Abstract

In computer-generated Fresnel holography, direct sampling (DS) and simple shading (SS) are two common ways to generate sampled Fresnel zone plates (FZPs) on the hologram plane. Nevertheless, either aliasing or vignetting, or both, will occur in the reconstructed image when the DS method or the SS method is applied. To avoid vignetting together with aliasing in the two sampling methods, either the object size or the object distance must be restricted in generating the holograms. In this paper we propose a mask-shifting (MS) method to generate the sampled FZPs. The main concept of the MS method is that the center of the FZP can be shifted relative to the center of the mask against the FZP when the FZP is at the margin of the hologram. The shifting of the mask will result in only a phase shift and will not change the intensity distribution of the reconstructed point. Thus, by using the MS method, aliasing and vignetting are simultaneously alleviated in any combination of object size and object distance.

© 2014 Optical Society of America

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References

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  1. T.-C. Poon, ed., Digital Holography and Three-Dimensional Display (Springer, 2006).
  2. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (McGraw-Hill, 2005).
  3. T. Kozacki, “On resolution and viewing of holographic image generated by 3D holographic display,” Opt. Express 18, 27118–27129 (2010).
    [Crossref]
  4. W. J. Smith, Modern Optical Engineering, 4th ed. (McGraw-Hill, 2008).
  5. T. Kozacki, M. Kujawińska, G. Finke, B. Hennelly, and N. Pandey, “Extended viewing angle holographic display system with tilted SLMs in a circular configuration,” Appl. Opt. 51, 1771–1780 (2012).
    [Crossref]
  6. 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]
  7. K. Hong, S.-G. Park, J. Yeom, J. Kim, N. Chen, K. Pyun, C. Choi, S. Kim, J. An, H.-S. Lee, U. i. Chung, and B. Lee, “Resolution enhancement of holographic printer using a hogel overlapping method,” Opt. Express 21, 14047–14055 (2013).
    [Crossref]
  8. T. Yamaguchi, G. Okabe, and H. Yoshikawa, “Real-time image plane full-color and full-parallax holographic video display system,” Opt. Eng. 46, 125801 (2007).
    [Crossref]
  9. J.-P. Liu, “Controlling the aliasing by zero-padding in the digital calculation of the scalar diffraction,” J. Opt. Soc. Am. A 29, 1956–1964 (2012).
    [Crossref]
  10. K. Matsushima and S. Nakahara, “Extremely high-definition full-parallax computer-generated hologram created by the polygon-based method,” Appl. Opt. 48, H54–H63 (2009).
    [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, D117–D127 (2008).
    [Crossref]
  12. L. Ahrenberg, P. Benzie, M. Magnor, and J. Watson, “Computer generated holograms from three dimensional meshes using an analytic light transport model,” Appl. Opt. 47, 1567–1574 (2008).
    [Crossref]
  13. S.-C. Kim, J.-H. Yoon, and E.-S. Kim, “Fast generation of three-dimensional video holograms by combined use of data compression and lookup table techniques,” Appl. Opt. 47, 5986–5995 (2008).
    [Crossref]
  14. S.-C. Kim and E.-S. Kim, “Fast computation of hologram patterns of a 3D object using run-length encoding and novel look-up table methods,” Appl. Opt. 48, 1030–1041 (2009).
    [Crossref]
  15. S.-C. Kim and E.-S. Kim, “Effective generation of digital holograms of three-dimensional objects using a novel look-up table method,” Appl. Opt. 47, D55–D62 (2008).
    [Crossref]
  16. P. Tsang, T.-C. Poon, W. K. Cheung, and J.-P. Liu, “Computer generation of binary Fresnel holography,” Appl. Opt. 50, B88–B95 (2011).
    [Crossref]
  17. W. K. Cheung, P. Tsang, T.-C. Poon, and C. Zhou, “Enhanced method for the generation of binary Fresnel holograms based on grid-cross downsampling,” Chin. Opt. Lett. 9, 120005 (2011).
    [Crossref]
  18. P. Tsang, W. K. Cheung, T.-C. Poon, and J.-P. Liu, “An enhanced method for generation of binary Fresnel hologram based on adaptive and uniform grid-cross down-sampling,” Opt. Commun. 285, 4027–4032 (2012).
    [Crossref]
  19. H. Yoshikawa and H. Taniguchi, “Computer generated rainbow hologram,” Opt. Rev. 6, 118–123 (1999).
    [Crossref]
  20. H. Yoshikawa, “Fast computation of Fresnel holograms employing difference,” Opt. Rev. 8, 331–335 (2001).
    [Crossref]
  21. H. Yoshikawa and A. Kagotani, “Full color computer-generated rainbow hologram with enlarged viewing angle,” Opt. Rev. 9, 251–254 (2002).
    [Crossref]
  22. R. Bräuer, F. Wyrowski, and O. Bryngdahl, “Diffusers in digital holography,” J. Opt. Soc. Am. A 8, 572–578 (1991).
    [Crossref]
  23. J. W. Goodman, Statistical Optics (Wiley, 1985).

