## Abstract

A novel curved computational integral imaging reconstruction (C-CIIR)
technique for the virtually curved integral imaging (VCII) system is proposed, and its performances are analyzed. In the C-CIIR model, an additional virtual large-aperture lens is included to provide a multidirectional curving effect in the reconstruction process, and its effect is analyzed in detail by using the ABCD matrix. With this method, resolution-enhanced 3D object images can be computationally reconstructed from the picked-up elemental images of the VCII system. To confirm the feasibility of the proposed model, some experiments are carried out. Experiments revealed that the sampling rate in the VCII system could be kept at a maximum value within some range of the distance *z*, whereas in the conventional integral imaging system it linearly decreased as the distance *z* increased. It is also shown that resolutions of the object images reconstructed by the C-CIIR method have been significantly improved compared with those of the conventional CIIR method.

© 2007 Optical Society of America

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### Equations (16)

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(1)
$$\left[\begin{array}{cc}{H}_{nx}^{kx}\left(z=-g\right)& {H}_{ny}^{ky}\left(z=-g\right)\\ {A}_{nx}^{kx}\left(z=-g\right)& {A}_{ny}^{ky}\left(z=-g\right)\end{array}\right]=\left[\begin{array}{cc}kxP+nxd& kyP+nyd\\ -\frac{nxd}{g}& -\frac{nyd}{g}\end{array}\right]\text{,}$$
(2)
$$\left[\begin{array}{cc}{H}_{nx}^{kx}\left(0\right)& {H}_{ny}^{ky}\left(0\right)\\ {A}_{nx}^{kx}\left(0\right)& {A}_{ny}^{ky}\left(0\right)\end{array}\right]=\left[\begin{array}{cc}kxP& kyP\\ -\frac{nxd}{g}& -\frac{nyd}{g}\end{array}\right].$$
(3)
$$T=\left[\begin{array}{cc}1& z\\ 0& 1\end{array}\right]\left[\begin{array}{cc}1& 0\\ -1/f& 1\end{array}\right].$$
(4)
$$\left[\begin{array}{cc}{H}_{nx}^{kx}\left(z\right)& {H}_{ny}^{ky}\left(z\right)\end{array}\right]=\left[\begin{array}{cc}kxP\left(1-\frac{z}{f}\right)-\frac{znxd}{g}& kyP\left(1-\frac{z}{f}\right)-\frac{znyd}{g}\end{array}\right].$$
(5)
$$\left[\begin{array}{cc}0<kx\le Vx,& 0<ky\le Vy\\ -\frac{Nx}{2}<nx\le \frac{Nx}{2}\text{,}& -\frac{Ny}{2}<ny\le \frac{Ny}{2}\end{array}\right],$$
(6)
$${X}_{nx}^{kx}\left(z\right)=kxP-\frac{znxd}{g}\text{,}$$
(7)
$${Y}_{ny}^{ky}\left(z\right)=kyP-\frac{znyd}{g}.$$
(8)
$${O}_{nxny}^{kxky}\left(z\right)=\{\begin{array}{cc}1\text{,}& \left(0,0\right)<\left({X}_{nx}^{kx}\left(z\right),{Y}_{ny}^{ky}\left(z\right)\right)\le \left(VxNx,VyNy\right)\\ 0\text{,}& \text{otherwise}\hfill \end{array}.$$
(9)
$$R={\displaystyle \sum _{kx=1}^{Vx}{\displaystyle \sum _{ky=1}^{Vy}{\displaystyle \sum _{nx=-Nx/2}^{Nx/2}{\displaystyle \sum _{ny=-Ny/2}^{Ny/2}{O}_{nxny}^{kxky}}}}}\left(z\right),$$
(10)
$${S}_{R}=\frac{R}{VxNxVyNy}\times 100\left(\%\right).$$
(11)
$$\left[\begin{array}{cc}0<kx\le Vx,& 0<ky\le Vy\\ -\frac{Nx}{2}<nx\le \frac{Nx}{2}\text{,}& -\frac{Ny}{2}<ny\le \frac{Ny}{2}\end{array}\right]\text{,}$$
(12)
$${H}_{nx}^{kx}\left(z\right)=kxP\left(1-\frac{z}{f}\right)-\frac{znxd}{g}\text{,}$$
(13)
$${H}_{ny}^{ky}\left(z\right)=kyP\left(1-\frac{z}{f}\right)-\frac{znyd}{g}.$$
(14)
$${Q}_{nxny}^{kxky}\left(z\right)=\{\begin{array}{cc}1\text{,}& \left(\begin{array}{c}\left(0,0\right)<\left({H}_{nx}^{kx}\left(z\right),{H}_{ny}^{ky}\left(z\right)\right)\le \left(VxNx,VyNy\right)\end{array}\right)\\ 0\text{,}& \text{otherwise}\hfill \end{array}\text{.}$$
(15)
$${R}_{\text{VCII}}={\displaystyle \sum _{kx=1}^{Vx}{\displaystyle \sum _{ky=1}^{Vy}{\displaystyle \sum _{nx=-Nx/2}^{Nx/2}{\displaystyle \sum _{ny=-Ny/2}^{Ny/2}{Q}_{nxny}^{kxky}}}}}\left(z\right),$$
(16)
$${S}_{R}=\frac{{R}_{\text{VCII}}}{VxNxVyNy}\times 100\left(\%\right).$$