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 ) .
The parameters for the best fit model are \phi ^ { * } = ( 0.0206 \pm 0.0009 ) h ^ { 3 } Mpc ^ { -3 } , M ^ { * } _ { b _ { j } } -5 \log h = ( -19.72 \pm 0.04 ) mag , \alpha = -1.05 \pm 0.02 , \beta _ { \mu } = 0.281 \pm 0.007 , \mu ^ { * } _ { e,b _ { j } } = ( 22.45 \pm 0.01 ) mag arcsec ^ { -2 } and \sigma _ { \mu } = 0.517 \pm 0.006 . \phi ^ { * } , M ^ { * } _ { b _ { j } } and \alpha equate to the conventional Schechter parameters . \beta _ { \mu } is the slope of the luminosity-surface brightness correlation , \mu _ { e,b _ { j } } ^ { * } is the characteristic effective surface brightness at M ^ { * } _ { b _ { j } } and \sigma _ { \mu } is the width of the Gaussian .

Using a BBF we explore the impact of the limiting detection isophote on classical measures of the galaxy luminosity distribution .
We demonstrate that if isophotal magnitudes are used then errors of \Delta M ^ { * } _ { b _ { j } } \sim 0.62 mags , \Delta \phi ^ { * } \sim 26 \% and \Delta \alpha \sim 0.04 are likely for \mu _ { lim,b _ { j } } = 24.0 mag arcsec ^ { -2 } .
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 \times 10 ^ { 8 } h L _ { \odot } Mpc ^ { -3 } see Cross et al .
2001 ) .
If total magnitudes are recovered then there is no change in the luminosity function within the errors for \mu _ { lim,b _ { j } } = 24.0 mag arcsec ^ { -2 } .
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 \times 10 ^ { 8 } h L _ { \odot } Mpc ^ { -3 } .