The novel application of symbolic computing techniques to analytical lens design described in this proposal has the potential to dramatically increase the capabilities and performance of current optical design programs. Merit functions based on symbolically calculated Nth-order aberration theory expressions can be rapidly evaluated as they consist of rational polynomials based on Gaussian (paraxial) ray-trace data. This will result in greatly increased speed over programs whose merit functions are calculated from multiple skew ray traces. These features facilitate the construction of accurate functional approximations to the merit function surface which in turn allow novel mathematical methods to be used to analytically search the configuration space for globally optimum solutions. In addition merit functions of this type give detailed information as to the magnitude of error created by each element in the optical system. This information will allow standard optimization algorithms to adjust system parameters more efficiently and "intelligently". The promise of analytical lens design has not been fulfilled due to the inability of humans to deal with the sheer size of the expressions involved. The great power of current symbolic calculation programs now makes possible the effective use of this theory to significantly advance the art of optical design.