2013 (1)

2012 (3)

2011 (2)

2010 (1)

2009 (2)

2008 (5)

2007 (1)

T. Yamaguchi, G. Okabe, and H. Yoshikawa, “Real-time image plane full-color and full-parallax holographic video display system,” Opt. Eng. 46, 125801 (2007).
[Crossref]

2002 (1)

H. Yoshikawa and A. Kagotani, “Full color computer-generated rainbow hologram with enlarged viewing angle,” Opt. Rev. 9, 251–254 (2002).
[Crossref]

2001 (1)

H. Yoshikawa, “Fast computation of Fresnel holograms employing difference,” Opt. Rev. 8, 331–335 (2001).
[Crossref]

1999 (1)

H. Yoshikawa and H. Taniguchi, “Computer generated rainbow hologram,” Opt. Rev. 6, 118–123 (1999).
[Crossref]

1991 (1)

Ahrenberg, L.

An, J.

Benzie, P.

Bräuer, R.

Bryngdahl, O.

Chen, N.

Cheung, W. K.

Choi, C.

Chung, U. i.

Finke, G.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (McGraw-Hill, 2005).

J. W. Goodman, Statistical Optics (Wiley, 1985).

Hahn, J.

Hennelly, B.

Hong, K.

Kagotani, A.

H. Yoshikawa and A. Kagotani, “Full color computer-generated rainbow hologram with enlarged viewing angle,” Opt. Rev. 9, 251–254 (2002).
[Crossref]

Kim, E.-S.

Kim, H.

Kim, J.

Kim, S.

Kim, S.-C.

Kozacki, T.

Kujawinska, M.

Lee, B.

Lee, H.-S.

Lim, Y.

Liu, J.-P.

Magnor, M.

Matsushima, K.

Nakahara, S.

Okabe, G.

T. Yamaguchi, G. Okabe, and H. Yoshikawa, “Real-time image plane full-color and full-parallax holographic video display system,” Opt. Eng. 46, 125801 (2007).
[Crossref]

Pandey, N.

Park, G.

Park, S.-G.

Poon, T.-C.

Pyun, K.

Smith, W. J.

W. J. Smith, Modern Optical Engineering, 4th ed. (McGraw-Hill, 2008).

Taniguchi, H.

H. Yoshikawa and H. Taniguchi, “Computer generated rainbow hologram,” Opt. Rev. 6, 118–123 (1999).
[Crossref]

Tsang, P.

Watson, J.

Wyrowski, F.

Yamaguchi, T.

T. Yamaguchi, G. Okabe, and H. Yoshikawa, “Real-time image plane full-color and full-parallax holographic video display system,” Opt. Eng. 46, 125801 (2007).
[Crossref]

Yeom, J.

Yoon, J.-H.

Yoshikawa, H.

T. Yamaguchi, G. Okabe, and H. Yoshikawa, “Real-time image plane full-color and full-parallax holographic video display system,” Opt. Eng. 46, 125801 (2007).
[Crossref]

H. Yoshikawa and A. Kagotani, “Full color computer-generated rainbow hologram with enlarged viewing angle,” Opt. Rev. 9, 251–254 (2002).
[Crossref]

H. Yoshikawa, “Fast computation of Fresnel holograms employing difference,” Opt. Rev. 8, 331–335 (2001).
[Crossref]

H. Yoshikawa and H. Taniguchi, “Computer generated rainbow hologram,” Opt. Rev. 6, 118–123 (1999).
[Crossref]

Zhou, C.

Appl. Opt. (8)

T. Kozacki, M. Kujawińska, G. Finke, B. Hennelly, and N. Pandey, “Extended viewing angle holographic display system with tilted SLMs in a circular configuration,” Appl. Opt. 51, 1771–1780 (2012).
[Crossref]

K. Matsushima and S. Nakahara, “Extremely high-definition full-parallax computer-generated hologram created by the polygon-based method,” Appl. Opt. 48, H54–H63 (2009).
[Crossref]

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

L. Ahrenberg, P. Benzie, M. Magnor, and J. Watson, “Computer generated holograms from three dimensional meshes using an analytic light transport model,” Appl. Opt. 47, 1567–1574 (2008).
[Crossref]

S.-C. Kim, J.-H. Yoon, and E.-S. Kim, “Fast generation of three-dimensional video holograms by combined use of data compression and lookup table techniques,” Appl. Opt. 47, 5986–5995 (2008).
[Crossref]

S.-C. Kim and E.-S. Kim, “Fast computation of hologram patterns of a 3D object using run-length encoding and novel look-up table methods,” Appl. Opt. 48, 1030–1041 (2009).
[Crossref]

S.-C. Kim and E.-S. Kim, “Effective generation of digital holograms of three-dimensional objects using a novel look-up table method,” Appl. Opt. 47, D55–D62 (2008).
[Crossref]

