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 OSA

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2012

2011

2008

2006

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

C. Slinger, C. Cameron, and M. Stanley, “Computer-generated holography as a generic display technology,” IEEE. Computer38(8), 46–53 (2005).
[CrossRef]

2003

1996

1978

1969

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. Computer38(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. Computer38(8), 46–53 (2005).
[CrossRef]

Stanley, M.

C. Slinger, C. Cameron, and M. Stanley, “Computer-generated holography as a generic display technology,” IEEE. Computer38(8), 46–53 (2005).
[CrossRef]

Tsang, P.

Ulusoy, E.

Usukura, N.

Z. Jaroszewicz, Z. J.

Appl. Opt.

Chin. Opt. Lett.

IBM J. Res. Develop.

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

IEEE. Computer

C. Slinger, C. Cameron, and M. Stanley, “Computer-generated holography as a generic display technology,” IEEE. Computer38(8), 46–53 (2005).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

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.

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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

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.

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.

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.

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( Φψ ) ],
exp( j Θ up )=exp[ j( Φ+ψ ) ],
exp( j Θ low )=exp[ j( Φψ ) ].
SNR= S | F( x,y ) | 2 dxdy /{ S | F( x,y ) | 2 dxdy + N | F( x,y ) | 2 dxdy },
Μ( x,y;Δd )=Γ( xd ) e j Θ up ( xd,y ) +Γ( x+d+Δd ) e j Θ down ( x+d+Δd,y ) ,
Μ( x,y;Δd,Δθ )= 1 2 Γ( xd ) e j Θ up ( xd,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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