Weighted truncation of power series and the computation of chromatic aberration coefficients

In keeping with the recent growth of interest in the use of analytic computational methods in the analysis of the behavior of optical systems, this paper reports on the incorporation of chromatic dependence into these schemes. A novel prescription for the truncation of power series in several variables (which is also of value outside this context) is introduced in order to avoid much unnecessary computation. Subsequently, a process is devised for computing chromatic aberration coefficients to arbitrary orders for symmetric systems composed of homogeneous lenses and mirrors. It is found that, in less than the time required for the analytical analysis of a system at two distinct wavelengths, this process can yield the required results for the entire visible spectrum and beyond, if necessary.