- Email: [email protected]
Lighting effects rendering in three-dimensional computer-generated holographic display
Optics Communications 370 (2016) 192–197
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Lighting effects rendering in three-dimensional computer-generated holographic display Hao Zhang n, Liangcai Cao, Guofan Jin State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instruments, Tsinghua University, Beijing 100084, China
art ic l e i nf o
a b s t r a c t
Article history: Received 17 December 2015 Received in revised form 3 March 2016 Accepted 4 March 2016
We present a technique for generating three-dimensional (3-D) computer-generated holograms (CGHs) with realistic lighting effects based on a phase-only spatial light modulator (SLM). Phong reflection model is employed in the calculation of reflectance distribution for CGH synthesizing. Directional pointbased algorithm produces realistic lighting effects of the 3-D scenes in processing the ambient, diffuse and specular reflections. A phase-only SLM is used to perform the optical experiments, and the results show that the proposed technique can perform quality reconstructions of the 3-D scenes with high optical efficiency and efficient utilization of the system space-bandwidth product. & 2016 Elsevier B.V. All rights reserved.
Keywords: Holography Computer holography Holographic display
1. Introduction Holographic display can reconstruct the whole optical wavefront of the 3-D scene and hence has the potential to provide all the depth cues that human eyes can perceive [1]. With the developments of computer technology and spatial light modulators (SLMs), computer-generated holograms (CGHs) of various 3-D images can be displayed dynamically without the complicated interference recording systems [2–5]. Both existing and synthetic 3-D scenes can be encoded into the CGHs as long as their mathematical descriptions are provided. The algorithms for generating the CGHs are directly related with the image qualities of the reconstructed 3-D scenes. Computer graphics rendering techniques can convert 3-D scenes into photorealistic two-dimensional (2-D) images, which have been used in the CGH algorithms to enhance fidelities of the reconstructed 3-D images [6–9]. Holographic stereograms can provide occlusion effects easily with the help of multi-viewpoint rendering process [6,7]. Physically based algorithms can generate CGHs with accurate geometric information by extracting coordinate information through the depth buffer [8,9]. In computer graphics, shading refers to the process of calculating the brightness of an object in the 3-D scene based on the relative positions between the light, object, and the viewer. It can depict the illumination and depth perception of the 3-D scene, which can benefit the visual effect of the rendered 2-D image. Shading process of n
Corresponding author. E-mail address: [email protected] (H. Zhang).
http://dx.doi.org/10.1016/j.optcom.2016.03.013 0030-4018/& 2016 Elsevier B.V. All rights reserved.
computer graphics could be integrated with CGH calculation to produce realistic lighting effects for the improvements of the reconstruction quality of the 3-D CGH. Lighting effects rendering in CGH calculation is crucial to the depth performance during optical reconstruction. Various algorithms have been proposed for simulating the wave reflection and propagation processes to render different lighting effects [10–15]. Spatial spectrum of the polygon-based algorithm was modified based on the Phong reflection model to imitate the specular reflection [10]. Zone plate based Phong reflection model was used to generate CGHs with characteristics of reflection [11,12]. Computer graphics rendering techniques were also used in the holographic stereogram computation to add lighting effects [13,14]. Recently, ray tracing method was introduced into the CGH calculation to simulate characteristic reflection effects [15]. However, the previous methods for generating CGHs are based on the amplitude modulation of the reconstruction wavefront, which would affect the optical efficiency and utilization rate of the system spacebandwidth product. Hence accurate and efficient lighting effects processing in CGH synthesizing needs to be further investigated. In this study, directional point-based algorithm is used for generating phase CGHs with multiple lighting effects. The wavefront distribution of each object point is calculated directly according to the Phong reflection model with anti-aliasing technique. The proposed technique is more efficient in its utilization of the space-bandwidth product compared to the zone plate method since no conjugate image is reconstructed. A phase-only SLM is used to perform the optical reconstructions of the 3-D scenes, which can reconstruct quality 3-D images with realistic lighting effects and high optical efficiency.
