Abstract

A method is proposed for the construction of a square pixel complex spatial light modulator (SLM) from a commercial oblong full-high-definition (full-HD) amplitude SLM using an anamorphic optical filter. In the proposed scheme, one half-band of the optical Fourier transform of the amplitude-only spatial light field is rejected in the optical Fourier plane and the other half-band is reformatted to be an effective complex SLM with square pixels. This has an advantage in the viewing window plane since the shape of the viewing window becomes square and more ideal for observers who watch the hologram contents through it. For optimal transformation, the amplitude computer generated hologram encoding scheme was developed. Mathematical modeling of the proposed system is described herein, and it was experimentally demonstrated that the effective complex SLM displays complex holographic three-dimensional images with a clear depth discrimination effect.

© 2014 Optical Society of America

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References

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2014 (1)

2012 (1)

2011 (2)

2010 (1)

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

2008 (3)

2005 (1)

2003 (1)

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 mega-pixel computer generated holographic images from active tiling: a dynamic and scalable electro-optic modulator system,” Proc. SPIE 5005, 247–258 (2003).
[CrossRef]

1996 (1)

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

1992 (1)

P. St.-Hilaire, S. A. Benton, M. Lucente, and P. M. Hubel, “Color images with the MIT holographic video display,” Proc. SPIE 1667, 73–84 (1992).

1978 (1)

1970 (1)

1968 (1)

1966 (1)

Arrizón, V.

Bannister, R. W.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 mega-pixel computer generated holographic images from active tiling: a dynamic and scalable electro-optic modulator system,” Proc. SPIE 5005, 247–258 (2003).
[CrossRef]

Benton, S. A.

P. St.-Hilaire, S. A. Benton, M. Lucente, and P. M. Hubel, “Color images with the MIT holographic video display,” Proc. SPIE 1667, 73–84 (1992).

Brown, B. R.

Bryngdahl, O.

Burckhardt, C. B.

Buschbeck, S.

N. Leister, A. Schwerdtner, G. Füutterer, S. Buschbeck, J.-C. Olaya, and S. Flon, “Full-color interactive holographic projection system for large 3D scene reconstruction,” Proc. SPIE 6911, 69110V (2008).
[CrossRef]

Cameron, C. D.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 mega-pixel computer generated holographic images from active tiling: a dynamic and scalable electro-optic modulator system,” Proc. SPIE 5005, 247–258 (2003).
[CrossRef]

Chen, N.

Choi, H.-J.

Choi, S.

Coomber, S. D.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 mega-pixel computer generated holographic images from active tiling: a dynamic and scalable electro-optic modulator system,” Proc. SPIE 5005, 247–258 (2003).
[CrossRef]

Cresswell, I. G.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 mega-pixel computer generated holographic images from active tiling: a dynamic and scalable electro-optic modulator system,” Proc. SPIE 5005, 247–258 (2003).
[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]

Flon, S.

N. Leister, A. Schwerdtner, G. Füutterer, S. Buschbeck, J.-C. Olaya, and S. Flon, “Full-color interactive holographic projection system for large 3D scene reconstruction,” Proc. SPIE 6911, 69110V (2008).
[CrossRef]

Fukaya, N.

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

Füutterer, G.

N. Leister, A. Schwerdtner, G. Füutterer, S. Buschbeck, J.-C. Olaya, and S. Flon, “Full-color interactive holographic projection system for large 3D scene reconstruction,” Proc. SPIE 6911, 69110V (2008).
[CrossRef]

Goodman, J.

J. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Hahn, J.

Honda, T.

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

Hong, J.

Hsueh, C. K.

Hubel, P. M.

P. St.-Hilaire, S. A. Benton, M. Lucente, and P. M. Hubel, “Color images with the MIT holographic video display,” Proc. SPIE 1667, 73–84 (1992).

Hughes, J. R.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 mega-pixel computer generated holographic images from active tiling: a dynamic and scalable electro-optic modulator system,” Proc. SPIE 5005, 247–258 (2003).
[CrossRef]

Hui, V.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 mega-pixel computer generated holographic images from active tiling: a dynamic and scalable electro-optic modulator system,” Proc. SPIE 5005, 247–258 (2003).
[CrossRef]

Im, D.

Jackson, P. O.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 mega-pixel computer generated holographic images from active tiling: a dynamic and scalable electro-optic modulator system,” Proc. SPIE 5005, 247–258 (2003).
[CrossRef]

Kang, H.

Kim, H.

Kim, Y.

Kozacki, T.

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

Kujawinska, M.

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

Lee, B.

Lee, D.

Lee, H.-S.

Leister, N.

