Efficient illumination of a sphere [report]

W.A. Beyer, R.J. Ryan, F.T. Adler
1973 unpublished
A sphere la to ba illuminated aa uniformly «a poeafble by N incident btaw, of light, each beam biing directed radially on the aphere and tha dlamster of cha croaa aectlon of the beta being equal to the diameter of cha aphere. Tha beams are assumed to be of the aaaa intensity. Two functions naaurlns the uniformity of the illumination *r« propoced: tjj t being the maximum of tha absolute valua of the lnteulcy on tha aphera.alnua the average lntanalty on tha aphcre; and tha function, F K , being
more » ... tion, F K , being tha squire root of the integral over the aphar* of tha square of the deviation of the Intensity item the average Intensity. Certain caaea are discussed analytically, othera computationally. Results frca the problem of T«sases relevant to this problem are summarised. Tames configuratioBa are suggested as providing favorable configurations in the absence of analytical or computatlonal results. Ee is concluded that H « 5 and 6 ihcuid be avoided. For K • « the best arrangement for the bMM euems to be at the vertices of a regular tetrahedron circumscribed about the sphere; for K • fl, tha vertices of a circumscribed anclprisa see* to be almoat tha beat. An opaque sphere of radius unity representing a peUet is to be illuminated aa uniformly a« possible by H beaae of light directed radially on O"t sphar*. The beams ar« aasumad to be of equal intensity 7. Tht •<nlta of T are selected ao that the illumination on an area dA In tha beam and normal to the «Ki« of the bus is TdA, A bsan la assumed to have a circular cross section of radius
doi:10.2172/4409711 fatcat:esoir3yvqrbw7phe6qsdce7764