H. Zhang et al. / Optics Communications 370 (2016) 192–197
2. Phong reflection model Phong reflection model is an empirical model for local illumination, which is widely used in 3-D computer graphics. During calculation, four unit vectors are used to compute the light intensity at an arbitrary point, as shown in Fig. 1(a). The light vector L denotes the direction vector from the point on the surface toward the light source. The normal vector N is perpendicular to the surface at the given point. The reflection vector R indicates the direction that a perfectly reflected ray of light would take from the point on the surface. According to the law of reflection, the angle of incidence equals the angle of reflection. The view vector V indicates the direction pointing towards the position of viewer or virtual camera. Phong reflection model uses ambient, diffuse and specular components to characterize the lighting effects of an object surface. The ambient reflection term is presented in the entire 3-D scene, where all of the objects are brightened with a specified light intensity:
Ia = k a I,
(1)
where ka is the ambient reflection constant, and I denotes the illumination light intensity. The diffuse reflection is the reflection of the light from a surface such that an incident ray is reflected at many angles. An illuminated ideal diffuse reflecting surface will have equal luminance from all directions. According to the Lambert’s cosine law, the diffuse reflection light intensity of the Phong reflection model is given by
Id = k d (L⋅N ) I,
(2)
193
where kd is the diffuse reflection constant, and ∙ denotes the dot product. The intensity of the diffuse reflection light depends on the angle of incidence, and has no relationship with the view vector. Hence the intensity of the diffuse reflection light would have the same value when viewed from any angle. The specular reflection is the bright spot of light that appears on shiny objects when illuminated, which can provide a strong visual cue for the shape of an object and its location with respect to the light source. The intensity of the specular reflection light depends on the angle between the reflection vector R and the view vector V:
Is = ks (R⋅V )α I,
(3)
where ks is the specular reflection constant, and α is a shininess constant of the surface. Specular reflection component has anisotropic distribution along different viewing directions, as shown in Fig. 1(b). ϕ denotes the angle between view vector and reflection vector. The specular reflection achieves its peak when ϕ is zero. As the shininess constant α increases, the specular spot becomes smaller, which would lead a smoother object surface. We can deduce the equation of Phong reflection model by combining the three reflection components:
Ip = Ia + Id + Is = ⎡⎣ k a + k d (L⋅N ) + ks (R⋅V )α ⎤⎦ I.
(4)
Fig. 2(a) schematically illustrates the ambient, diffuse and specular reflection components when the surface is illuminated by the light source. The ambient and diffuse reflection components have isotropic distributions over all viewing directions, while the specular lobe has the highest value along the reflection vector R. Fig. 2(b) is the visual illustration of the Phong reflection model. Photorealistic lighting effects can be rendered by combining ambient, diffuse and specular reflection components.
3. CGH generation with Phong reflection model In computer graphics, the Phong reflection model sets one viewpoint for each image during rendering process. Hence only one view vector is bundled with a specific object point. While for CGH computation, each hologram sample corresponds with one viewpoint, and multiple view vectors need to be considered in calculating a single object point. Fig. 3 illustrates the difference of the viewing parameters between computer graphics and CGH computation. A viewpoint array is formed in the hologram plane to fetch lighting information from the corresponding viewing directions. In conventional point-based method, the complex amplitude distribution on the hologram plane can be calculated by superposing the optical wavefronts of all the point sources [16,17]: n
H (x, y) =
∑ j=1
Aj exp ⎡⎣ i kr j + ϕj ⎤⎦, rj
(
)
(5)
where n is the number of object points, Aj is the amplitude of the jth point, k ¼2π/λ is the wave number in free space, and ϕj is the initial phase. The distance between the jth object point and the sampling point (x, y, 0) on the hologram plane is given by
rj =
Fig. 1. (a) Vectors in Phong reflection model. (b) Specular reflections with different shininess constants.
(
( x − xj )2 + y − yj
2
)
+ z j2 .
(6)
With the proper choice of random initial phase, we may assume a uniform amplitude distribution in the hologram plane, and thus we could achieve quality reconstruction with the pure phase information [18,19]. Ambient and diffuse reflections can be reconstructed using Eq. (5) since the wave amplitude Aj of the jth point is uniformly distributed on the hologram plane, since these two reflection
194
H. Zhang et al. / Optics Communications 370 (2016) 192–197
Fig. 2. (a) Ambient, diffuse and specular components in Phong reflection model. (b) Visual illustration of Phong equation.