N. Leister, A. Schwerdtner, G. Füutterer, S. Buschbeck, J.-C. Olaya, and S. Flon, “Full-color interactive holographic projection system for large 3D scene reconstruction,” Proc. SPIE 6911, 69110V (2008).
[CrossRef]

Lim, Y.

Lohmann, A.

Lohmann, A. W.

Lucente, M.

P. St.-Hilaire, S. A. Benton, M. Lucente, and P. M. Hubel, “Color images with the MIT holographic video display,” Proc. SPIE 1667, 73–84 (1992).

Maeno, K.

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

Méndez, G.

Milham, K. A.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 mega-pixel computer generated holographic images from active tiling: a dynamic and scalable electro-optic modulator system,” Proc. SPIE 5005, 247–258 (2003).
[CrossRef]

Miller, R. J.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 mega-pixel computer generated holographic images from active tiling: a dynamic and scalable electro-optic modulator system,” Proc. SPIE 5005, 247–258 (2003).
[CrossRef]

Min, S.-W.

Moon, E.

Nishikawa, O.

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

Olaya, J.-C.

N. Leister, A. Schwerdtner, G. Füutterer, S. Buschbeck, J.-C. Olaya, and S. Flon, “Full-color interactive holographic projection system for large 3D scene reconstruction,” Proc. SPIE 6911, 69110V (2008).
[CrossRef]

Onural, L.

Park, G.

Park, J.-H.

Park, Y.

Payne, D. A.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 mega-pixel computer generated holographic images from active tiling: a dynamic and scalable electro-optic modulator system,” Proc. SPIE 5005, 247–258 (2003).
[CrossRef]

Quarrel, J.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 mega-pixel computer generated holographic images from active tiling: a dynamic and scalable electro-optic modulator system,” Proc. SPIE 5005, 247–258 (2003).
[CrossRef]

Sánchez-de-La-Llave, D.

Sato, K.

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

Sawchuck, A. A.

Scattergood, D. C.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 mega-pixel computer generated holographic images from active tiling: a dynamic and scalable electro-optic modulator system,” Proc. SPIE 5005, 247–258 (2003).
[CrossRef]

Schwerdtner, A.

N. Leister, A. Schwerdtner, G. Füutterer, S. Buschbeck, J.-C. Olaya, and S. Flon, “Full-color interactive holographic projection system for large 3D scene reconstruction,” Proc. SPIE 6911, 69110V (2008).
[CrossRef]

Slinger, C. W.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 mega-pixel computer generated holographic images from active tiling: a dynamic and scalable electro-optic modulator system,” Proc. SPIE 5005, 247–258 (2003).
[CrossRef]

Smith, A. P.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 mega-pixel computer generated holographic images from active tiling: a dynamic and scalable electro-optic modulator system,” Proc. SPIE 5005, 247–258 (2003).
[CrossRef]

Smith, M. A.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 mega-pixel computer generated holographic images from active tiling: a dynamic and scalable electro-optic modulator system,” Proc. SPIE 5005, 247–258 (2003).
[CrossRef]

Song, H.

St.-Hilaire, P.

P. St.-Hilaire, S. A. Benton, M. Lucente, and P. M. Hubel, “Color images with the MIT holographic video display,” Proc. SPIE 1667, 73–84 (1992).

Stanley, M.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 mega-pixel computer generated holographic images from active tiling: a dynamic and scalable electro-optic modulator system,” Proc. SPIE 5005, 247–258 (2003).
[CrossRef]

Sung, G.

Tipton, D. L.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 mega-pixel computer generated holographic images from active tiling: a dynamic and scalable electro-optic modulator system,” Proc. SPIE 5005, 247–258 (2003).
[CrossRef]

Watson, P. J.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 mega-pixel computer generated holographic images from active tiling: a dynamic and scalable electro-optic modulator system,” Proc. SPIE 5005, 247–258 (2003).
[CrossRef]

Webber, P. J.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 mega-pixel computer generated holographic images from active tiling: a dynamic and scalable electro-optic modulator system,” Proc. SPIE 5005, 247–258 (2003).
[CrossRef]

Won, K.

Yaras, F.

Appl. Opt. (5)

J. Opt. Soc. Am. (1)

Opt. Express (4)

Opt. Lett. (1)

Proc. SPIE (5)

N. Leister, A. Schwerdtner, G. Füutterer, S. Buschbeck, J.-C. Olaya, and S. Flon, “Full-color interactive holographic projection system for large 3D scene reconstruction,” Proc. SPIE 6911, 69110V (2008).
[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]

P. St.-Hilaire, S. A. Benton, M. Lucente, and P. M. Hubel, “Color images with the MIT holographic video display,” Proc. SPIE 1667, 73–84 (1992).

