## Abstract

A new class of radiation concentrators is described that achieve maximal concentration of radiation from a uniform source. Unlike ideal concentrators, which accept all radiation within a given acceptance angle and none outside, the new maximal concentration collectors may reject some radiation from within the nominal acceptance angle. However, the new concentrators offer small mirror or refractor area, high practical concentration levels (unlike ideal designs, which must be truncated), and an adaptable concentration response versus radiation incident angle. The new concentrators are exceptionally well suited to solar-energy applications and should also prove useful for radiation detection or distribution.

© 1980 Optical Society of America

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### Equations (5)

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(1)
$$\begin{array}{l}B{\int}_{{\theta}_{1}}^{{\theta}_{2}}f(\theta ){A}_{1}\hspace{0.17em}\text{cos}\hspace{0.17em}\theta \text{d}\theta =B{\int}_{-\pi /2}^{\pi /2}{A}_{2}\hspace{0.17em}\text{cos}\hspace{0.17em}{\theta}^{\prime}\text{d}{\theta}^{\prime}\\ =2B{A}_{2},\end{array}$$
(2)
$$\frac{{A}_{1}}{{A}_{2}}=2/{\int}_{{0}_{1}}^{{0}_{2}}f(\theta )\text{cos}\hspace{0.17em}\theta \text{d}\theta .$$
(3)
$$\begin{array}{l}{X}_{\text{avg}}=\frac{1}{t}{\int}_{t}\frac{{A}_{1}}{{A}_{2}}f[\theta (t)]\text{cos}\hspace{0.17em}\theta (t)\text{d}t\\ =\frac{{A}_{1}}{{A}_{2}{\theta}_{\text{max}}}{\int}_{{0}_{1}}^{{0}_{2}}f(\theta )\hspace{0.17em}\text{cos}\theta \text{d}\theta ,\end{array}$$
(4)
$${X}_{\text{avg}}=2/{\theta}_{\text{max}},$$
(5)
$${X}_{\text{avg}}=\frac{{n}_{2}}{{n}_{1}}\frac{\text{sin}\hspace{0.17em}{{\theta}^{\prime}}_{2}-\text{sin}\hspace{0.17em}{{\theta}^{\prime}}_{1}}{{\theta}_{\text{max}}},$$