Fig. 3. (a) Viewing frustum in computer graphics. (b) Diagram in CGH computation.
components have no relationship with the view vectors. While for specular reflection, the uniform distribution of Aj on the hologram plane is not valid due to its anisotropic property. We need to calculate Aj for each hologram sample independently, since different hologram samples correspond with different viewpoints and view vectors, as shown in Fig. 3(b). In order to calculate all the
Fig. 4. Contributed area of one object point on the hologram plane: (a) overall view, (b) top view.
reflection components of Phong reflection model, the amplitude in Eq. (5) should be directionally modulated:
Aj (x, y) =
⎡⎣ k a + k d (L⋅N ) + ks (R⋅V )α ⎤⎦ I ,
(7)
H. Zhang et al. / Optics Communications 370 (2016) 192–197
195
where rb is linear with the wave propagation distance:
rb = zj tan β,
(11)
The aliasing boundaries are then compared with the SLM boundaries and the inner ones are chosen to determine the contribution area for each object point. By using directional point-based algorithm with anti-aliasing technique, photorealistic lighting effects can be reconstructed for a 3-D object with an arbitrary position. And the algorithm is applicable to the SLM with different pixelated parameters. Fig. 5. Optical setup of the holographic display system.
where L, N, R and V are the corresponding vectors of the jth object point. Hence Eq. (5) becomes n
H (x, y) =
∑ j=1
Aj (x, y) exp ⎡⎣ i kr j + ϕj ⎤⎦. rj
(
)
(8)
Ambient, diffuse and specular reflection components can be reconstructed with the help of the directionally modulated wave amplitude for each object point. Thus Phong reflection model can be integrated with the CGH generation to provide multiple lighting effects. During calculation, the sampling parameters of CGH should be set according to the pixelated structure of SLM. Since the spatial resolution of the SLM is limited, it is necessary to prevent aliasing error in CGH calculation, especially for the object points which are close to the hologram plane. The maximum diffraction angle of the SLM is given by
sin β = fmax λ =
1 λ, 2d
(9)
where fmax is the highest spatial frequency that SLM can display, and d is the pixel pitch of the SLM. Hence the contribution area on the hologram plane for each object point needs to be restricted due to this angular limitation, as shown in Fig. 4. The aliasing boundaries for each object point can be calculated as
xb = xj ± rb, yb = yj ± rb,
(10)
4. Experiment results Optical experiments are performed to demonstrate the performance of our proposed method. The optical setup of the holographic display system is shown in Fig. 5. During optical reconstruction, LETO phase-only SLM (HOLOEYE Photonics AG) is used to display CGHs. It is a reflective liquid crystal on silicon (LCOS) device with 1920 1080 pixels. The pixel pitch is 6.4 μm and the SLM is addressed with 8 bit gray-scale levels. The wavelength of the laser is 532 nm. The wavefront reconstructed from the SLM is reproduced by a 4-f system. A spatial filter is placed at the intermediate focal plane of the 4-f system to eliminate the zero-order interruption and unwanted orders [20]. The 3-D scene used to generate the CGHs is a sphere with a diameter 5.5 mm, which is composed of 9412 point sources. The distance between the sphere and the hologram plane is set to 160 mm. All the CGHs generated in the experiments are calculated by using a PC with a CPU of Intel Xeon E5-2620 (2.10 GHz) and a memory of DELL DDR3 ECC RDIMM (16GB). The calculation time for one CGH is 4116 s. The optical reconstructed images are captured by a Canon 500D camera. Fig. 6 shows the optical reconstruction results of the CGHs based on the Phong reflection model when applying ambient (ka ¼ 0.2), ambient with diffuse (ka ¼ 0.2, kd ¼ 0.5), and three reflection components (ka ¼0.2, kd ¼0.5, ks ¼ 0.5), respectively. The reconstruction results clearly demonstrate the lighting effects of each reflection component. The intensity of the ambient component is uniformly scattered in
Fig. 6. CGHs and optical reconstructions based on the Phong reflection model: (a) and (d) ambient reflection, (b) and (e) ambient and diffuse reflections, (c) and (f) ambient, diffuse and specular reflections.
