In summer 1999, we performed a survey optimized for discovery of irregular satellites of Uranus and Neptune. We imaged 11.85 square degrees of sky and discovered 66 new outer solar system objects (not counting the three new uranian satellites). Given the very short orbital arcs of our observations, only the heliocentric distance can be reliably determined. We were able to model the radial distribution of TNOs. Our data support the idea of a strong depletion in the surface density beyond 45 AU. After fully characterizing this survey's detection efficiency as function of object magnitude and rate of motion, we find that the apparent luminosity function of the trans-neptunian region in the range m R =22-25 is steep with a best fit cumulative power law index of α 0.76 with one object per square degree estimated at magnitude R o =23.3. This steep slope, corresponding to a differential size index of q 4.8, agrees with other older and more recent analyses for the luminosity function brighter than 25th magnitude. A double power-law fit to the new data set turns out to be statistically unwarrented; this large and homogeneous data set provides no evidence for a break in the power law slope, which must eventually occur if the Bernstein et al. (2004) sky density measurements are correct.