Abstract
If light comes from a fixed direction and is to be collected onto an absorbing body which is approximately a point or a straight line, it is well known that a mirror of parabolic profile serves the purpose efficiently. If the light is diffuse, or its direction of incidence variable, or if the absorber is not approximately a point or a straight line, the parabola is less useful. This paper describes various particular collecting problems of this more general sort, together with efficient solutions for them, mainly by means of mirrors. The subject represents a corner of geometric optics little explored until recently, in which the notion of image formation scarcely appears. A unifying principle is the invariance of the ‘Lagrange-Helmholtz’ invariant, which is related to Liouville's theorem of Hamiltonian mechanics, and there is a unifying method of construction of the mirror profiles by means of string.
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Bassett, I.M., Derrick, G.H. The collection of diffuse light onto an extended absorber. Opt Quant Electron 10, 61–82 (1978). https://doi.org/10.1007/BF00620244
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DOI: https://doi.org/10.1007/BF00620244