## Abstract

We propose an efficient algorithm for calculating photorealistic three-dimensional (3D) computer-generated hologram with Fourier domain segmentation. The segmentation of the spatial frequency processes the depth information from multiple parallel projections, recombining the wave fields of different viewing directions in the Fourier domain. Segmented angular spectrum with layer based processing is introduced to calculate the partitioned elements, which effectively extends the limited region of conventional angular spectrum. The algorithm can provide accurate depth cues and is compatible with computer graphics rendering techniques to provide quality view-dependent properties. Experiments demonstrate the proposed method can reconstruct photorealistic 3D images with accurate depth information.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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### Equations (14)

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(1)
$$h\left(x,y\right)\text{=}{F}^{-1}\left[O\left({f}_{x},{f}_{y}\right)\mathrm{exp}\left(j2\pi z\sqrt{{\lambda}^{-2}-{f}_{x}{}^{2}-{f}_{y}{}^{2}}\right)\right]={F}^{-1}\left[H\left({f}_{x},{f}_{y}\right)\right],$$
(2)
$${H}_{e}\left({f}_{x},{f}_{y}\right)\text{=}{\displaystyle \sum _{i=1}^{m}{O}_{i}\left({f}_{x},{f}_{y}\right)\mathrm{exp}\left(j2\pi {z}_{i}\sqrt{{\lambda}^{-2}-{f}_{x}{}^{2}-{f}_{y}{}^{2}}\right)},$$
(3)
$${f}_{x}=\frac{\mathrm{cos}{\alpha}_{x}}{\lambda}.$$
(4)
$${f}_{x}\in \left[-\frac{1}{2p},\frac{1}{2p}\right],$$
(5)
$${S}_{fx}=\frac{1}{Np}$$
(6)
$$I\left(x,y\right)=2\mathrm{Re}\left[h\left(x,y\right){r}^{*}\left(x,y\right)\right]+C,$$
(7)
$$T=\mathrm{exp}\left(j2\pi z\sqrt{{\lambda}^{-2}-{f}_{x}{}^{2}-{f}_{y}{}^{2}}\right).$$
(8)
$$\left|{f}_{lx}\right|=\frac{1}{2\pi}\left|\frac{\partial}{\partial {f}_{x}}\left(2\pi z\sqrt{{\lambda}^{-2}-{f}_{x}{}^{2}}\right)\right|=\left|\frac{z{f}_{x}}{\sqrt{{\lambda}^{-2}-{f}_{x}{}^{2}}}\right|.$$
(9)
$$\frac{1}{2\Delta {f}_{x}}\ge \left|{f}_{lx}\right|.$$
(10)
$$z\le L\sqrt{{\lambda}^{-2}{f}_{x}{}^{-2}-1}.$$
(11)
$$z\le L\sqrt{4{p}^{2}{\lambda}^{-2}-1}.$$
(12)
$$z\le L\sqrt{4{\left(Np\right)}^{2}{\lambda}^{-2}-1}.$$
(13)
$$\left|{f}_{I}\right|=\frac{1}{2\pi}\left|\frac{\partial \left(2\pi {f}_{y}y-2\pi \frac{\mathrm{cos}{\alpha}_{y}}{\lambda}y\right)}{\partial y}\right|\text{=}\left|{f}_{y}-\frac{\mathrm{cos}{\alpha}_{y}}{\lambda}\right|,$$
(14)
$$\frac{1}{2p}\ge \left|{f}_{y}-\frac{\mathrm{cos}{\alpha}_{y}}{\lambda}\right|.$$