Abstracts Category : Other

Piecewise interpolation of spot diagrams

by Yali Ellen Chan

Spot diagrams are useful analytical tools fordetermining the characteristics of optical images in thegeometrical optical approximation. The most common method forcalculating a spot diagram involves the tracing of many (typicallyhundreds) of rays. A large number of rays are needed to obtain goodstatistical information describing the spot diagram, but thetracing of these rays is expensive, even on a large computer. Toreduce the time in preparing spot diagrams, interpolation methodsmay be employed. A method that interpolates the spot diagram usinga high-order polynomial has been described by Stavroudis and Feder.In this thesis, a piecewise interpolation technique is introduced,and it is compared with the Stavroudis-Feder method regarding boththe accuracy in results and the efficiency in computing time. It isshown that the present method has economical merit, but the lattergives more accurate results. The applicability of the piecewiseinterpolation approach depends on the aberrations in the system,the region within which the image forming rays are restricted, andthe interpolation range.