  We are working on the development of a method for optimizing wide-field X-ray
telescope mirror prescriptions, including polynomial coefficients, mirror shell
relative displacements, and (assuming 4 focal plane detectors) detector
placement along the optical axis and detector tilt. With our methods, we hope
to reduce number of Monte-Carlo ray traces required to search the
multi-dimensional design parameter space, and to lessen the complexity of
finding the optimum design parameters in that space. Regarding higher order
polynomial terms as small perturbations of an underlying Wolter I optic design,
we begin by using the results of Monte-Carlo ray traces to devise trial
analytic functions, for an individual Wolter I mirror shell, that can be used
to represent the spatial resolution on an arbitrary focal surface. We then
introduce a notation and tools for Monte-Carlo ray tracing of a polynomial
mirror shell prescription which permits the polynomial coefficients to remain
symbolic. In principle, given a set of parameters defining the underlying
Wolter I optics, a single set of Monte-Carlo ray traces are then sufficient to
determine the polymonial coefficients through the solution of a large set of
linear equations in the symbolic coefficients. We describe the present status
of this development effort.