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

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100 mega-pixel computer generated holographic images from active tiling: a dynamic and scalable electro-optic modulator system,” Proc. SPIE 5005, 247–258 (2003).
[CrossRef]

Other (1)

J. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

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Figures (9)

Fig. 1.
Fig. 1.

Optical Fourier transform of amplitude modulation pixels and its field distribution at the Fourier domain.

Fig. 2.
Fig. 2.

Spatial frequency distributions of (a) an original target wave, (b) a shifted target wave with a carrier frequency, and (c) a target and its conjugate waves. (d) Spatial frequency distributions of the encoded non-negative real hologram.

Fig. 3.
Fig. 3.

(a) Pixel apodization and (b) optical filtering of the signal at the Fourier domain and its reconstruction leading to a complex modulation pixel.

Fig. 4.
Fig. 4.

Transformation of an amplitude SLM to a complex SLM through a symmetric 4f filtering system.

Fig. 5.
Fig. 5.

Transformation of an amplitude SLM to a complex SLM through an anamorphic 4f filtering system.

Fig. 6.
Fig. 6.

Holographic imaging system: (a) schematic description and (b) experimental setup.

Fig. 7.
Fig. 7.

Optical reconstruction experiment in the holographic imaging system with a symmetric 4f filter: (a) target image (1920×1080 size with a pixel pitch of 8.5 μm), (b) CGH pattern, and (c) captured images with focuses at different distances of 0, 500, and 1000 mm from the second mirror.

Fig. 8.
Fig. 8.

Implementation of the anamorphic optical transformation model: (a) experimental implementation and (b) schematic of the optical system.

Fig. 9.
Fig. 9.

Comparison of the (a) numerical reconstruction and (b) optical reconstruction.

Equations (12)

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

T(x)=m=MM[Am[cos(kc(2m+12)Δx+ϕm)+1]rect(x(2m+12)ΔxΔx)+Am[cos(kc(2m12)Δx+ϕm)+1]rect(x(2m12)ΔxΔx)].
T(x)=m=MM[Amcos(kc(2m+12)Δx+ϕm)rect(x(2m+12)ΔxΔx)+Amcos(kc(2m12)Δx+ϕm)rect(x(2m12)ΔxΔx)]+rect(x(2M+1)Δx).
F(kx)=T(x)exp(jkxx)dx=m=MM[Amcos(kc(2m+12)Δx+ϕm)exp(jkx(2m+12)Δx)+Amcos(kc(2m12)Δx+ϕm)exp(jkx(2m12)Δx)]×Δxsinc(kxΔx2π)+(2M+1)Δxsinc(kx(2M+1)Δx2π).
Amcos(kc(2m+12)Δx+ϕm)exp(jkx(2m+12)Δx)+Amcos(kc(2m12)Δx+ϕm)exp(jkx(2m12)Δx)=Amexp(jϕm)exp(j((kckx)(2m)Δx))cos((kckx)12Δx)+Amexp(jϕm)exp(j((kc+kx)(2m)Δx))cos((kc+kx)12Δx).
F(kx)=Δxsinc(kxΔx2π)cos((kckx)12Δx)m=MM[Amexp(jϕm)exp(j((kckx)(2m)Δx))]+Δxsinc(kxΔx2π)cos((kc+kx)12Δx)m=MM[Amexp(jϕm)exp(j((kc+kx)(2m)Δx))]+(2M+1)Δxsinc(kx(2M+1)Δx2π).
Fsignal(kx)=Δxsinc(kxΔx2π)cos((kckx)12Δx)×m=MM[Amexp(jϕm)exp(j((kckx)(2m)Δx))],
Fconjugate(kx)=Δxsinc(kxΔx2π)cos((kc+kx)12Δx)×m=MM[Amexp(jϕm)exp(j((kc+kx)(2m)Δx))],
FDC(kx)=(2M+1)Δxsinc(kx(2M+1)Δx2π).
signal:conjugate=cos((kckx)12Δx):cos((kc+kx)12Δx).
Tcpx(x)=0π/ΔxFsignal(kx)exp(jkxx)dkxm=MMAmexp(jϕm)exp(jkc(2mΔx))0π/ΔxΔxsinc(kxΔx2π)exp(jkx(x2mΔx))dkx.
Tf1=(002λf10000λf112λf100001λf100).
Tf2·Tf1=(00λf20000λf21λf200001λf200)(002λf10000λf112λf100001λf100)=(f2/(2f1)0000f2/f10000(2f1)/f20000f1/f2).

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