## Abstract

Cylindrical concentrators are viewed as a limit case of toroidal concentrators with the purpose of applying to them some results obtained for axisymmetrical optical systems. This enables us to obtain easily the directional intercept factor of a cylindrical nonimaging concentrator called the Ideal Tubular Concentrator. A useful tool for designing new cylindrical concentrators is also derived.

© 1984 Optical Society of America

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### Equations (10)

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(1)
$$h=\rho {p}^{\prime}.$$
(2)
$$\underset{R\to \infty}{\text{lim}}{h}^{\prime}=\underset{R\to \infty}{\text{lim}}\frac{\rho}{R}{p}^{\prime}=p.$$
(3)
$$m(\rho ,z)={\left[{n}^{2}(\rho ,z)-\frac{{h}^{2}}{{\rho}^{2}}\right]}^{1/2}.$$
(4)
$$m(Y,Z)={[{n}^{2}(Y,Z)-{p}^{2}]}^{1/2}.$$
(5)
$${n}_{r}={\left(\frac{{n}^{2}-{p}^{2}}{1-{p}^{2}}\right)}^{1/2}.$$
(6)
$$\alpha (0,q)=1\hspace{0.17em}\text{if}\hspace{0.17em}\mid q\mid \hspace{0.17em}\le \text{sin}{\varphi}_{a},$$
(7)
$$\alpha (0,q)=0\hspace{0.17em}\text{if}\hspace{0.17em}\mid q\mid \hspace{0.17em}>\text{sin}{\varphi}_{a}.$$
(8)
$$2R\hspace{0.17em}\left[{\varphi}_{m}+{\varphi}_{a}-\frac{\pi}{2}+\text{cos}({\varphi}_{m}-{\varphi}_{a})\right]\hspace{0.17em}{(1-{p}^{2})}^{1/2}=2{({n}^{2}-{p}^{2})}^{1/2}{A}_{c},$$
(9)
$$2R\hspace{0.17em}\left[{\varphi}_{m}+{\varphi}_{a}-\frac{\pi}{2}+\text{cos}({\varphi}_{m}-{\varphi}_{a})\right]=2{n}_{r}{A}_{c},$$
(10)
$$\frac{{C}_{g}}{{\varphi}_{m}}\left[{\varphi}_{m}+{\varphi}_{a}-\frac{\pi}{2}+\text{cos}({\varphi}_{m}-{\varphi}_{a})\right]=2{n}_{r}.$$