Abstract

A realistic rendering technique is presented for creating large-scale computer-generated holograms. The technique is based on the polygon-based method, but allows specular curved surfaces to be reconstructed without increasing the number of polygons. In this technique, specular flat surfaces are transformed into curved surfaces. This is achieved by controlling the direction of reflected light, using fragmentary plane waves. An actual large-scale computer-generated hologram is created, and is used to verify the validity and practicality of the technique.

© 2017 Optical Society of America

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References

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  1. T. Yatagai, “Stereoscopic approach to 3-D display using computer-generated holograms,” Appl. Opt. 15, 2722–2729 (1976).
    [Crossref]
  2. H. Kang, T. Fujii, T. Yamaguchi, and H. Yoshikawa, “Compensated phase-added stereogram for real-time holographic display,” Opt. Eng. 46, 095802 (2007).
    [Crossref]
  3. K. Wakunami and M. Yamaguchi, “Calculation for computer generated hologram using ray-sampling plane,” Opt. Express 19, 9086–9101 (2011).
    [Crossref]
  4. J. P. Waters, “Holographic image synthesis utilizing theoretical methods,” Appl. Phys. Lett. 9, 405–407 (1966).
    [Crossref]
  5. A. D. Stein, Z. Wang, and J. J. S. Leigh, “Computer-generated holograms: a simplified ray-tracing approach,” Comput. Phys. 6, 389–392 (1992).
    [Crossref]
  6. M.-W. Kwon, S.-C. Kim, S.-E. Yoon, Y.-S. Ho, and E.-S. Kim, “Object tracking mask-based NLUT on GPUs for real-time generation of holographic videos of three-dimensional scenes,” Opt. Express 23, 2101–2120 (2015).
    [Crossref]
  7. T. Nishitsuji, T. Shimobaba, T. Kakue, and T. Ito, “Fast calculation of computer-generated hologram using run-length encoding based recurrence relation,” Opt. Express 23, 9852–9857 (2015).
    [Crossref]
  8. T. Nishitsuji, T. Shimobaba, T. Kakue, and T. Ito, “Simple and fast cosine approximation method for computer-generated hologram calculation,” Opt. Express 23, 32465–32470 (2015).
    [Crossref]
  9. T. Shimobaba, H. Nakayama, N. Masuda, and T. Ito, “Rapid calculation of Fresnel computer-generated-hologram using look-up table and wavefront-recording plane methods for three-dimensional display,” Opt. Express 18, 19504–19509 (2010).
    [Crossref]
  10. A. Symeonidou, D. Blinder, A. Munteanu, and P. Schelkens, “Computer-generated hologram by multiple wavefront recording plane method with occlusion culling,” Opt. Express 23, 22149–22161 (2015).
    [Crossref]
  11. T. Kurihara and Y. Takaki, “Shading of a computer-generated hologram by zone plate modulation,” Opt. Express 20, 3529–3540 (2012).
    [Crossref]
  12. T. Ichikawa, K. Yamaguchi, and Y. Sakamoto, “Realistic expression for full-parallax computer-generated holograms with the ray-tracing method,” Appl. Opt. 52, A201–A209 (2013).
    [Crossref]
  13. K. Matsushima, “Computer-generated holograms for three dimensional surface objects with shade and texture,” Appl. Opt. 44, 4607–4614 (2005).
    [Crossref]
  14. 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]
  15. 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]
  16. 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]
  17. Y.-Z. Liu, J.-W. Dong, Y.-Y. Pu, B.-C. Chen, H.-X. He, and H.-Z. Wang, “High-speed full analytical holographic computations for true-life scenes,” Opt. Express 18, 3345–3351 (2010).
    [Crossref]
  18. K. Yamaguchi, T. Ichikawa, and Y. Sakamoto, “Calculation method for computer-generated holograms considering various reflectance distributions based on microfacets with various surface roughnesses,” Appl. Opt. 50, H195–H202 (2011).
    [Crossref]
  19. T. Ichikawa, Y. Sakamoto, A. Subagyo, and K. Sueoka, “Calculation method of reflectance distributions for computer-generated holograms using the finite-difference time-domain method,” Appl. Opt. 50, H211–H219 (2011).
    [Crossref]
  20. N. Nishi, K. Matsushima, and S. Nakahara, “Rendering of specular surfaces in polygon-based computer-generated holograms,” Appl. Opt. 50, H245–H252 (2011).
    [Crossref]
  21. 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]
  22. H. Nishi, K. Matsushima, and S. Nakahara, “A novel method for rendering specular and smooth surfaces in polygon-based high-definition CGH,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (Optical Society of America, 2011), paper DWC29.
  23. H. Nishi, K. Matsushima, and S. Nakahara, “Smooth shading of specular surfaces in polygon-based high-definition CGH,” in Proceedings of 2011 3DTV Conference: The True Vision—Capture, Transmission and Display of 3D Video (3DTV-CON) (2011), pp. 1–4.
  24. H. Nishi, K. Matsushima, and S. Nakahara, “Advanced rendering techniques for producing specular smooth surfaces in polygon-based high-definition computer holography,” Proc. SPIE 8281, 828110 (2012).
    [Crossref]
  25. K. Matsushima, M. Nakamura, and S. Nakahara, “Silhouette method for hidden surface removal in computer holography and its acceleration using the switch-back technique,” Opt. Express 22, 24450–24465 (2014).
    [Crossref]
  26. Y. Tsuchiyama and K. Matsushima, “Full-color large-scaled computer-generated holograms using RGB color filters,” Opt. Express 25, 2016–2030 (2017).
    [Crossref]
  27. B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311–317 (1975).
    [Crossref]