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H. Zhang et al. / Optics Communications 370 (2016) 192–197
Fig. 7. CGHs and optical reconstructions when illuminating from (a) and (d) left, (b) and (e) middle, (c) and (f) right.
Fig. 8. CGHs and optical reconstructions when (a) and (d) α¼ 3, (b) and (e) α ¼ 7, (c) and (f) α ¼11.
the entire scene, and the diffuse component varies with the direction of the surface. The specular reflection component forms a highlight spot, which illustrates the smoothness level of the object surface. Fig. 7 shows the optical reconstructions of the CGHs based on the Phong reflection model when illuminating from different directions. The results show that the shading induced by the diffuse component and the highlight spot induced by the specular reflection component would change along with the illumination direction. Fig. 8 demonstrates the optical reconstructions of the CGHs with different shininess constants. The highlight spot would become smaller when the shininess constant α increases, which is in consistent with the simulation results shown in Fig. 1(b).
5. Conclusion We propose an efficient method in rendering photorealistic lighting effects of 3-D phase CGHs using directional point-based algorithm with anti-aliasing technique. The Phong reflection model is implemented in the calculation of CGHs, which uses ambient, diffuse and specular reflection components to characterize the lighting parameters. A phase-only SLM is used in the optical reconstruction, which leads the system with higher optical efficiency and better utilization of the system space-bandwidth product. Multiple lighting effects with adjustable reflection parameters are illustrated in the optical experiments, which demonstrate that our proposed method can provide quality 3-D images with photorealistic lighting effects.
H. Zhang et al. / Optics Communications 370 (2016) 192–197
Acknowledgment This work is supported by the National Basic Research Program of China (No. 2013CB328801), the National Natural Science Foundation of China (Nos. 61505095, 61275013, 61361160418, 61327902), and the Innovation Method Fund of China (No. 2015IM020500).
References [1] S.A. Benton, V.M. Bove, Holographic Imaging, Wiley, Hoboken, 2007. [2] H. Zhang, Y. Zhao, L. Cao, G. Jin, Three-dimensional display technologies in wave and ray optics: a review (Invited Paper), Chin. Opt. Lett. 12 (2014) 060002. [3] Y. Endo, E. Wakunami, T. Shimobaba, T. Kakue, D. Arai, Y. Ichihashi, K. Yamamoto, T. Ito, Computer-generated hologram calculation for real scenes using a commercial portable plenoptic camera, Opt. Commun. 356 (2015) 468–471. [4] Y. Pan, J. Liu, X. Li, Y. Wang, A review of dynamic holographic 3D display: algorithms, devices, and systems, IEEE Trans. Ind. Inform. 99 (2015) 1-1. [5] D. Teng, L. Liu, Y. Zhang, Z. Pang, B. Wang, The holographic display of threedimensional medical objects through the usage of a shiftable cylindrical lens, Opt. Commun. 326 (2014) 1–5. [6] H. Kang, T. Yamaguchi, H. Yoshikawa, Accurate phase-added stereogram to improve the coherent stereogram, Appl. Opt. 47 (2008) D44–D54. [7] H. Zhang, Y. Zhao, L. Cao, G. Jin, Fully computed holographic stereogram based algorithm for computer-generated holograms with accurate depth cues, Opt. Express 23 (2015) 3901–3913. [8] Y. Zhao, L. Cao, H. Zhang, D. Kong, G. Jin, Accurate calculation of computergenerated holograms using angular-spectrum layer-oriented method, Opt. Express 23 (2015) 25440–25449.
