Abstract

In this paper, we analyze a holographic display system utilizing a phase-only spatial light modulator (SLM) based on liquid crystal on silicon (LCoS). An LCoS SLM works in reflection, and, in some applications, it is convenient to use with an inclined illumination. Even with a highly inclined illumination, the holographic display is capable of good-quality image generation. We show that the key to obtain high-quality reconstructions is the tilt-dependent calibration and algorithms. Typically, an LCoS SLM is illuminated with a plane wave with normal wave vector. We use inclined illumination, which requires development of new algorithms and display characterization. In this paper we introduce two algorithms. The first one is designed to process a digital hologram captured in CCD normal configuration, so it can be displayed in SLM tilted geometry, while the second one is capable of synthetic hologram generation for tilted SLM configuration. The inclined geometry asymmetrically changes the field of view of a holographic display. The presented theoretical analysis of the aliasing effect provides a formula for the field of view as a function of SLM tilt. The incidence angle affects SLM performance. Both elements of SLM calibration, i.e., pixel phase response and wavefront aberrations, strongly depend on SLM tilt angle. The effect is discussed in this paper. All of the discussions are accompanied with experimental results.

© 2011 Optical Society of America

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References

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2010 (3)

G. Finke, T. Kozacki, and M. Kujawinska, “Wide viewing angle holographic display with multi spatial light modulator array,” Proc. SPIE 7723, 77230A (2010).
[CrossRef]

D. P. Kelly, D. S. Monaghan, N. Pandey, T. Kozacki, A. Michałkiewicz, B. M. Hennelly, and M. Kujawinska, “Digital holographic capture and optoelectronic reconstruction for 3D displays,” Int. J. Digit. Multimedia Broadcast. 2010, 759323 (2010).
[CrossRef]

T. Kozacki, “On resolution and viewing of holographic image generated by 3D holographic display,” Opt. Express 18, 27118–27129 (2010).
[CrossRef]

2009 (1)

2008 (3)

J. Hahn, H. Kim, Y. Lim, G. Park, and B. Lee, “Wide viewing angle dynamic holographic stereogram with a curved array of spatial light modulators,” Opt. Express 16, 12372–12386(2008).
[CrossRef] [PubMed]

H. M. Ozaktas and L. Onural, Three-Dimensional Television (Springer, 2008).
[CrossRef]

T. Kozacki, “Numerical errors of diffraction computing using plane wave spectrum decomposition,” Opt. Commun. 281, 4219–4223 (2008).
[CrossRef]

2007 (1)

T. Latychevskaia and H.-W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98, 23390–23393(2007).
[CrossRef]

2006 (1)

D. P. Kelly, B. M. Hennelly, W. T. Rhodes, and J. T. Sheridan, “Analytical and numerical analysis of linear optical systems,” Opt. Eng. 45, 088201 (2006).
[CrossRef]

2005 (2)

2004 (2)

X. Xun and R. W. Cohn, “Phase calibration of spatially nonuniform spatial light modulators,” Appl. Opt. 43, 6400–6406(2004).
[CrossRef] [PubMed]

A. Michałkiewicz, M. Kujawińska, T. Kozacki, X. Wang, and P. J. Bos, “Holographic three-dimensional displays with liquid crystal on silicon spatial light modulator,” Proc. SPIE 5531, 85–94 (2004).
[CrossRef]

2003 (1)

2001 (1)

V. Soifer, Methods for Computer Design of Diffractive Optical Elements (Wiley-Interscience2001).

1999 (1)

T. M. Lehmann, C. Gonner, K. Spitzer, “Survey: interpolation methods in medical image processing,” IEEE Trans. Med. Imag. 18, 1049–1075 (1999).
[CrossRef]

1998 (2)

1997 (1)

1996 (2)

K. Maeno, N. Fukaya, O. Nishikawa, K. Sato, and T. Honda, “Electro-holographic display using 15 megapixels LCD,” Proc. SPIE 2652, 15–23 (1996).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics2nd ed. (McGraw-Hill, 1996).

1995 (1)

1986 (1)

J. J. Stamnes, Waves in Focal Regions (Hilger, 1986).

1982 (2)

R. Jóźwicki, “Transformation of reference spheres by an aberration free and infinitely large optical system in the Fresnel approximation,” J. Mod. Opt. 29, 1383–1393 (1982).
[CrossRef]

J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
[CrossRef] [PubMed]

1948 (1)

D. Gabor, “A new microscopic principle,” Nature 161, 777–778(1948).
[CrossRef] [PubMed]

Arsenault, H. H.

Bergeron, A.

Bos, P. J.

