The ellipsometric function

for an ambient-film-substrate system is defined as the ratio of complex-amplitude reflection coefficients for the

and

polarization:
where

are functions of Fresnel interface reflection coefficients

,
r12p,
r01s, and
r12s. The pairs

and

signify the ambient-film and film-substrate interfaces. Here

is an exponential function of metric film thickness

and

is the thickness period. If the ambient and film media are transparent, the point representing

moves uniformly in a clockwise direction around the unit circle in the complex

plane as

increases from 0 to

. Because
ρr is related to

by an analytic rational function, the point representing

must trace a closed contour in the complex

plane as

traces the unit circle in the complex

plane.
The figure shows such a family of non-intersecting,
constant angle of incidence contours (CAIC) for

(normal incidence) to

(grazing incidence) for the

system at

.