The equations of ellipsometry are intractable. They have not been inve
rted, and thus require numerical techniques for solution in all but th
e simplest of reflecting surface configurations. In prior work, the au
thors have presented algorithms for creating approximate solutions for
these equations in the case of a sequence of measurements being taken
at successive times. In this paper, we extend one of these algorithms
to the case of readings taken at one time at multiple angles of incid
ence. The algorithm is described in some detail, and sample results ar
e presented. In addition, statistical means are used to assess the rel
iability of the values computed.