2017 (1)

2015 (4)

2014 (1)

2013 (1)

2012 (3)

T. Kurihara and Y. Takaki, “Shading of a computer-generated hologram by zone plate modulation,” Opt. Express 20, 3529–3540 (2012).
[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]

H. Nishi, K. Matsushima, and S. Nakahara, “Advanced rendering techniques for producing specular smooth surfaces in polygon-based high-definition computer holography,” Proc. SPIE 8281, 828110 (2012).
[Crossref]

2011 (4)

2010 (2)

2009 (1)

2008 (2)

2007 (1)

H. Kang, T. Fujii, T. Yamaguchi, and H. Yoshikawa, “Compensated phase-added stereogram for real-time holographic display,” Opt. Eng. 46, 095802 (2007).
[Crossref]

2005 (1)

1992 (1)

A. D. Stein, Z. Wang, and J. J. S. Leigh, “Computer-generated holograms: a simplified ray-tracing approach,” Comput. Phys. 6, 389–392 (1992).
[Crossref]

1976 (1)

1975 (1)

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

1966 (1)

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

Ahrenberg, L.

Benzie, P.

Blinder, D.

Chen, B.-C.

Dong, J.-W.

Fujii, T.

H. Kang, T. Fujii, T. Yamaguchi, and H. Yoshikawa, “Compensated phase-added stereogram for real-time holographic display,” Opt. Eng. 46, 095802 (2007).
[Crossref]

Hahn, J.

He, H.-X.

Ho, Y.-S.

Ichikawa, T.

Ito, T.

Kakue, T.

Kang, H.

H. Kang, T. Fujii, T. Yamaguchi, and H. Yoshikawa, “Compensated phase-added stereogram for real-time holographic display,” Opt. Eng. 46, 095802 (2007).
[Crossref]

Kim, E.-S.

Kim, H.

Kim, S.-C.

Kurihara, T.

Kwon, M.-W.

Lee, B.

Leigh, J. J. S.

A. D. Stein, Z. Wang, and J. J. S. Leigh, “Computer-generated holograms: a simplified ray-tracing approach,” Comput. Phys. 6, 389–392 (1992).
[Crossref]

Liu, Y.-Z.

Magnor, M.

Masuda, N.

Matsushima, K.

Y. Tsuchiyama and K. Matsushima, “Full-color large-scaled computer-generated holograms using RGB color filters,” Opt. Express 25, 2016–2030 (2017).
[Crossref]

K. Matsushima, M. Nakamura, and S. Nakahara, “Silhouette method for hidden surface removal in computer holography and its acceleration using the switch-back technique,” Opt. Express 22, 24450–24465 (2014).
[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]

H. Nishi, K. Matsushima, and S. Nakahara, “Advanced rendering techniques for producing specular smooth surfaces in polygon-based high-definition computer holography,” Proc. SPIE 8281, 828110 (2012).
[Crossref]

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

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

H. Nishi, K. Matsushima, and S. Nakahara, “Smooth shading of specular surfaces in polygon-based high-definition CGH,” in Proceedings of 2011 3DTV Conference: The True Vision—Capture, Transmission and Display of 3D Video (3DTV-CON) (2011), pp. 1–4.

