We have performed an ecliptic imaging survey of the Kuiper belt with our deepest and widest field achieving a limiting flux of m ( g ^ { \prime } ) _ { 50 \% } \sim 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 \pm 0.05 and an on ecliptic sky density of 1 object per square-degree brighter than m _ { R } = 23.42 \pm 0.13 .
Assuming constant albedos , this slope suggests a differential size-distribution slope of 4.25 \pm 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 ) \sim 24.6 .