A. Michałkiewicz, M. Kujawińska, T. Kozacki, X. Wang, and P. J. Bos, “Holographic three-dimensional displays with liquid crystal on silicon spatial light modulator,” Proc. SPIE 5531, 85–94 (2004).
[CrossRef]

Campos, J.

Cohn, R. W.

Delen, N.

Doucet, M.

Estapé, M.

Fernández, E.

Fienup, J. R.

Fink, H.-W.

T. Latychevskaia and H.-W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98, 23390–23393(2007).
[CrossRef]

Finke, G.

G. Finke, T. Kozacki, and M. Kujawinska, “Wide viewing angle holographic display with multi spatial light modulator array,” Proc. SPIE 7723, 77230A (2010).
[CrossRef]

Fukaya, N.

K. Maeno, N. Fukaya, O. Nishikawa, K. Sato, and T. Honda, “Electro-holographic display using 15 megapixels LCD,” Proc. SPIE 2652, 15–23 (1996).
[CrossRef]

Gabor, D.

D. Gabor, “A new microscopic principle,” Nature 161, 777–778(1948).
[CrossRef] [PubMed]

Gagnon, F.

Gauvin, J.

Gingras, D.

Gonner, C.

T. M. Lehmann, C. Gonner, K. Spitzer, “Survey: interpolation methods in medical image processing,” IEEE Trans. Med. Imag. 18, 1049–1075 (1999).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics2nd ed. (McGraw-Hill, 1996).

Hahn, J.

Hennelly, B. M.

D. P. Kelly, D. S. Monaghan, N. Pandey, T. Kozacki, A. Michałkiewicz, B. M. Hennelly, and M. Kujawinska, “Digital holographic capture and optoelectronic reconstruction for 3D displays,” Int. J. Digit. Multimedia Broadcast. 2010, 759323 (2010).
[CrossRef]

D. P. Kelly, B. M. Hennelly, W. T. Rhodes, and J. T. Sheridan, “Analytical and numerical analysis of linear optical systems,” Opt. Eng. 45, 088201 (2006).
[CrossRef]

Honda, T.

K. Maeno, N. Fukaya, O. Nishikawa, K. Sato, and T. Honda, “Electro-holographic display using 15 megapixels LCD,” Proc. SPIE 2652, 15–23 (1996).
[CrossRef]

Hooker, B.

Iemmi, C.

Józwicki, R.

R. Jóźwicki, “Transformation of reference spheres by an aberration free and infinitely large optical system in the Fresnel approximation,” J. Mod. Opt. 29, 1383–1393 (1982).
[CrossRef]

Kelly, D. P.

D. P. Kelly, D. S. Monaghan, N. Pandey, T. Kozacki, A. Michałkiewicz, B. M. Hennelly, and M. Kujawinska, “Digital holographic capture and optoelectronic reconstruction for 3D displays,” Int. J. Digit. Multimedia Broadcast. 2010, 759323 (2010).
[CrossRef]

D. P. Kelly, B. M. Hennelly, W. T. Rhodes, and J. T. Sheridan, “Analytical and numerical analysis of linear optical systems,” Opt. Eng. 45, 088201 (2006).
[CrossRef]

Kim, H.

Kozacki, T.

T. Kozacki, “On resolution and viewing of holographic image generated by 3D holographic display,” Opt. Express 18, 27118–27129 (2010).
[CrossRef]

D. P. Kelly, D. S. Monaghan, N. Pandey, T. Kozacki, A. Michałkiewicz, B. M. Hennelly, and M. Kujawinska, “Digital holographic capture and optoelectronic reconstruction for 3D displays,” Int. J. Digit. Multimedia Broadcast. 2010, 759323 (2010).
[CrossRef]

G. Finke, T. Kozacki, and M. Kujawinska, “Wide viewing angle holographic display with multi spatial light modulator array,” Proc. SPIE 7723, 77230A (2010).
[CrossRef]

T. Kozacki, “Numerical errors of diffraction computing using plane wave spectrum decomposition,” Opt. Commun. 281, 4219–4223 (2008).
[CrossRef]

A. Michałkiewicz, M. Kujawińska, T. Kozacki, X. Wang, and P. J. Bos, “Holographic three-dimensional displays with liquid crystal on silicon spatial light modulator,” Proc. SPIE 5531, 85–94 (2004).
[CrossRef]

Kreis, T.

T. Kreis, Handbook of Holographic Interferometry(Weinheim, 2005).

Kujawinska, M.

