Abstract

This paper proposes a new computer generated hologram (CGH) method that considers the reflectance distribution on object surfaces and reflected images. The reflectance distributions are generated from phase differences determined by the shape of the object surface, which is constructed by using the Blinn and Torrance–Sparrow reflection models. Moreover, the reflected images are adapted when they are mapped onto metallic objects such as mirrors. Incorporating these two characteristics of reflection means that CGHs can express metallic objects realistically. Computer simulations and computational and optical reconstructed experiments were carried out. These results show the potential of the proposed method for showing metallic objects.

© 2009 Optical Society of America

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References

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    [CrossRef]
  15. R. L. Cook and K. E. Torrance, “A reflectance model for computer graphics,” ACM Trans. Graph. 1, 7-24 (1982).
    [CrossRef]

2009

2008

2005

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

Y. Sakamoto and A. Tsuruno, “A representation method for object surface glossiness in computer-generated hologram,” IEICE Trans. Information Syst. 2 J88-D-2, 2046-2053 (2005).

2003

2002

Y. Sakamoto and Y. Yamashita, “An algorithm for object-light calculation considering reflectance distribution for computer-generated holograms,” J. Inst. Image Information Television Engineers 56, 611-616 (2002) (in Japanese).
[CrossRef]

1991

1982

R. L. Cook and K. E. Torrance, “A reflectance model for computer graphics,” ACM Trans. Graph. 1, 7-24 (1982).
[CrossRef]

1977

J. F. Blinn, “Models of light reflection for computer synthesized pictures,” SIGGRAPH Comput. Graph. 11, 192-198(1977).
[CrossRef]

1975

B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311-317 (1975).
[CrossRef]

1967

1966

J. P. Waters, “Holographic image synthesis utilizing theoretical methods,” Appl. Phys. Lett. 9, 405-407 (1966).
[CrossRef]

Blinn, J. F.

J. F. Blinn, “Models of light reflection for computer synthesized pictures,” SIGGRAPH Comput. Graph. 11, 192-198(1977).
[CrossRef]

Bräuer, R.

Bryngdahl, O.

Cook, R. L.

R. L. Cook and K. E. Torrance, “A reflectance model for computer graphics,” ACM Trans. Graph. 1, 7-24 (1982).
[CrossRef]

Fujii, T.

Goodman, J. W.

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

Hahn, J.

Ichihashi, Y.

Ito, T.

Kang, H.

Kim, E.-S.

Kim, H.

Kim, S.-C.

Lee, B.

Masuda, N.

Matsushima, K.

Nakayama, H.

Phong, B. T.

B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311-317 (1975).
[CrossRef]

Sakamoto, Y.

Y. Sakamoto and A. Tsuruno, “A representation method for object surface glossiness in computer-generated hologram,” IEICE Trans. Information Syst. 2 J88-D-2, 2046-2053 (2005).

Y. Sakamoto and Y. Yamashita, “An algorithm for object-light calculation considering reflectance distribution for computer-generated holograms,” J. Inst. Image Information Television Engineers 56, 611-616 (2002) (in Japanese).
[CrossRef]

Schimmel, H.

Shimobaba, T.

Shiraki, A.

Sparrow, E. M.

Sugie, T.

Torrance, K. E.

R. L. Cook and K. E. Torrance, “A reflectance model for computer graphics,” ACM Trans. Graph. 1, 7-24 (1982).
[CrossRef]

K. E. Torrance and E. M. Sparrow, “Theory for off-specular reflection from roughened surfaces,” J. Opt. Soc. Am. 57, 1105-1112 (1967).
[CrossRef]

Tsuruno, A.

Y. Sakamoto and A. Tsuruno, “A representation method for object surface glossiness in computer-generated hologram,” IEICE Trans. Information Syst. 2 J88-D-2, 2046-2053 (2005).

Waters, J. P.

J. P. Waters, “Holographic image synthesis utilizing theoretical methods,” Appl. Phys. Lett. 9, 405-407 (1966).
[CrossRef]

Wyrowski, F.

Yamaguchi, T.

Yamashita, Y.

Y. Sakamoto and Y. Yamashita, “An algorithm for object-light calculation considering reflectance distribution for computer-generated holograms,” J. Inst. Image Information Television Engineers 56, 611-616 (2002) (in Japanese).
[CrossRef]

Yoshikawa, H.

ACM Trans. Graph.

