We have performed an ecliptic imaging survey of the Kuiper belt with our
deepest and widest field achieving a limiting flux of m(g') = 26.4, with a sky
coverage of 3.0 square-degrees. This is the largest coverage of any other
Kuiper belt survey to this depth. We detect 72 objects, two of which have been
previously observed. We have improved the Bayesian maximum likelihood fitting
technique presented in Gladman et al. (1998) to account for calibration and sky
density variations and have used this to determine the luminosity function of
the Kuiper belt. Combining our detections with previous surveys, we find the
luminosity function is well represented by a single power-law with slope alpha
= 0.65 +/- 0.05 and an on ecliptic sky density of 1 object per square-degree
brighter than m(R)=23.42 +/- 0.13. Assuming constant albedos, this slope
suggests a differential size-distribution slope of 4.25 +/- 0.25, which is
steeper than the Dohnanyi slope of 3.5 expected if the belt is in a state of
collisional equilibrium. We find no evidence for a roll-over or knee in the
luminosity function and reject such models brightward of m(R) ~ 24.6.Comment: 50 Pages, 8 Figure