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[9] J.S. Chen, D.P. Chu, Improved layer-based method for rapid hologram generation and real-time interactive holographic display applications, Opt. Express 23 (2015) 18143–18155. [10] H. Nishi, K. Matsushima, S. Nakahara, Rendering of specular surfaces in polygon-based computer-generated holograms, Appl. Opt. 50 (2011) H245–H252. [11] T. Kurihara, Y. Takaki, Shading of a computer-generated hologram by zone plate modulation, Opt. Express 20 (2012) 3529–3540. [12] T. Kurihara, Y. Takaki, Speckle-free, shaded 3D images produced by computergenerated holography, Opt. Express 21 (2013) 4044–4054. [13] K. Wakunami, M. Yamaguchi, Calculation for computer generated hologram using ray-sampling plane, Opt. Express 19 (2011) 9086–9101. [14] K. Wakunami, H. Yamashita, M. Yamaguchi, Occlusion culling for computer generated hologram based on ray-wavefront conversion, Opt. Express 21 (2013) 21811–21822. [15] T. Ichikawa, T. Yoneyama, Y. Sakamoto, CGH calculation with the ray tracing method for the Fourier transform optical system, Opt. Express 21 (2013) 32019–32031. [16] H. Niwase, N. Takada, H. Araki, H. Nakayama, A. Sugiyama, T. Kakue, T. Shimobaba, T. Ito, Real-time spatiotemporal division multiplexing electroholography with a single graphics processing unit utilizing movie features, Opt. Express 22 (2014) 28052–28057. [17] H. Araki, N. Takada, H. Niwase, S. Ikawa, M. Fujiwara, H. Nakayama, T. Kakue, T. Shimobaba, T. Ito, Real-time time-division color electroholography using a single GPU and a USB module for synchronizing reference light, Appl. Opt. 54 (2015) 10029–10034. [18] Matoba, T.J. Naughton, Y. Frauel, N. Bertaux, B. Javidi, Real-time three-dimensional object reconstruction by use of a phase-encoded digital hologram, Appl. Opt. 41 (2002) 6187–6192. [19] H. Zhang, J. Xie, J. Liu, Y. Wang, Optical reconstruction of 3D images by use of pure-phase computer-generated holograms, Chin. Opt. Lett. 7 (2009) 1101–1103. [20] H. Zhang, J. Xie, J. Liu, Y. Wang, Elimination of a zero-order beam induced by a pixelated spatial light modulator for holographic projection, Appl. Opt. 48 (2009) 5834–5841.
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Lighting effects rendering in three-dimensional computer-generated holographic display Hao Zhang n, Liangcai Cao, Guofan Jin State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instruments, Tsinghua University, Beijing 100084, China
art ic l e i nf o
a b s t r a c t
Article history: Received 17 December 2015 Received in revised form 3 March 2016 Accepted 4 March 2016
We present a technique for generating three-dimensional (3-D) computer-generated holograms (CGHs) with realistic lighting effects based on a phase-only spatial light modulator (SLM). Phong reflection model is employed in the calculation of reflectance distribution for CGH synthesizing. Directional pointbased algorithm produces realistic lighting effects of the 3-D scenes in processing the ambient, diffuse and specular reflections. A phase-only SLM is used to perform the optical experiments, and the results show that the proposed technique can perform quality reconstructions of the 3-D scenes with high optical efficiency and efficient utilization of the system space-bandwidth product. & 2016 Elsevier B.V. All rights reserved.
Keywords: Holography Computer holography Holographic display
1. Introduction Holographic display can reconstruct the whole optical wavefront of the 3-D scene and hence has the potential to provide all the depth cues that human eyes can perceive [1]. With the developments of computer technology and spatial light modulators (SLMs), computer-generated holograms (CGHs) of various 3-D images can be displayed dynamically without the complicated interference recording systems [2–5]. Both existing and synthetic 3-D scenes can be encoded into the CGHs as long as their mathematical descriptions are provided. The algorithms for generating the CGHs are directly related with the image qualities of the reconstructed 3-D scenes. Computer graphics rendering techniques can convert 3-D scenes into photorealistic two-dimensional (2-D) images, which have been used in the CGH algorithms to enhance fidelities of the reconstructed 3-D images [6–9]. Holographic stereograms can provide occlusion effects easily with the help of multi-viewpoint rendering process [6,7]. Physically based algorithms can generate CGHs with accurate geometric information by extracting coordinate information through the depth buffer [8,9]. In computer graphics, shading refers to the process of calculating the brightness of an object in the 3-D scene based on the relative positions between the light, object, and the viewer. It can depict the illumination and depth perception of the 3-D scene, which can benefit the visual effect of the rendered 2-D image. Shading process of n
Corresponding author. E-mail address: [email protected] (H. Zhang).