D. P. Kelly, D. S. Monaghan, N. Pandey, T. Kozacki, A. Michałkiewicz, B. M. Hennelly, and M. Kujawinska, “Digital holographic capture and optoelectronic reconstruction for 3D displays,” Int. J. Digit. Multimedia Broadcast. 2010, 759323 (2010).
[CrossRef]

G. Finke, T. Kozacki, and M. Kujawinska, “Wide viewing angle holographic display with multi spatial light modulator array,” Proc. SPIE 7723, 77230A (2010).
[CrossRef]

A. Michałkiewicz, M. Kujawińska, T. Kozacki, X. Wang, and P. J. Bos, “Holographic three-dimensional displays with liquid crystal on silicon spatial light modulator,” Proc. SPIE 5531, 85–94 (2004).
[CrossRef]

Latychevskaia, T.

T. Latychevskaia and H.-W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98, 23390–23393(2007).
[CrossRef]

Lee, B.

Lehmann, T. M.

T. M. Lehmann, C. Gonner, K. Spitzer, “Survey: interpolation methods in medical image processing,” IEEE Trans. Med. Imag. 18, 1049–1075 (1999).
[CrossRef]

Lim, Y.

Lizana, A.

Maeno, K.

K. Maeno, N. Fukaya, O. Nishikawa, K. Sato, and T. Honda, “Electro-holographic display using 15 megapixels LCD,” Proc. SPIE 2652, 15–23 (1996).
[CrossRef]

Márquez, A.

Martín, N.

Matsushima, K.

Michalkiewicz, A.

D. P. Kelly, D. S. Monaghan, N. Pandey, T. Kozacki, A. Michałkiewicz, B. M. Hennelly, and M. Kujawinska, “Digital holographic capture and optoelectronic reconstruction for 3D displays,” Int. J. Digit. Multimedia Broadcast. 2010, 759323 (2010).
[CrossRef]

A. Michałkiewicz, M. Kujawińska, T. Kozacki, X. Wang, and P. J. Bos, “Holographic three-dimensional displays with liquid crystal on silicon spatial light modulator,” Proc. SPIE 5531, 85–94 (2004).
[CrossRef]

Monaghan, D. S.

D. P. Kelly, D. S. Monaghan, N. Pandey, T. Kozacki, A. Michałkiewicz, B. M. Hennelly, and M. Kujawinska, “Digital holographic capture and optoelectronic reconstruction for 3D displays,” Int. J. Digit. Multimedia Broadcast. 2010, 759323 (2010).
[CrossRef]

Moreno, I.

Nishikawa, O.

K. Maeno, N. Fukaya, O. Nishikawa, K. Sato, and T. Honda, “Electro-holographic display using 15 megapixels LCD,” Proc. SPIE 2652, 15–23 (1996).
[CrossRef]

Onural, L.

H. M. Ozaktas and L. Onural, Three-Dimensional Television (Springer, 2008).
[CrossRef]

Ozaktas, H. M.

H. M. Ozaktas and L. Onural, Three-Dimensional Television (Springer, 2008).
[CrossRef]

Pandey, N.

D. P. Kelly, D. S. Monaghan, N. Pandey, T. Kozacki, A. Michałkiewicz, B. M. Hennelly, and M. Kujawinska, “Digital holographic capture and optoelectronic reconstruction for 3D displays,” Int. J. Digit. Multimedia Broadcast. 2010, 759323 (2010).
[CrossRef]

Park, G.

Rhodes, W. T.

D. P. Kelly, B. M. Hennelly, W. T. Rhodes, and J. T. Sheridan, “Analytical and numerical analysis of linear optical systems,” Opt. Eng. 45, 088201 (2006).
[CrossRef]

Rohrbach, A.

Sato, K.

K. Maeno, N. Fukaya, O. Nishikawa, K. Sato, and T. Honda, “Electro-holographic display using 15 megapixels LCD,” Proc. SPIE 2652, 15–23 (1996).
[CrossRef]

Schimmel, H.

Sheridan, J. T.

D. P. Kelly, B. M. Hennelly, W. T. Rhodes, and J. T. Sheridan, “Analytical and numerical analysis of linear optical systems,” Opt. Eng. 45, 088201 (2006).
[CrossRef]

Singer, W.

Soifer, V.

V. Soifer, Methods for Computer Design of Diffractive Optical Elements (Wiley-Interscience2001).

Spitzer, K.

T. M. Lehmann, C. Gonner, K. Spitzer, “Survey: interpolation methods in medical image processing,” IEEE Trans. Med. Imag. 18, 1049–1075 (1999).
[CrossRef]

Stamnes, J. J.

J. J. Stamnes, Waves in Focal Regions (Hilger, 1986).

Wang, X.

