IBM J. Res. Develop. 13(2), 160–168 (1969).
[Crossref]

M. Makowski, M. M.

M. Sypek, M. S.

Neto, L. G.

Onural, L.

Ozaktas, H. M.

Poon, T.-C.

Reichelt, S.

Roberge, D.

Sawchuk, A. A.

Sheng, Y.

Slinger, C.

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

Stanley, M.

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

Tsang, P.

Ulusoy, E.

Usukura, N.

Z. Jaroszewicz, Z. J.

Appl. Opt. (4)

Chin. Opt. Lett. (1)

IBM J. Res. Develop. (1)

B. R. Brown and A. W. Lohmann, “Computer-generated binary holograms,” IBM J. Res. Develop. 13(2), 160–168 (1969).
[Crossref]

IEEE. Computer (1)

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

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

Opt. Commun. (1)

H. Kim and B. Lee, “Analytic design of an anamorphic optical system for generation anisotropic partially coherent Gaussian Schell-model beams,” Opt. Commun. 260(2), 383–397 (2006).
[Crossref]

Opt. Lett. (2)

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Figures (4)

Fig. 1
Fig. 1 DPH configurations of synthesizing complex optical field based on (a) spherical 4-f system with grating filter and (b) cylindrical 4-f system with grating filter

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Fig. 2
Fig. 2 (a) 2D target image ‘SAMSUNG’ and its DPH for (b) the spherical 4-f system, and (c) the cylindrical 4-f system. (d) 3D target image ‘SAIT’ and its DPHs for (e) the spherical 4-f system and (f) the cylindrical 4-f system.

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Fig. 3
Fig. 3 SNR variations for the misalignment factors in the cases of (a) spherical 4-f system with sinusoidal grating, (b) cylindrical 4-f system with sinusoidal grating, (c) spherical 4-f system with binary grating, and (d) cylindrical 4-f system with binary grating.

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Fig. 4
Fig. 4 Observation of holographic 3D images generated by the spherical 4-f system with (a) sinusoidal grating filter and (b) binary phase grating filter, and cylindrical 4-f system with (c) sinusoidal grating and (d) binary phase grating.

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Equations (21)

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G( x 2 , y 2 )= ∫ −∞ ∞ h y ( y 2 , y 1 )[ ∫ −∞ ∞ h x ( x 2 , x 1 )F( x 1 , y 1 ) d x 1 ] d y 1 ,
h x ( x 2 , x 1 )= ( λf ) −1/2 e −jπ/4 exp[ −j2π x 1 x 2 /( λf ) ],
h y ( x 2 , x 1 )= ( λf ) −1 e −jπ/4 exp[ −j2π y 1 y 2 /( λf ) ],
h y ( x 2 , x 1 )= ( 2λf ) −1 e −jπ/4 exp[ jπ{ y 1 2 −2 y 1 y 2 + y 2 2 }/( 2λf ) ],
F( x 1 , y 1 )= ∫ −∞ ∞ h y −1 ( y 1 , y 2 )[ ∫ −∞ ∞ h x −1 ( x 1 , x 2 )G( x 2 , y 2 ) d x 2 ] d y 2 ,
h x −1 ( x 2 , x 1 )= ( λf ) −1 e jπ/4 exp[ j2π x 2 x 1 /( λf ) ],
h y −1 ( y 2 , y 1 )= ( λf ) −1 e jπ/4 exp[ j2π y 2 y 1 /( λf ) ],
h y −1 ( y 2 , y 1 )= ( 2λf ) −1/2 e jπ/4 exp[ −jπ{ y 1 2 −2 y 1 y 2 + y 2 2 }/( 2λf ) ].
G={ H y · H x [ t GR { H y · H x [ F ] } ] },
F={ H y −1 · H x −1 [ { H y −1 · H x −1 [ G ] } ] },
Aexp( jΦ )={ h y −1 · h x −1 [ { h y −1 · h x −1 [ G ] } ] }.
Aexp( jΦ )={ h y −1 · h x −1 [ { h y −1 · h x −1 [ G+δ ] } ] }.
Aexp( jΦ )= 1 2 exp[ j( Φ+ψ ) ]+ 1 2 exp[ j( Φ−ψ ) ],
exp( j Θ up )=exp[ j( Φ+ψ ) ],
exp( j Θ low )=exp[ j( Φ−ψ ) ].
SNR= ∬ S | F( x,y ) | 2 dxdy /{ ∬ S | F( x,y ) | 2 dxdy + ∬ N | F( x,y ) | 2 dxdy },
Μ( x,y;Δd )=Γ( x−d ) e j Θ up ( x−d,y ) +Γ( x+d+Δd ) e j Θ down ( x+d+Δd,y ) ,
Μ( x,y;Δd,Δθ )= 1 2 Γ( x−d ) e j Θ up ( x−d,y ) + 1 2 Γ( x+d+Δd ) e j Θ low ( x+d+Δd,y ) e jΔθ .
F ¯ ={ h y · h x [ t GR { h y · h x [ M ] } ] }.
t GR ( x )=cos( 2πx/Λ ),
t GR ( x )=sgn( cos( 2πx/Λ ) ),

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