http://dx.doi.org/10.1016/j.optcom.2016.03.013 0030-4018/& 2016 Elsevier B.V. All rights reserved.
computer graphics could be integrated with CGH calculation to produce realistic lighting effects for the improvements of the reconstruction quality of the 3-D CGH. Lighting effects rendering in CGH calculation is crucial to the depth performance during optical reconstruction. Various algorithms have been proposed for simulating the wave reflection and propagation processes to render different lighting effects [10–15]. Spatial spectrum of the polygon-based algorithm was modified based on the Phong reflection model to imitate the specular reflection [10]. Zone plate based Phong reflection model was used to generate CGHs with characteristics of reflection [11,12]. Computer graphics rendering techniques were also used in the holographic stereogram computation to add lighting effects [13,14]. Recently, ray tracing method was introduced into the CGH calculation to simulate characteristic reflection effects [15]. However, the previous methods for generating CGHs are based on the amplitude modulation of the reconstruction wavefront, which would affect the optical efficiency and utilization rate of the system spacebandwidth product. Hence accurate and efficient lighting effects processing in CGH synthesizing needs to be further investigated. In this study, directional point-based algorithm is used for generating phase CGHs with multiple lighting effects. The wavefront distribution of each object point is calculated directly according to the Phong reflection model with anti-aliasing technique. The proposed technique is more efficient in its utilization of the space-bandwidth product compared to the zone plate method since no conjugate image is reconstructed. A phase-only SLM is used to perform the optical reconstructions of the 3-D scenes, which can reconstruct quality 3-D images with realistic lighting effects and high optical efficiency.
H. Zhang et al. / Optics Communications 370 (2016) 192–197
2. Phong reflection model Phong reflection model is an empirical model for local illumination, which is widely used in 3-D computer graphics. During calculation, four unit vectors are used to compute the light intensity at an arbitrary point, as shown in Fig. 1(a). The light vector L denotes the direction vector from the point on the surface toward the light source. The normal vector N is perpendicular to the surface at the given point. The reflection vector R indicates the direction that a perfectly reflected ray of light would take from the point on the surface. According to the law of reflection, the angle of incidence equals the angle of reflection. The view vector V indicates the direction pointing towards the position of viewer or virtual camera. Phong reflection model uses ambient, diffuse and specular components to characterize the lighting effects of an object surface. The ambient reflection term is presented in the entire 3-D scene, where all of the objects are brightened with a specified light intensity:
Ia = k a I,
(1)
where ka is the ambient reflection constant, and I denotes the illumination light intensity. The diffuse reflection is the reflection of the light from a surface such that an incident ray is reflected at many angles. An illuminated ideal diffuse reflecting surface will have equal luminance from all directions. According to the Lambert’s cosine law, the diffuse reflection light intensity of the Phong reflection model is given by
Id = k d (L⋅N ) I,
(2)
193
where kd is the diffuse reflection constant, and ∙ denotes the dot product. The intensity of the diffuse reflection light depends on the angle of incidence, and has no relationship with the view vector. Hence the intensity of the diffuse reflection light would have the same value when viewed from any angle. The specular reflection is the bright spot of light that appears on shiny objects when illuminated, which can provide a strong visual cue for the shape of an object and its location with respect to the light source. The intensity of the specular reflection light depends on the angle between the reflection vector R and the view vector V:
Is = ks (R⋅V )α I,
(3)
where ks is the specular reflection constant, and α is a shininess constant of the surface. Specular reflection component has anisotropic distribution along different viewing directions, as shown in Fig. 1(b). ϕ denotes the angle between view vector and reflection vector. The specular reflection achieves its peak when ϕ is zero. As the shininess constant α increases, the specular spot becomes smaller, which would lead a smoother object surface. We can deduce the equation of Phong reflection model by combining the three reflection components:
Ip = Ia + Id + Is = ⎡⎣ k a + k d (L⋅N ) + ks (R⋅V )α ⎤⎦ I.