A. Michałkiewicz, M. Kujawińska, T. Kozacki, X. Wang, and P. J. Bos, “Holographic three-dimensional displays with liquid crystal on silicon spatial light modulator,” Proc. SPIE 5531, 85–94 (2004).
[CrossRef]

Wyrowski, F.

Xun, X.

Yamaguchi, I.

Yzuel, M. J.

Zhang, T.

Appl. Opt. (4)

IEEE Trans. Med. Imag. (1)

T. M. Lehmann, C. Gonner, K. Spitzer, “Survey: interpolation methods in medical image processing,” IEEE Trans. Med. Imag. 18, 1049–1075 (1999).
[CrossRef]

Int. J. Digit. Multimedia Broadcast. (1)

D. P. Kelly, D. S. Monaghan, N. Pandey, T. Kozacki, A. Michałkiewicz, B. M. Hennelly, and M. Kujawinska, “Digital holographic capture and optoelectronic reconstruction for 3D displays,” Int. J. Digit. Multimedia Broadcast. 2010, 759323 (2010).
[CrossRef]

J. Mod. Opt. (1)

R. Jóźwicki, “Transformation of reference spheres by an aberration free and infinitely large optical system in the Fresnel approximation,” J. Mod. Opt. 29, 1383–1393 (1982).
[CrossRef]

J. Opt. Soc. Am. A (3)

Nature (1)

D. Gabor, “A new microscopic principle,” Nature 161, 777–778(1948).
[CrossRef] [PubMed]

Opt. Commun. (1)

T. Kozacki, “Numerical errors of diffraction computing using plane wave spectrum decomposition,” Opt. Commun. 281, 4219–4223 (2008).
[CrossRef]

Opt. Eng. (1)

D. P. Kelly, B. M. Hennelly, W. T. Rhodes, and J. T. Sheridan, “Analytical and numerical analysis of linear optical systems,” Opt. Eng. 45, 088201 (2006).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

T. Latychevskaia and H.-W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98, 23390–23393(2007).
[CrossRef]

Proc. SPIE (3)

A. Michałkiewicz, M. Kujawińska, T. Kozacki, X. Wang, and P. J. Bos, “Holographic three-dimensional displays with liquid crystal on silicon spatial light modulator,” Proc. SPIE 5531, 85–94 (2004).
[CrossRef]

K. Maeno, N. Fukaya, O. Nishikawa, K. Sato, and T. Honda, “Electro-holographic display using 15 megapixels LCD,” Proc. SPIE 2652, 15–23 (1996).
[CrossRef]

G. Finke, T. Kozacki, and M. Kujawinska, “Wide viewing angle holographic display with multi spatial light modulator array,” Proc. SPIE 7723, 77230A (2010).
[CrossRef]

Other (5)

J. W. Goodman, Introduction to Fourier Optics2nd ed. (McGraw-Hill, 1996).

J. J. Stamnes, Waves in Focal Regions (Hilger, 1986).

H. M. Ozaktas and L. Onural, Three-Dimensional Television (Springer, 2008).
[CrossRef]

V. Soifer, Methods for Computer Design of Diffractive Optical Elements (Wiley-Interscience2001).

T. Kreis, Handbook of Holographic Interferometry(Weinheim, 2005).

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Figures (12)

Fig. 1
Fig. 1

Experimental setup for holographic image generation with tilted SLM; laser, 532 nm ; HW, half-wave plate; P, polarizer; X ( x , y ) is a plane of an SLM and Ξ ( ξ , n ) of the reconstruction.

Fig. 2
Fig. 2

Illustration of algorithm steps for generation of CGH for tilted SLM.

Fig. 3
Fig. 3

Measured wavefront aberration for normal SLM orientation in radians; contour step corresponds to 2 π phase increment.

Fig. 4
Fig. 4

Ewald sphere for plane-wave reflection from tilted SLM; k i and k r , illumination and reflection local wave vectors.

Fig. 5
Fig. 5

Comparison of focal point images for spherical wave (focal 462 mm ) produced by SLM tilted by 20 ° with applied wavefront aberration compensation (a) with tilt correction, (b) without tilt correction.

Fig. 6
Fig. 6

Pixel phase response calibration for series of angular orientation of SLM, θ = 0 ° , 10 ° , 20 ° , 30 ° , 45 ° and voltage range of 0 2.59 V .

Fig. 7
Fig. 7

Comparison of image reconstruction of CGH reconstructed in holographic display with tilted SLM ( θ = 20 ° ) with (a) applied proper calibration curve for 20 ° and (b) for 0 ° .

Fig. 8
Fig. 8

Plot of the FoV and the EFoV for θ = 25 ° as a function of reconstruction distance.

