Abstract

In three-dimensional (3D) holographic display, current brightness compensation algorithm of the traditional polygon-based method experimentally obtains the compensation factor, which depends on the fabrication process. In this paper, we proposed an analytical brightness compensation method discarding the influence of the fabrication. The surface property function with the flat power spectral density and the compensation factor obtained from the simplified relationship between the original and the rotated frequencies are used to analytically compensate the radiant energy of the tilted polygon. The optical reconstruction results show the proposed method could effectively compensate the brightness and ensure the further shading process. The proposed method separates the brightness compensation from the fabrication process, which is important for deepening the investigation of the hologram fabrication and achieving realistic 3D reconstruction.

© 2013 Optical Society of America

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References

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    [CrossRef]
  8. 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]
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2013 (2)

2012 (2)

K. Matsushima, H. Nishi, and S. Nakahara, “Simple wave-field rendering for photorealistic reconstruction in polygon-based high-definition computer holography,” J. Electron. Imaging 21, 023002 (2012).
[CrossRef]

J. Weng, T. Shimobaba, N. Okada, H. Nakayama, M. Oikawa, N. Masuda, and T. Ito, “Generation of real-time large computer generated hologram using wavefront recording method,” Opt. Express 20, 4018–4023 (2012).
[CrossRef]

2011 (1)

2009 (3)

2008 (3)

2005 (2)

K. Matsushima, “Computer-generated holograms for three-dimensional surface objects with shade and texture,” Appl. Opt. 44, 4607–4614 (2005).
[CrossRef]

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

2004 (1)

2003 (1)

1995 (1)

1993 (1)

M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2, 28–34 (1993).
[CrossRef]

1991 (1)

1989 (1)

Ahrenberg, L.

Amako, J.

Benzie, P.

Bräuer, R.

Bryngdahl, O.

Cameron, C.

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

Chong, T.-C.

Feiner, S. K.

J. D. Foley, A. van Dam, S. K. Feiner, and J. F. Hughes, Computer Graphics: Principles and Practice, Second Edition in C (Addison-Wesley, 1996).

Foley, J. D.

J. D. Foley, A. van Dam, S. K. Feiner, and J. F. Hughes, Computer Graphics: Principles and Practice, Second Edition in C (Addison-Wesley, 1996).

Goodman, J. W.

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

Hahn, J.

Hartley, R.

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, 2nd ed. (Cambridge University, 2003).

Hosoyachi, K.

Hughes, J. F.

J. D. Foley, A. van Dam, S. K. Feiner, and J. F. Hughes, Computer Graphics: Principles and Practice, Second Edition in C (Addison-Wesley, 1996).

Ichikawa, T.

Ito, T.

Jia, J.

Kim, H.

Lee, B.

Li, X.

Liang, X.

Liu, J.

Lucente, M.

M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2, 28–34 (1993).
[CrossRef]

Magnor, M.

Masuda, N.

Matsushima, K.

Miura, H.

Nakahara, S.

Nakayama, H.

Nishi, H.

K. Matsushima, H. Nishi, and S. Nakahara, “Simple wave-field rendering for photorealistic reconstruction in polygon-based high-definition computer holography,” J. Electron. Imaging 21, 023002 (2012).
[CrossRef]

H. Nishi, K. Matsushima, and S. Nakahara, “Rendering of specular surfaces in polygon-based computer-generated holograms,” Appl. Opt. 50, H245–H252 (2011).
[CrossRef]

Oikawa, M.

Okada, N.

Pan, Y.

Sakamoto, Y.

Sakata, H.

Schimmel, H.

Shimobaba, T.

Slinger, C.

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

Solanki, S.

Sonehara, T.

Stanley, M.

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

Tan, C.

Tanjung, R.

Trisnadi, J. I.

van Dam, A.

J. D. Foley, A. van Dam, S. K. Feiner, and J. F. Hughes, Computer Graphics: Principles and Practice, Second Edition in C (Addison-Wesley, 1996).

Wang, Y.

Watson, J.

Weng, J.

Wyrowski, F.

Xu, X.

Yamaguchi, K.

Zisserman, A.

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, 2nd ed. (Cambridge University, 2003).

Appl. Opt. (10)

K. Matsushima, “Computer-generated holograms for three-dimensional surface objects with shade and texture,” Appl. Opt. 44, 4607–4614 (2005).
[CrossRef]

K. Matsushima, “Formulation of the rotational transformation of wave fields and their application to digital holography,” Appl. Opt. 47, D110–D116 (2008).
[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. Nishi, K. Matsushima, and S. Nakahara, “Rendering of specular surfaces in polygon-based computer-generated holograms,” Appl. Opt. 50, H245–H252 (2011).
[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]

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]

H. Sakata and Y. Sakamoto, “Fast computation method for a Fresnel hologram using three-dimensional affine transformations in real space,” Appl. Opt. 48, H212–H221 (2009).
[CrossRef]

K. Hosoyachi, K. Yamaguchi, T. Ichikawa, and Y. Sakamoto, “Precalculation method using spherical basic object light for computer-generated hologram,” Appl. Opt. 52, A33–A44 (2013).
[CrossRef]

Y. Pan, Y. Wang, J. Liu, X. Li, and J. Jia, “Fast polygon-based method for calculating computer-generated holograms in three-dimensional display,” Appl. Opt. 52, A290–A299 (2013).
[CrossRef]

J. Amako, H. Miura, and T. Sonehara, “Speckle-noise reduction on kinoform reconstruction using a phase-only spatial light modulator,” Appl. Opt. 34, 3165–3171 (1995).
[CrossRef]

Computer (1)

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

J. Electron. Imaging (2)

M. Lucente, “Interactive computation of holograms using a look-up table,” J. Electron. Imaging 2, 28–34 (1993).
[CrossRef]

K. Matsushima, H. Nishi, and S. Nakahara, “Simple wave-field rendering for photorealistic reconstruction in polygon-based high-definition computer holography,” J. Electron. Imaging 21, 023002 (2012).
[CrossRef]

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

Opt. Express (2)

Opt. Lett. (1)

Other (3)

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

J. D. Foley, A. van Dam, S. K. Feiner, and J. F. Hughes, Computer Graphics: Principles and Practice, Second Edition in C (Addison-Wesley, 1996).