P. Tsang, T.-C. Poon, W. K. Cheung, and J.-P. Liu, “Computer generation of binary Fresnel holography,” Appl. Opt. 50, B88–B95 (2011).
[Crossref]

Chin. Opt. Lett. (1)

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

P. Tsang, W. K. Cheung, T.-C. Poon, and J.-P. Liu, “An enhanced method for generation of binary Fresnel hologram based on adaptive and uniform grid-cross down-sampling,” Opt. Commun. 285, 4027–4032 (2012).
[Crossref]

Opt. Eng. (1)

T. Yamaguchi, G. Okabe, and H. Yoshikawa, “Real-time image plane full-color and full-parallax holographic video display system,” Opt. Eng. 46, 125801 (2007).
[Crossref]

Opt. Express (3)

Opt. Rev. (3)

H. Yoshikawa and H. Taniguchi, “Computer generated rainbow hologram,” Opt. Rev. 6, 118–123 (1999).
[Crossref]

H. Yoshikawa, “Fast computation of Fresnel holograms employing difference,” Opt. Rev. 8, 331–335 (2001).
[Crossref]

H. Yoshikawa and A. Kagotani, “Full color computer-generated rainbow hologram with enlarged viewing angle,” Opt. Rev. 9, 251–254 (2002).
[Crossref]

Other (4)

W. J. Smith, Modern Optical Engineering, 4th ed. (McGraw-Hill, 2008).

T.-C. Poon, ed., Digital Holography and Three-Dimensional Display (Springer, 2006).

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (McGraw-Hill, 2005).

J. W. Goodman, Statistical Optics (Wiley, 1985).

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Figures (10)

Fig. 1.
Fig. 1.

Schematic of holographic display. Dx is the width of the SLM, Lx is the width of the reconstructed image, and z and d are the object distance and the distance between the observer and the hologram, respectively.

Fig. 2.
Fig. 2.

(a) Aliased FZP generated by the DS method. (b)–(d) Shaded FZPs by the SS method. (c) and (d) correspond to an off-axis object point and an object point located at the periphery of the SLM, respectively, and will result in vignetting upon reconstruction. The masked region is represented by charcoal, and its transmittance is zero.

Fig. 3.
Fig. 3.

(a) Shaded FZP of an on-axis object point and (b) shaded FZP of a marginal object point in the MS method. Note the mask size in (a) and (b) is identical, and thus no vignetting occurs in the reconstruction.

Fig. 4.
Fig. 4.

Three geometric configurations of the CGFH. The square with width Dx represents the SLM. The gray square with width Wmax represents a maximum well-sampled FZP centered at (Lx/2,0). (a) The well-sampled FZP is inside the SLM. (b) The well-sampled FZP covers the whole SLM. (c) Part of the well-sampled FZP is outside the SLM. In the case in which vignetting occurs for the SS method, it can be alleviated by applying an additional mask with smaller width Wx (i.e., MS method).

Fig. 5.
Fig. 5.

Resolution versus object distance for different sampling methods (Lx=Dx=10.94mm, λ=0.633μm).

Fig. 6.
Fig. 6.

Resolution versus object distance for the MS method. Parameters are the same as in Fig. 5, but Lx=20mm.

Fig. 7.
Fig. 7.

Binary holograms generated based on (a) DS method, (b) SS method, and (c) MS method, and selected portions (left-central) of the holograms are enlarged in (d)–(f), respectively.

Fig. 8.
Fig. 8.

Simulation results. (a) Original object and (b)–(d) reconstructed images for holograms based on (b) DS method, (c) SS method, and (d) MS method. Note that uniformity of brightness is within the whole reconstruction plane when employing the proposed MS method.

Fig. 9.
Fig. 9.

Diagram of experimental setup for hologram reconstruction; f is the focal length of the lens.

Fig. 10.
Fig. 10.

Photographs of the reconstructed images for holograms generated by (a) DS method, (b) SS method, and (c) MS method.

Equations (12)

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FZP=Ci+Aicos{π[(xxi)2+(yyi)2]λzi},
2|xxi|maxλzi1Δx,
zc=(Dx+2|xi|max)Δxλ,
Wmax=λziΔx
Wss=Wmaxforzi<DxΔxλ,=Dxotherwise.
I(x,y)=(Wx×Wy)2sinc2(Wxxλzi)sinc2(Wyyλzi),
(a)Lx+WmaxDx,(b)WmaxLx>Dx,(c)otherwise,
Wx(Dx2Lx2)Wmax2
R=λziWx,
Wms=WmaxforLxDxWmax,=DxforLx<WmaxDx,=Wmax+DxLx2otherwise.
Hon=C+iWms(i)(x,y)×Aicos{π[(xxi)2+(yyi)2]λzi},
Hoff=iWi(x,y)×Aicos{π[(xxi)2+(yyi)2]λzi2π(sinθ)xλ},

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