(4)
Fig. 2(a) schematically illustrates the ambient, diffuse and specular reflection components when the surface is illuminated by the light source. The ambient and diffuse reflection components have isotropic distributions over all viewing directions, while the specular lobe has the highest value along the reflection vector R. Fig. 2(b) is the visual illustration of the Phong reflection model. Photorealistic lighting effects can be rendered by combining ambient, diffuse and specular reflection components.
3. CGH generation with Phong reflection model In computer graphics, the Phong reflection model sets one viewpoint for each image during rendering process. Hence only one view vector is bundled with a specific object point. While for CGH computation, each hologram sample corresponds with one viewpoint, and multiple view vectors need to be considered in calculating a single object point. Fig. 3 illustrates the difference of the viewing parameters between computer graphics and CGH computation. A viewpoint array is formed in the hologram plane to fetch lighting information from the corresponding viewing directions. In conventional point-based method, the complex amplitude distribution on the hologram plane can be calculated by superposing the optical wavefronts of all the point sources [16,17]: n
H (x, y) =
∑ j=1
Aj exp ⎡⎣ i kr j + ϕj ⎤⎦, rj
(
)
(5)
where n is the number of object points, Aj is the amplitude of the jth point, k ¼2π/λ is the wave number in free space, and ϕj is the initial phase. The distance between the jth object point and the sampling point (x, y, 0) on the hologram plane is given by
rj =
Fig. 1. (a) Vectors in Phong reflection model. (b) Specular reflections with different shininess constants.
(
( x − xj )2 + y − yj
2
)
+ z j2 .
(6)
With the proper choice of random initial phase, we may assume a uniform amplitude distribution in the hologram plane, and thus we could achieve quality reconstruction with the pure phase information [18,19]. Ambient and diffuse reflections can be reconstructed using Eq. (5) since the wave amplitude Aj of the jth point is uniformly distributed on the hologram plane, since these two reflection
194
H. Zhang et al. / Optics Communications 370 (2016) 192–197
Fig. 2. (a) Ambient, diffuse and specular components in Phong reflection model. (b) Visual illustration of Phong equation.
Fig. 3. (a) Viewing frustum in computer graphics. (b) Diagram in CGH computation.
components have no relationship with the view vectors. While for specular reflection, the uniform distribution of Aj on the hologram plane is not valid due to its anisotropic property. We need to calculate Aj for each hologram sample independently, since different hologram samples correspond with different viewpoints and view vectors, as shown in Fig. 3(b). In order to calculate all the
Fig. 4. Contributed area of one object point on the hologram plane: (a) overall view, (b) top view.
reflection components of Phong reflection model, the amplitude in Eq. (5) should be directionally modulated:
Aj (x, y) =
⎡⎣ k a + k d (L⋅N ) + ks (R⋅V )α ⎤⎦ I ,
(7)
H. Zhang et al. / Optics Communications 370 (2016) 192–197
195
where rb is linear with the wave propagation distance:
rb = zj tan β,
(11)
The aliasing boundaries are then compared with the SLM boundaries and the inner ones are chosen to determine the contribution area for each object point. By using directional point-based algorithm with anti-aliasing technique, photorealistic lighting effects can be reconstructed for a 3-D object with an arbitrary position. And the algorithm is applicable to the SLM with different pixelated parameters. Fig. 5. Optical setup of the holographic display system.
