The collection properties of generalized nonimaging radiation concentrators are studied for the case of geometrical optics. The second law of thermodynamics is applied to a concentrator located at the center of a cavity radiation source. It is shown that for three-dimensional concentrators the concentration <i>C</i> and the angular acceptance α(θ, ø) obey the relation 1 = <i>C</i> ∫<sub>θ</sub><sup>π/2</sup> = 0 ∫<sub>ø</sub><sup>2π</sup> = 0<sup>π-1</sup>α(θ,ø)cosθsinθ <i>d</i>θ<i>d</i>ø. For cylindrical concentrators, the concentration and angular acceptance α(θ) obey the relation 1 = <i>C</i> ∫<sub>-π/2</sub>-<sup>π/2</sup>(½)α(θ)cosθ<i>d</i>θ. These relationships are shown to reduce to those previously known for the special case of ideal concentrators.
© 1977 Optical Society of AmericaPDF Article