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Nonimaging optics was d2vlop2d to solve a wll—posd but narrow s2t of probl2ms1. A prototjpical xampl is th concentration of a light beam with div2rgnc half—angl2 e and cross—s2ctional area A1 into th2 minimum possible area A1 without loss of throughput or convrslj, th design of illumination sstms that convert a lambrtian source into a beam with divrg2nc half—angle e and no stray light without loss of throughput. Two class2s of algorithms have bn found which solve ths probl2ms xactl or narftj so. Ths ar summarized hr; th details can b found in Rf.2. Th first is th "string' or 'dg2—raj" m2thod (the 'Hottl string is a useful construct for calculating radiative transfer b2tw22n lamb2rtian surfacs3). It maj b succinctly charactrizd as: I ndl = constant along a string. (1) Notice that replacing string b 'ra" gives all of imaging optics. Th second class of algorithms places rflctors along th2 lines of flow of a radiation fi2ld st up bj a radiating sourc2. In cases of high sjmmtrj such as a sph2r or disc, on obtains ideal solutions in both two and thr22 dim2nsions. In cithr case rflcting and somtims rfracting 2l2mnts ar shaped in specific wags in combination to solv2 th problem. Rcntlj I addr2ss2d a wider class of problems that could not b solved bj th old methods. Hr ar two xampls: It is w2ll— known that th2 far—field illuminance from a lamb2rtian source falls off with a power of the cosine of the radiating angle cx. For example, strip radiators produce a cos3cx illuminance on a distant plane, while circular disc radiators produce a cos4cx illuminance. But suppose one desires a predetermined far—field illuminance pattern e.g., uniform illuminance? The old designs will not suffice; thej simpftj transform a lambertian source radiating over 2'rr into a lambertian source radiating over a restricted set of angles. Another example is more technical. We recall1 that older nonimaging designs require that reflectors be positioned verj c1os to th source (or r2civr). Violating this ru1 introduccs undsirab1c structure in th radiating or angular accptanc2 pattern of th d2vic, tpica1ftj a dip in th forward direction. Th limitation o th old d2signs is that thj ar too static and d2pnd on a fw paramtrs such as, th area of th beam A1 and th div2rgnc2 angl2 e. 0n2 n2ds to introduce additional dgr2s of rdom into th nonimaging designs to solve a wider class of probIms. Th purpose of this communication is to indicate th lines along which this additional frdom can b introduced.
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