## Abstract

We propose a three-dimensional (3D) imaging technique that can sense a 3D scene and computationally reconstruct it as a 3D volumetric image. Sensing of the 3D scene is carried out by obtaining elemental images optically using a pickup microlens array and a detector array. Reconstruction of volume pixels of the scene is accomplished by computationally simulating optical reconstruction according to ray optics. The entire pixels of the recorded elemental images contribute to volumetric reconstruction of the 3D scene. Image display planes at arbitrary distances from the display microlens array are computed and reconstructed by back propagating the elemental images through a computer synthesized pinhole array based on ray optics. We present experimental results of 3D image sensing and volume pixel reconstruction to test and verify the performance of the algorithm and the imaging system. The volume pixel values can be used for 3D image surface reconstruction.

© 2004 Optical Society of America

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### Equations (3)

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(1)
$${O}_{\mathit{pq}}(x,y,z)=\frac{{I}_{\mathit{pq}}\left({s}_{x}p-\frac{\left(x-{s}_{x}p\right)}{M},\phantom{\rule{.2em}{0ex}}{s}_{y}q-\frac{\left(y-{s}_{y}q\right)}{M}\right)}{{\left(z+g\right)}^{2}+\left[{\left(x-{s}_{x}p\right)}^{2}+{\left(y-{s}_{y}q\right)}^{2}\right]{\left(1+\frac{1}{M}\right)}^{2}},\mathrm{for}\{\begin{array}{c}{s}_{x}\left(p-\frac{M}{2}\right)\le x\le {s}_{x}\left(p+\frac{M}{2}\right)\\ {s}_{y}\left(q-\frac{M}{2}\right)\le y\le {s}_{y}\left(p+\frac{M}{2}\right)\end{array}$$
(2)
$${O}_{\mathit{pq}}(x,y,z)=\frac{{I}_{\mathit{pq}}\left(-\frac{x}{M}+\left(1+\frac{1}{M}\right){s}_{x}p,\phantom{\rule{.2em}{0ex}}-\frac{y}{M}+\left(1+\frac{1}{M}\right){s}_{y}q\right)}{{\left(z+g\right)}^{2}+\left[{\left(x-{s}_{x}p\right)}^{2}+{\left(y-{s}_{y}q\right)}^{2}\right]{\left(1+\frac{1}{M}\right)}^{2}},\mathrm{for}\{\begin{array}{c}{s}_{x}\left(p-\frac{M}{2}\right)\le x\le {s}_{x}\left(p+\frac{M}{2}\right)\\ {s}_{y}\left(q-\frac{M}{2}\right)\le y\le {s}_{y}\left(p+\frac{M}{2}\right)\end{array}$$
(3)
$$O(x,y,z)=\sum _{p=0}^{m-1}\sum _{q=0}^{n-1}{O}_{\mathit{pq}}(x,y,z),$$