## Abstract

We present a three-dimensional (3D) measurement and imaging based on a multicamera system.
In the presented system, projected images of 3D objects are taken by cameras located at random positions on a circumference, and then the 3D objects can be reconstructed numerically. We introduce an angle correction function to improve the quality of the reconstructed object. The angle correction function can correct the angle error caused by the position errors in the projected images due to the finite pixel size of the image sensor. The numerical results show that the point source was reconstructed successfully by introducing the angle correction function. We also demonstrate experiments: the two objects are located on a rotary stage controlled by a computer, the projected images are taken by a single camera, and by using 33 projected images, the two objects are reconstructed successfully.

© 2008 Optical Society of America

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### Equations (7)

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(1)
$$\left({x}_{k},{y}_{k}\right)=\left(x\text{\hspace{0.17em}}\mathrm{cos}\text{\hspace{0.17em}}{\theta}_{k}+z\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}{\theta}_{k},y\right)\text{.}$$
(2)
$${\tilde{P}}_{k}\left(u\right)={\displaystyle \int {p}_{k}\left({x}_{k}\right)\mathrm{exp}\left(-i\text{\hspace{0.17em}}\frac{2\pi}{\lambda f}\text{\hspace{0.17em}}{x}_{k}u\right)\mathrm{d}{x}_{k}\text{.}}$$
(3)
$${\tilde{P}}_{k}\left(s\right)={\displaystyle \sum _{n=0}^{N-1}{p}_{k}\left(n\right)\mathrm{exp}\left(-i2\pi \text{\hspace{0.17em}}\frac{ns}{N}\right)}\text{,}$$
(4)
$$r\left(p\Delta x\prime ,q\Delta z\prime \right)={\displaystyle \sum _{s=0}^{N-1}{\displaystyle \sum _{k=0}^{M-1}{\tilde{P}}_{k}\left(s\right)\mathrm{exp}\left\{i\text{\hspace{0.17em}}\frac{2\pi s}{\lambda f}\times \Delta u\left(p\Delta x\prime \text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}{\theta}_{k}+q\Delta z\prime \text{\hspace{0.17em}}\mathrm{cos}\text{\hspace{0.17em}}{\theta}_{k}\right)\right\}}}\text{,}$$
(5)
$$r\left(p,q\right)={\displaystyle \sum _{s=0}^{N-1}{\displaystyle \sum _{k=0}^{M-1}{\tilde{P}}_{k}\left(s\right)\mathrm{exp}\left\{i\text{\hspace{0.17em}}\frac{2\pi s}{N}\left(p\text{\hspace{0.17em}}\mathrm{cos}\text{\hspace{0.17em}}{\theta}_{k}+q\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}{\theta}_{k}\right)\right\}\text{.}}}$$
(6)
$$\text{\hspace{0.17em}}{\theta}_{k}^{\prime}={\mathrm{sin}}^{-1}\left(\frac{\left[{x}_{k}\right]{z}_{0}\pm \sqrt{{\left(\left[{x}_{k}\right]{z}_{0}\right)}^{2}-\left({\left[{x}_{k}\right]}^{2}-{x}_{0}^{2}\left)\right({x}_{0}^{2}+{z}_{0}^{2}\right)}}{{x}_{0}^{2}+{z}_{0}^{2}}\right).$$
(7)
$$r\left(p,q\right)={\displaystyle \sum _{s=0}^{N-1}{\displaystyle \sum _{k=0}^{M-1}{\tilde{P}}_{k}\left(s\right)\mathrm{exp}\left\{i\text{\hspace{0.17em}}\frac{2\pi s}{N}\left(p\text{\hspace{0.17em}}\mathrm{cos}\text{\hspace{0.17em}}{\theta}_{k}^{\prime}+q\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}{\theta}_{k}^{\prime}\right)\right\}\text{.}}}$$