We present the results of a pencil-beam survey of the Kuiper Belt using the Keck 10-m telescope .
A single 0.01 square degree field is imaged 29 times for a total integration time of 4.8 hr .
Combining exposures in software allows the detection of Kuiper Belt Objects ( KBOs ) having visual magnitude m _ { V } \lesssim 27.9 .
Two new KBOs are discovered .
One object having m _ { V } = 25.5 lies at a probable heliocentric distance R \approx 33 { AU } .
The second object at m _ { V } = 27.2 is located at R \approx 44 { AU } .
Both KBOs have diameters of about 50 km , assuming comet-like albedos of 4 % .

Data from all surveys are pooled to construct the luminosity function from m _ { R } = 20 to 27 .
The cumulative number of objects per square degree , \Sigma ( < m _ { R } ) , is fitted to a power law of the form \log _ { 10 } \Sigma = \alpha ( m _ { R } -23.5 ) , where the slope \alpha = 0.52 \pm 0.02 .
Differences between slopes reported in the literature are due mainly to which survey data are incorporated in the fit , and not to the method of analysis .
The luminosity function is consistent with a power-law size distribution for objects having diameters s = 50–500 km ; d N \propto s ^ { - q } ds , where the differential size index q = 3.6 \pm 0.1 .
The distribution is such that the smallest objects possess most of the surface area , but the largest bodies contain the bulk of the mass .
We estimate to order-of-magnitude that 0.2 M _ { \oplus } and 1 \times 10 ^ { 10 } comet progenitors lie between 30 and 50 AU .
Though our inferred size index nearly matches that derived by \markcite d69Dohnanyi ( 1969 ) , it is unknown whether catastrophic collisions are responsible for shaping the size distribution .
Impact strengths may increase strongly with size from 50 to 500 km , whereas the derivation by \markcite d69Dohnanyi ( 1969 ) assumes impact strength to be independent of size .
In the present-day Belt , collisional lifetimes of KBOs having diameters 50–500 km exceed the age of the Solar System by at least 2 orders of magnitude , assuming bodies consist of solid , cohesive rock .
Implications of the absence of detections of classical KBOs beyond 50 AU are discussed .