Ellipsometry is an optical analytical method based on measuring the change in polarization state of reflected or transmitted polarized light, A major challenge for those utilizing this method has been the computation of reflecting surface physical parameters of interest from the raw measured data. The methods in common use are plagued by local minima and algorithm performance. The mathematics of the light reflection has long taken advantage of some aspects of Complex Analysis. The authors have used Complex Analysis to treat the case of a metal film oil a transparent insulator substrate (nickel on BK7 glass). The work presented here explores this advanced treatment considering other combinations of metal, semiconductor, and insulator materials. While there are differences between these material combinations, all could be treated successfully with the new method. These results lay the groundwork for a set of solution algorithms which are much more powerful and convenient than existing algorithms and also provides guidance for eliminating the multiple solution problems inherent in least squares methods. (C) 2008 Published by Elsevier B.V