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, 2nd ed. (Cambridge University, 2003).

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Figures (6)

Fig. 1.
Fig. 1.

Local and the global coordinates of a tilted polygon.

Fig. 2.
Fig. 2.

Original, the new and the approximated new frequency domains. The square ABCD represents the original domain. The curved edge shape ABCD defines the new frequency domain. The shape EAFGCH is the effective domain. The parallelogram ABCD represents the approximated new frequency domain. The shape EAFGCH is the approximated effective domain.

Fig. 3.
Fig. 3.

Three geometric relationships between the approximated new and the original frequency domain. The gray area is the corresponding approximated effective domain. (a) One pair of the vertices of the parallelogram BD is outside the square. (b) The other pair of the vertices of the parallelogram AC is outside the square. (c) All the vertices of the parallelogram are inside the square.

Fig. 4.
Fig. 4.

Experimental setup: SF, spatial filter; CL, collimating lens; HWP, half-wave plate; SLM, spatial light modulator; FL, Fourier lens; HPF, high-pass filter; CCD, CCD camera.

Fig. 5.
Fig. 5.

Two sets of optical reconstruction results. (a) and (e) are results without the compensation method. (b) and (f) are results with the proposed compensation approach. (c), (g) and (d), (h) are two pairs of reconstruction results with the proposed brightness compensation method and the illumination by the parallel lights with light vectors equaling (2,1,1) and (2,1,1), respectively.

Fig. 6.
Fig. 6.

Optical reconstruction of the traditional polygon-based method with the proposed brightness compensation method and the texture approach.

Equations (32)

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

(x,y,z)=Tyxz×(x,y,z),
Tyxz=Ry×Rx×Rz=|a1a2a3a4a5a6a7a8a9|,
g(x,y,z)=f(a1x+a2y+a3z,a4x+a5y+a6z,a7x+a8y+a9z)=f(x,y,z=0).
f(x,y,z=0)=a(x,y)ψ(x,y),
F(μ,ν)=f(x,y,z=0)ej2π(μx+νy)dxdy,
G(μ,ν)=g(x,y,z)ei2π(μx+νy+ϖz)dxdy,
ϖ=(λ2μ2ν2)1/2.
μx+νy+ϖz=(a1μ+a2ν+a3ϖ)x+(a4μ+a5ν+a6ϖ)y+(a7μ+a8ν+a9ϖ)z.
G(u,v)=g(x,y,z)ej2π(μx+νy+ϖz)dxdy=J·f(x,y,z=0)ej2π[(a1μ+a2ν+a3ϖ)x+(a4μ+a5ν+a6ϖ)y+(a7μ+a8ν+a9ϖ)z]dxdy=J·f(x,y,z=0)ej2π(μx+νy+ϖz)dxdy=J·F(μ,ν),
(μ,ν,ϖ)=Tyxz×(μ,ν,ϖ).
J=|xxxyyxyy|=|a1a5a2a4|.
μ0=a3/λν0=a6/λ.
μ=a1μ+a2ν+a3ϖ(μ,ν)μ0ν=a4μ+a5ν+a6ϖ(μ,ν)ν0.
G(u,v)J·F(μ,ν),
L=d2ΦdAdΩcosθv=dIdAcosθv,
Φ=D1|h(x,y)|2dxdy=D2|H(μ,ν)|2dμdν=D2PSD(μ,ν)dμdν,
Φorig=P·Sorig,
Φnew=P·Seff,
G(μ,ν)=G(μ,ν)/C.
Φcomp=D2|G(μ,ν)/C|2dμdν=P·Seff/C2.
C=(Seff/Sorig)1/2.
Rx=[1000cosαsinα0sinαcosα],Ry=[cosβ0sinβ010sinβ0cosβ].
Tyx=[cosβsinαsinβcosαsinβ0cosαsinαsinβsinαcosβcosαcosβ].
μ=μcosβ+νsinαsinβ+a3ϖμ0ν=νcosα+a6ϖν0.
μ=μcosβ+νsinαsinβ+o(μ,ν)ν=νcosα+o(μ,ν),
μ^=μcosβ+νsinαsinβν^=νcosα.
C={cosα|(1+sinαsinβcosβ)24sinαsinβ)|cosαfor relation(a)cosα|(cosβ+sinαsinβ1)24sinαsinβ)|cosαfor relation(b)cosαcosβfor relation(c).
Rz=[cosγsinγ0sinγcosγ0001],
vpa=Tyx×Rz×vpa.
ϖ=1λ(1λ2μ2λ2ν2)=1λ+[λu2+λν22]+[(λu2+λν2)28]++1(n+1)!fn+1(0)(λu2+λν2)n+1.
μ=μcosβ+νsinαsinβcosαsinβλu2+λν22ν=νcosα+sinαλu2+λν22.
νBνBνB=cosα+λνBsinα1=(1+λ2νB2)1/2sin(ψ+α)1,

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