## Abstract

A type of optical system consisting of one total internal reflection (TIR) lens and two reflectors is designed for collimating the light of an LED to a uniform pattern. Application of this kind of optical system includes underwater light communication and an underwater image system. The TIR lens collimates all the light of the LED to a nonuniform plane wavefront. The double-reflector system redistributes the plane wavefront uniformly and collimates again. Three optical systems that produce a different radius of the output light patterns are designed. The simulation result shows that the uniformity of the designed optical system is greater than 0.76, and the total output efficiency (TOE) is greater than 89%. At the same time, we conclude that the radius of the output reflector should not be smaller than that of the input reflector in order to keep high uniformity and TOE. One of the designed optical systems is fabricated by computer numeric control, and the experiment results satisfy that goal.

© 2014 Optical Society of America

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### Equations (8)

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(1)
$$\iint I(\mathrm{\Omega})\mathrm{d}\mathrm{\Omega}=\iint I(T)\mathrm{d}T.$$
(2)
$$\iint {E}_{\mathrm{\Omega}}(r,\theta )r\mathrm{d}r\mathrm{d}\theta =\iint {E}_{T}(r,\theta )r\mathrm{d}r\mathrm{d}\theta .$$
(3)
$${\int}_{0}^{2\pi}({\int}_{{r}_{i-1}}^{{r}_{i}}{E}_{\mathrm{\Omega}}(r,\theta )r\mathrm{d}r)\mathrm{d}\theta ={\int}_{0}^{2\pi}({\int}_{{r}_{i-1}}^{{r}_{i}}{E}_{T}(r,\theta )r\mathrm{d}r)\mathrm{d}\theta =\frac{\mathrm{\Phi}}{N}.$$
(4)
$${\int}_{{r}_{i-1}}^{{r}_{i}}({\int}_{{\theta}_{i-1}}^{{\theta}_{i}}{E}_{\mathrm{\Omega}}(r,\theta )\mathrm{d}\theta )r\mathrm{d}r={\int}_{{r}_{i-1}}^{{r}_{i}}({\int}_{{\theta}_{i-1}}^{{\theta}_{i}}{E}_{T}(r,\theta )\mathrm{d}\theta )r\mathrm{d}r=\frac{\mathrm{\Phi}}{MN}.$$
(5)
$${[1+{n}^{2}-2n(\mathbf{O}\xb7\mathbf{I})]}^{1/2}\mathbf{N}=\mathbf{O}-n\mathbf{I}.$$
(6)
$$\{\begin{array}{l}{x}_{1}=\frac{{y}_{0}+{x}_{0}k}{\mathrm{cot}\text{\hspace{0.17em}}{\theta}_{1}+k}\\ {y}_{1}={x}_{1}\text{\hspace{0.17em}}\mathrm{cot}\text{\hspace{0.17em}}{\theta}_{1}\end{array}.$$
(7)
$$\{\begin{array}{ll}2\pi {\int}_{0}^{{\theta}_{r}}I(\theta )\mathrm{sin}\text{\hspace{0.17em}}\theta \mathrm{d}\theta =2\pi {\int}_{0}^{r}{E}_{\mathrm{\Omega}}(r)r\mathrm{d}r& {\theta}_{r}<{\theta}_{\mathrm{th}}\\ 2\pi {\int}_{{\theta}_{th}}^{{\theta}_{x}}I(\theta )\mathrm{sin}\text{\hspace{0.17em}}\theta \mathrm{d}\theta =2\pi {\int}_{r}^{{r}_{th}}{E}_{\mathrm{\Omega}}(r)r\mathrm{d}r& {\theta}_{x}>{\theta}_{\mathrm{th}}\end{array}.$$
(8)
$$r=R\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}\theta .$$