H. Nishi, K. Matsushima, and S. Nakahara, “A novel method for rendering specular and smooth surfaces in polygon-based high-definition CGH,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (Optical Society of America, 2011), paper DWC29.

Munteanu, A.

Nakahara, S.

K. Matsushima, M. Nakamura, and S. Nakahara, “Silhouette method for hidden surface removal in computer holography and its acceleration using the switch-back technique,” Opt. Express 22, 24450–24465 (2014).
[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]

H. Nishi, K. Matsushima, and S. Nakahara, “Advanced rendering techniques for producing specular smooth surfaces in polygon-based high-definition computer holography,” Proc. SPIE 8281, 828110 (2012).
[Crossref]

N. Nishi, K. Matsushima, and S. Nakahara, “Rendering of specular surfaces in polygon-based computer-generated holograms,” Appl. Opt. 50, H245–H252 (2011).
[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, “Smooth shading of specular surfaces in polygon-based high-definition CGH,” in Proceedings of 2011 3DTV Conference: The True Vision—Capture, Transmission and Display of 3D Video (3DTV-CON) (2011), pp. 1–4.

H. Nishi, K. Matsushima, and S. Nakahara, “A novel method for rendering specular and smooth surfaces in polygon-based high-definition CGH,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (Optical Society of America, 2011), paper DWC29.

Nakamura, M.

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, “Advanced rendering techniques for producing specular smooth surfaces in polygon-based high-definition computer holography,” Proc. SPIE 8281, 828110 (2012).
[Crossref]

H. Nishi, K. Matsushima, and S. Nakahara, “Smooth shading of specular surfaces in polygon-based high-definition CGH,” in Proceedings of 2011 3DTV Conference: The True Vision—Capture, Transmission and Display of 3D Video (3DTV-CON) (2011), pp. 1–4.

H. Nishi, K. Matsushima, and S. Nakahara, “A novel method for rendering specular and smooth surfaces in polygon-based high-definition CGH,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (Optical Society of America, 2011), paper DWC29.

Nishi, N.

Nishitsuji, T.

Phong, B. T.

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

Pu, Y.-Y.

Sakamoto, Y.

Schelkens, P.

Shimobaba, T.

Stein, A. D.

A. D. Stein, Z. Wang, and J. J. S. Leigh, “Computer-generated holograms: a simplified ray-tracing approach,” Comput. Phys. 6, 389–392 (1992).
[Crossref]

Subagyo, A.

Sueoka, K.

Symeonidou, A.

Takaki, Y.

Tsuchiyama, Y.

Wakunami, K.

Wang, H.-Z.

Wang, Z.

A. D. Stein, Z. Wang, and J. J. S. Leigh, “Computer-generated holograms: a simplified ray-tracing approach,” Comput. Phys. 6, 389–392 (1992).
[Crossref]

Waters, J. P.

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

Watson, J.

Yamaguchi, K.

Yamaguchi, M.

Yamaguchi, T.

H. Kang, T. Fujii, T. Yamaguchi, and H. Yoshikawa, “Compensated phase-added stereogram for real-time holographic display,” Opt. Eng. 46, 095802 (2007).
[Crossref]

Yatagai, T.

Yoon, S.-E.

Yoshikawa, H.

H. Kang, T. Fujii, T. Yamaguchi, and H. Yoshikawa, “Compensated phase-added stereogram for real-time holographic display,” Opt. Eng. 46, 095802 (2007).
[Crossref]

Appl. Opt. (9)

T. Ichikawa, K. Yamaguchi, and Y. Sakamoto, “Realistic expression for full-parallax computer-generated holograms with the ray-tracing method,” Appl. Opt. 52, A201–A209 (2013).
[Crossref]

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

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]

K. Yamaguchi, T. Ichikawa, and Y. Sakamoto, “Calculation method for computer-generated holograms considering various reflectance distributions based on microfacets with various surface roughnesses,” Appl. Opt. 50, H195–H202 (2011).
[Crossref]