where L, N, R and V are the corresponding vectors of the jth object point. Hence Eq. (5) becomes n
H (x, y) =
∑ j=1
Aj (x, y) exp ⎡⎣ i kr j + ϕj ⎤⎦. rj
(
)
(8)
Ambient, diffuse and specular reflection components can be reconstructed with the help of the directionally modulated wave amplitude for each object point. Thus Phong reflection model can be integrated with the CGH generation to provide multiple lighting effects. During calculation, the sampling parameters of CGH should be set according to the pixelated structure of SLM. Since the spatial resolution of the SLM is limited, it is necessary to prevent aliasing error in CGH calculation, especially for the object points which are close to the hologram plane. The maximum diffraction angle of the SLM is given by
sin β = fmax λ =
1 λ, 2d
(9)
where fmax is the highest spatial frequency that SLM can display, and d is the pixel pitch of the SLM. Hence the contribution area on the hologram plane for each object point needs to be restricted due to this angular limitation, as shown in Fig. 4. The aliasing boundaries for each object point can be calculated as
xb = xj ± rb, yb = yj ± rb,
(10)
4. Experiment results Optical experiments are performed to demonstrate the performance of our proposed method. The optical setup of the holographic display system is shown in Fig. 5. During optical reconstruction, LETO phase-only SLM (HOLOEYE Photonics AG) is used to display CGHs. It is a reflective liquid crystal on silicon (LCOS) device with 1920 1080 pixels. The pixel pitch is 6.4 μm and the SLM is addressed with 8 bit gray-scale levels. The wavelength of the laser is 532 nm. The wavefront reconstructed from the SLM is reproduced by a 4-f system. A spatial filter is placed at the intermediate focal plane of the 4-f system to eliminate the zero-order interruption and unwanted orders [20]. The 3-D scene used to generate the CGHs is a sphere with a diameter 5.5 mm, which is composed of 9412 point sources. The distance between the sphere and the hologram plane is set to 160 mm. All the CGHs generated in the experiments are calculated by using a PC with a CPU of Intel Xeon E5-2620 (2.10 GHz) and a memory of DELL DDR3 ECC RDIMM (16GB). The calculation time for one CGH is 4116 s. The optical reconstructed images are captured by a Canon 500D camera. Fig. 6 shows the optical reconstruction results of the CGHs based on the Phong reflection model when applying ambient (ka ¼ 0.2), ambient with diffuse (ka ¼ 0.2, kd ¼ 0.5), and three reflection components (ka ¼0.2, kd ¼0.5, ks ¼ 0.5), respectively. The reconstruction results clearly demonstrate the lighting effects of each reflection component. The intensity of the ambient component is uniformly scattered in
Fig. 6. CGHs and optical reconstructions based on the Phong reflection model: (a) and (d) ambient reflection, (b) and (e) ambient and diffuse reflections, (c) and (f) ambient, diffuse and specular reflections.
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Fig. 7. CGHs and optical reconstructions when illuminating from (a) and (d) left, (b) and (e) middle, (c) and (f) right.
Fig. 8. CGHs and optical reconstructions when (a) and (d) α¼ 3, (b) and (e) α ¼ 7, (c) and (f) α ¼11.
the entire scene, and the diffuse component varies with the direction of the surface. The specular reflection component forms a highlight spot, which illustrates the smoothness level of the object surface. Fig. 7 shows the optical reconstructions of the CGHs based on the Phong reflection model when illuminating from different directions. The results show that the shading induced by the diffuse component and the highlight spot induced by the specular reflection component would change along with the illumination direction. Fig. 8 demonstrates the optical reconstructions of the CGHs with different shininess constants. The highlight spot would become smaller when the shininess constant α increases, which is in consistent with the simulation results shown in Fig. 1(b).
5. Conclusion We propose an efficient method in rendering photorealistic lighting effects of 3-D phase CGHs using directional point-based algorithm with anti-aliasing technique. The Phong reflection model is implemented in the calculation of CGHs, which uses ambient, diffuse and specular reflection components to characterize the lighting parameters. A phase-only SLM is used in the optical reconstruction, which leads the system with higher optical efficiency and better utilization of the system space-bandwidth product. Multiple lighting effects with adjustable reflection parameters are illustrated in the optical experiments, which demonstrate that our proposed method can provide quality 3-D images with photorealistic lighting effects.
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Acknowledgment This work is supported by the National Basic Research Program of China (No. 2013CB328801), the National Natural Science Foundation of China (Nos. 61505095, 61275013, 61361160418, 61327902), and the Innovation Method Fund of China (No. 2015IM020500).
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