Fig. 9
Fig. 9

FoV extension for exemplary θ = 25 ° and z = 500 mm .

Fig. 10
Fig. 10

Image of a generated target (a) and its image reconstruction, (b) from CGH.

Fig. 11
Fig. 11

Comparison of image reconstruction obtained for digital hologram of screw set and series of SLM tilts: θ = 0 ° , 10 ° , 20 ° , 30 ° , 40 ° ; reconstructions (b)–(e) are obtained for processed holograms with tilt correction algorithm and (f)–(i) for unprocessed ones.

Fig. 12
Fig. 12

Comparison of image reconstructions obtained for CGHs of gargoyle statue designed for series of SLM tilts: θ = 0 ° , 10 ° , 20 ° , 30 ° , 40 ° and corresponding statue perspectives.

Equations (23)

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

u ( x ) = u p ( x ) exp ( 2 π i x · f c ) ,
U X ( f ) = u ( x ) exp { i 2 π f · x } d x ,
f = T [ f ] + f c ,
T ± = [ a 1 ± a 2 ± a 3 ± a 4 ± a 5 ± a 6 ± a 7 ± a 8 ± a 9 ± ] .
T ± = [ cos θ 0 ± sin θ 0 1 0 ± sin θ 0 cos θ ] .
f x = α ( f x , f y ) + f c x = a 1 f x + a 2 f y + a 3 ( λ 2 f x 2 f y 2 ) 1 / 2 + f c x , f y = β ( f x , f y ) + f c x = a 4 f x + a 5 f y + a 6 ( λ 2 f x 2 f y 2 ) 1 / 2 + f c y .
U p X ( f x , f y ) = U X ( α ( f x , f y ) + f c x , β ( f x , f y ) + f c y ) ,
U X ( f x , f y ) = U p X ( α + ( f x f c x , f y f c y ) , β + ( f x f c x , f y f c y ) ) .
U p X ( n ) ( f x , f y ) = A 0 ( x , y ) exp { i ARG ( u ¯ p ( n 1 ) ( x , y ) ) } exp { 2 π i ( f x x + f y y ) } d x d y ,
U X ( n ) ( f x , f y ) = U p X ( n ) ( α + ( f x f c x , f y f c y ) , β + ( f x f c x , f y f c y ) ) ,
u S ( n ) ( ξ , η ) = ( λ z ) 1 U X ( n ) ( f x , f y ) exp { 2 π i ( f x x + f y y ) } d f x d f y exp { i k 2 z ( x 2 + y 2 ) } exp { i k z ( x ξ + y η ) } d x d y ,
u ¯ S ( n ) ( ξ , η ) = B 0 ( ξ , η ) exp { i ARG ( u S ( n ) ( ξ , η ) ) } .
U ¯ X ( n ) ( f x , f y ) = λ z u ¯ S ( n ) ( ξ , η ) exp { i k z ( x ξ + y η ) } d ξ d η exp { i k 2 z ( x 2 + y 2 ) } exp { 2 π i ( f x x + f y y ) } d x d y .
U ¯ p X ( n ) ( f x , f y ) = U ¯ X ( n ) ( α ( f x , f y ) + f c x , β ( f x , f y ) + f c y ) ,
u ¯ p ( n ) ( x , y ) = U ¯ p X ( n ) ( f x , f y ) exp { 2 π i ( f x x + f y y ) } d f x d f y .
u ( x , y ) = exp { i k 2 h ( x , y ) cos ( θ ) } ,
f l ( x ) = ϕ ( x ) 2 π x = R ( x , ξ FOV ± ) λ x = { λ 1 sin θ + ( 2 Δ ) 1 for x = x + , λ 1 sin θ ( 2 Δ ) 1 for x = x .
ξ FOV ± = x z sin θ z cos θ tan β ± cos θ sin θ tan β ± ,
z min = B x cos θ 0.5 sin θ ( tan β + + tan β ) tan β tan β + .
f l ( x ) = ϕ ( x ) 2 π x = R ( x , ξ A ± ) λ x = { λ 1 sin θ + ( Δ ) 1 for x = ξ A + / cos θ , λ 1 sin θ ( Δ ) 1 for x = ξ A / cos θ .
ξ A ± = cos θ ( z sin θ + ξ 0 cos θ tan γ ± ( z cos θ ξ 0 sin θ ) ) ,
ξ A = cos θ ( z sin θ + ξ 0 + cos θ tan γ + ( z cos θ ξ 0 + sin θ ) ) for ξ FOV + < ξ 0 + < ξ FOV + + N Δ cos θ .
ξ EFOV ± = z tan θ tan γ ± 1 + cos 2 θ + tan θ tan γ ± .

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