R. L. Cook and K. E. Torrance, “A reflectance model for computer graphics,” ACM Trans. Graph. 1, 7-24 (1982).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

J. P. Waters, “Holographic image synthesis utilizing theoretical methods,” Appl. Phys. Lett. 9, 405-407 (1966).
[CrossRef]

Commun. ACM

B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311-317 (1975).
[CrossRef]

J. Inst. Image Information Television Engineers

Y. Sakamoto and Y. Yamashita, “An algorithm for object-light calculation considering reflectance distribution for computer-generated holograms,” J. Inst. Image Information Television Engineers 56, 611-616 (2002) (in Japanese).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Express

SIGGRAPH Comput. Graph.

J. F. Blinn, “Models of light reflection for computer synthesized pictures,” SIGGRAPH Comput. Graph. 11, 192-198(1977).
[CrossRef]

Other

Y. Sakamoto and A. Tsuruno, “A representation method for object surface glossiness in computer-generated hologram,” IEICE Trans. Information Syst. 2 J88-D-2, 2046-2053 (2005).

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

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Figures (13)

Fig. 1
Fig. 1

Basic coordinate system.

Fig. 2
Fig. 2

Reflections on the object surface: (a) specular reflection and (b) diffuse reflection.

Fig. 3
Fig. 3

Reflection (a) on the object surface and (b) on the microfacet.

Fig. 4
Fig. 4

Gaussian distribution function.

Fig. 5
Fig. 5

Reflection on the mirror. The virtual image is located at a symmetric position with respect to the original image in the mirror.

Fig. 6
Fig. 6

Setup of computer simulations.

Fig. 7
Fig. 7

Intensity distributions for different values of m: (a)  m = 0.0100 , (b)  m = 0.0075 , (c)  m = 0.0050 , (d)  m = 0.0025 .

Fig. 8
Fig. 8

Setup of computational and optical reconstructed experiments.

Fig. 9
Fig. 9

Optical reconstruction system.

Fig. 10
Fig. 10

Block diagram of the calculation used in computational and optical reconstructed experiments.

Fig. 11
Fig. 11

Amplitude and phase distribution images: (a) amplitude image, (b) phase image with the random phase method, (c) phase image with m = 0.1000 , (d) phase image with m = 0.0001 .

Fig. 12
Fig. 12

Computational reconstructed images with (a)  the random phase method, (b) no phase differences, (c)  m = 0.1000 , (d)  m = 0.0100 , (e)  m = 0.0010 , (f)  m = 0.0001 .

Fig. 13
Fig. 13

Optical reconstructed images with (a)  the random phase method, (b) no phase differences, (c)  m = 0.1000 , (d)  m = 0.0100 , (e)  m = 0.0010 , (f)  m = 0.0001 .

Tables (2)

Tables Icon

Table 1 Parameters of Computer Simulations

Tables Icon

Table 2 Parameters of Optical Reconstructed Experiments

Equations (14)

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g I ( ξ , η ) = A ( ξ , η ) ,
g R ( ξ , η ) = g I ( ξ , η ) exp [ j ϕ ( ξ , η ) ] ,
g R ( ξ , η ) = g I ( ξ , η ) s ( ξ , η ) ,
u ( x , y ) = g ^ R ( ξ , η ) h ( ξ , η ) ,
D ( θ ) = exp [ - ( θ / m ) 2 ] ,
g R ( ξ , η ) = g I ( ξ , η ) exp [ - j 2 ϕ M ( ξ , η ) ] ,
ϕ M ( k ) ( ξ ) = ϕ M ( k ) ( ξ k 0 ) + 2 π λ ( ξ - ξ k 0 ) tan θ ξ ( k ) ,
ϕ M ( ξ ) = k M ξ ϕ M ( k ) ( ξ ) ,
ϕ M ( k ) ( ξ ) = { ϕ M ( k ) ( ξ k 0 ) + 2 π λ ( ξ - ξ k 0 ) tan θ ξ ( k ) ξ k 0 ξ < ξ ( k + 1 ) 0 0 otherwise .
G V ( f x , f y ) = G V ( f x , f y ) exp [ - j 2 π ( - Δ z ) f z ] ,
U V ( f x , f y ) = G V ( f x , f y ) exp [ - j 2 π z 0 f z ] ,
= G V ( f x , f y ) exp [ - j 2 π ( z 0 - Δ z ) f z ] ,
0.0 °
1.0 °

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