  In this paper we fit an analytic function to the Bivariate Brightness
Distribution (BBD) of galaxies. It is a combination of the classical Schechter
Function convolved with a Gaussian distribution in surface brightness: thus
incorporating the luminosity-surface brightness correlation as seen in many
recent datasets. We fit this function to a recent measurement of the BBD based
on 45,000 galaxies from the two-degree field Galaxy Redshift Survey (Cross et
al. 2001).
  Using a BBF we explore the impact of the limiting detection isophote on
classical measures of the galaxy luminosity distribution. If Gaussian corrected
magnitudes are used these change to $\Delta M^*_{b_j} \sim 0.38 $ mags, $\Delta
\phi^* \sim 11%$ and $\Delta \alpha < 0.01$ for $\mu_{lim,b_j}=24.0$ mag
arcsec$^{-2}$. Hence while the faint-end slope, $\alpha$, appears fairly robust
to surface brightness issues, both the $M^*$ and $\phi^*$ values are highly
dependent. The range over which these parameters were seen to vary is fully
consistent with the scatter in the published values, reproducing the range of
observed luminosity densities ($1.1<j_{b_j}<2.2\times10^8h L_{\odot}$Mpc$^{-3}$
see Cross et al. 2001). We conclude that surface brightness selection effects
are primarily responsible for this variation. After due consideration of these
effects, we derive a value of $j_{b_j}=2.16\times10^8h L_{\odot}$Mpc$^{-3}$.
