  To complete the Tolman surface brightness test on the reality of the
expansion of the Universe, we need to measure accurately the surface brightness
profiles of the high-redshift galaxy sample. We, therefore, investigate the
effects of various sizes of point-spread-functions composed of telescope
diffraction, CCD pixel resolutions, and ground-based seeing on the measurements
of mean surface brightness. We have done the calculations using two synthetic
galaxies of effective radii of 0.70" and 0.25" with point-spread functions of
0.1, 0.3, and 0.9 arcseconds. We have also compared actual observations of
three high-redshift galaxies in the cluster Cl 1324 + 3011 (z = 0.76) made both
with the Keck telescopes in seeing of about 0.9" and with HST which has a PSF
that is approximately ten times smaller. The conclusion is that HST data can be
used as far into the galaxy image as a Petrosian metric radius of eta = 1.3
magnitudes, whereas the ground-based data will have systematic errors of up to
2.9 magnitudes in the mean surface brightness at eta values of less than 2.2
magnitudes. In the final section, we compare the differences in derived average
surface brightness for nearly circular galaxy images compared with highly
flattened images. The comparison is made by using the two reduction procedures
of (1) integrating the profile curves using circular apertures, and (2)
approximating an ``equivalent circular'' galaxy that is highly elongated by
using an ``effective'' radius of sqrt{ab}, where a and b are the semi-major and
semi-minor axis, respectively, of the best-fitting ellipse. The conclusion is
that the two methods of reduction give nearly identical results and that either
method can be used to analyze the low and high-redshift galaxy samples used in
the Tolman test.