T. Ichikawa, Y. Sakamoto, A. Subagyo, and K. Sueoka, “Calculation method of reflectance distributions for computer-generated holograms using the finite-difference time-domain method,” Appl. Opt. 50, H211–H219 (2011).
[Crossref]

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

T. Yatagai, “Stereoscopic approach to 3-D display using computer-generated holograms,” Appl. Opt. 15, 2722–2729 (1976).
[Crossref]

Appl. Phys. Lett. (1)

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

Commun. ACM (1)

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

Comput. Phys. (1)

A. D. Stein, Z. Wang, and J. J. S. Leigh, “Computer-generated holograms: a simplified ray-tracing approach,” Comput. Phys. 6, 389–392 (1992).
[Crossref]

J. Electron. Imaging (1)

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]

Opt. Eng. (1)

H. Kang, T. Fujii, T. Yamaguchi, and H. Yoshikawa, “Compensated phase-added stereogram for real-time holographic display,” Opt. Eng. 46, 095802 (2007).
[Crossref]

Opt. Express (10)

K. Wakunami and M. Yamaguchi, “Calculation for computer generated hologram using ray-sampling plane,” Opt. Express 19, 9086–9101 (2011).
[Crossref]

K. Matsushima, M. Nakamura, and S. Nakahara, “Silhouette method for hidden surface removal in computer holography and its acceleration using the switch-back technique,” Opt. Express 22, 24450–24465 (2014).
[Crossref]

Y. Tsuchiyama and K. Matsushima, “Full-color large-scaled computer-generated holograms using RGB color filters,” Opt. Express 25, 2016–2030 (2017).
[Crossref]

Y.-Z. Liu, J.-W. Dong, Y.-Y. Pu, B.-C. Chen, H.-X. He, and H.-Z. Wang, “High-speed full analytical holographic computations for true-life scenes,” Opt. Express 18, 3345–3351 (2010).
[Crossref]

M.-W. Kwon, S.-C. Kim, S.-E. Yoon, Y.-S. Ho, and E.-S. Kim, “Object tracking mask-based NLUT on GPUs for real-time generation of holographic videos of three-dimensional scenes,” Opt. Express 23, 2101–2120 (2015).
[Crossref]

T. Nishitsuji, T. Shimobaba, T. Kakue, and T. Ito, “Fast calculation of computer-generated hologram using run-length encoding based recurrence relation,” Opt. Express 23, 9852–9857 (2015).
[Crossref]

T. Nishitsuji, T. Shimobaba, T. Kakue, and T. Ito, “Simple and fast cosine approximation method for computer-generated hologram calculation,” Opt. Express 23, 32465–32470 (2015).
[Crossref]

T. Shimobaba, H. Nakayama, N. Masuda, and T. Ito, “Rapid calculation of Fresnel computer-generated-hologram using look-up table and wavefront-recording plane methods for three-dimensional display,” Opt. Express 18, 19504–19509 (2010).
[Crossref]

A. Symeonidou, D. Blinder, A. Munteanu, and P. Schelkens, “Computer-generated hologram by multiple wavefront recording plane method with occlusion culling,” Opt. Express 23, 22149–22161 (2015).
[Crossref]

T. Kurihara and Y. Takaki, “Shading of a computer-generated hologram by zone plate modulation,” Opt. Express 20, 3529–3540 (2012).
[Crossref]

Proc. SPIE (1)

H. Nishi, K. Matsushima, and S. Nakahara, “Advanced rendering techniques for producing specular smooth surfaces in polygon-based high-definition computer holography,” Proc. SPIE 8281, 828110 (2012).
[Crossref]

Other (2)

H. Nishi, K. Matsushima, and S. Nakahara, “A novel method for rendering specular and smooth surfaces in polygon-based high-definition CGH,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (Optical Society of America, 2011), paper DWC29.

H. Nishi, K. Matsushima, and S. Nakahara, “Smooth shading of specular surfaces in polygon-based high-definition CGH,” in Proceedings of 2011 3DTV Conference: The True Vision—Capture, Transmission and Display of 3D Video (3DTV-CON) (2011), pp. 1–4.

Supplementary Material (2)

NameDescription
» Visualization 1: MP4 (1723 KB)      Video of optical reconstruction using a laser.
» Visualization 2: MP4 (10935 KB)      Video of optical reconstruction by a LED.

