## Abstract

In this paper, we introduce an improved signal analysis of the computational integral imaging (CII) system having a pickup process of three-dimensional object and a volumetric computational reconstruction (VCR) process. We propose a signal model for the CII system. From the signal model and its analysis, we can define a granular noise caused by the non-uniform overlapping. We also analyze the characteristics of the granular noise. According to our model and analysis, there is a condition that the granular noise cancels out. To show the feasibility of our model, the preliminary experiments are carried out and the result is presented. This is the first time, to our knowledge, that a signal model for the analysis of CII systems is provided.

© 2007 Optical Society of America

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### Equations (7)

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(1)
$${r}_{z}\left(x\right)=\sum _{i=0}^{N-1}{f}_{z}\left(x\right){\pi}_{i}\left(\frac{x}{w}\right)={f}_{z}\left(x\right)\sum _{i=0}^{N-1}{\pi}_{i}\left(\frac{x}{w}\right)={f}_{z}\left(x\right){S}_{\pi}\left(x\right),$$
(2)
$${\pi}_{i}\left(\frac{x}{w}\right)={\pi}_{0}\left(\frac{\left(x-s\right)}{w}\right),$$
(3)
$$w=\mathrm{na}+b=a\left(n+\frac{b}{a}\right),$$
(4)
$$w=a\frac{z}{g}=\mathrm{aM}.$$
(5)
$${f}_{z}\left(x\right)=\frac{{r}_{z}\left(x\right)}{{S}_{\pi}\left(x\right)}.$$
(6)
$$\mathrm{gn}\left(x\right)=\{\begin{array}{c}{S}_{\pi}\left(x\right)-\lfloor \frac{w}{a}\rfloor ,0<b\le 0.5a\\ \lceil \frac{w}{a}\rceil -{S}_{\pi}\left(x\right),0.5a\le b<a\end{array}.$$
(7)
$$\mathrm{USNR}=10\phantom{\rule{.2em}{0ex}}{\mathrm{log}}_{10}\frac{{P}_{U}}{{P}_{\mathrm{gn}}}=10{\phantom{\rule{.2em}{0ex}}\mathrm{log}}_{10}\frac{\mathrm{round}{\left(\frac{w}{a}\right)}^{2}}{\frac{1}{a}{\int}_{0}^{a}\mathrm{gn}{\left(x\right)}^{2}\mathrm{dx}},$$