  We have constructed a model to describe the optical emission from
ultra-luminous X-ray sources (ULXs). We assume a binary model with a black hole
accreting matter from a Roche lobe filling companion star. We consider the
effects of radiative transport and radiative equilibrium in the irradiated
surfaces of both the star and a thin accretion disk. We have developed this
model as a tool with which to positively identify the optical counterparts of
ULXs, and subsequently derive parameters such as the black hole mass and the
luminosity class and spectral type of the counterpart. We examine the
dependence of the optical emission on these and other variables. We extend our
model to examine the magnitude variation at infrared wavelengths, and we find
that observations at these wavelengths may have more diagnostic power than in
the optical. We apply our model to existing HST observations of the candidates
for the optical counterpart of ULX X-7 in NGC 4559. All candidates could be
consistent with an irradiated star alone, but we find that a number of them are
too faint to fit with an irradiated star and disk together. Were one of these
the optical counterpart to X-7, it would display a significant temporal
variation.

Astrophysics