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Figures (13)

Fig. 1.
Fig. 1.

Three coordinate systems used in the polygon-based method.

Fig. 2.
Fig. 2.

Diffuse reflection in a (a) broadband field, and in narrowband fields, (b) without, and (c) with spectrum remapping.

Fig. 3.
Fig. 3.

Schematic illustration of the Phong reflection model.

Fig. 4.
Fig. 4.

Schematic illustration of the spectral envelopes of the diffuse and specular reflections. θ is the angle of regular reflection shown in Fig. 3 and λ is a wavelength.

Fig. 5.
Fig. 5.

Reflection from (a) planar polygons and (b) a curved surface.

Fig. 6.
Fig. 6.

Schematic illustrations of (a) normal vectors of a curved surface, (b) interpolated normal vectors in the Phong shading technique, and (c) field emission in the technique proposed in the current study.

Fig. 7.
Fig. 7.

Example of fragmentary plane waves. Each fragment corresponds to a segment of the specular surface function.

Fig. 8.
Fig. 8.

Procedure for rendering a specular curved polygon. (a) Specular surface function for flat shading, (b) diffuse surface function, (c) fragmentary plane waves, and (d) spectrum of the surface function for the specular curved surface.

Fig. 9.
Fig. 9.

Simulated reconstruction of object fields calculated using different segment sizes.

Fig. 10.
Fig. 10.

Three-dimensional scene of The Metal Venus II.

Fig. 11.
Fig. 11.

Measured computation time of The Metal Venus I [20] and The Metal Venus II (this work).

Fig. 12.
Fig. 12.

Optical reconstruction of (a) The Metal Venus I having specular flat surfaces [20] and (b) The Metal Venus II created using the proposed method (see Visualization 1). A He–Ne laser is used for the illumination light source.

Fig. 13.
Fig. 13.

Optical reconstruction of The Venus II by an ordinary red LED. The pictures are taken from different angles (see Visualization 2).

Tables (1)

Tables Icon

Table 1. Parameters Used for Creating The Metal Venus II

Equations (23)

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

r = T r ^ ,
T = [ a 1 a 2 a 3 a 4 a 5 a 6 a 7 a 8 a 9 ] ,
H ( u , v ) = F { h ( x , y ) } ,
H ( u , v ) = H ( u P x λ , v P y λ ) ,
P = T z ^ ,
P = [ a 3 a 6 a 9 ] T .
[ u v w ] T = T [ u ^ v ^ w ^ ] T ,
H ^ ( u ^ , v ^ ) = H ( a 1 u ^ + a 2 v ^ + a 3 w ^ , a 4 u ^ + a 5 v ^ + a 6 w ^ ) .
h ( x ^ , y ^ ) = F 1 { H ^ ( u ^ , v ^ ) } .
I Phong ( V ; L , N ) = K a + K d ( L · N ) + K s ( R · V ) α ,
R = L 2 ( L · N ) N | L 2 ( L · N ) N | .
L = T L ^ , V = T V ^ , and R = T R ^ .
h Phong ( x , y ; L , N ) = K a h d ( x , y ) + K d ( L · N ) h d ( x , y ) + K s h s ( x , y ; R ) .
h d ( x , y ) = a d ( x , y ) exp [ i φ d ( x , y ) ] ,
h s ( x , y ; R ) = a s ( x , y ) exp [ i φ s ( x , y ; R ) ] ,
H Phong ( u , v ; L , N ) = [ K a + K d ( L · N ) ] H d ( u , v ) + K s H s ( u , v ; R ) ,
H s ( u , v ; R ) = H 2 ( u , v ; R ) .
H s ( u , v ; R ) = H 2 ( u + P x λ , v + P y λ ; R ) .
g m ( x , y ; R m ) = Rect m ( x , y ) W ( R m ) exp [ i k R m · r ] ,
Rect m ( x , y ) = { 1 inside sement    m 0 otherwise .
W m ( R m ) = { 1 ( T 1 R m ) · z ^ 0 0 otherwise ,
h s ( x , y ; R ) = F 1 { H s ( u , v ; R ) } .
h s ( x , y ; R ) = h s ( x , y ; N ) m g m ( x , y ; R m ) .

Metrics