THE ANALYSIS OF GRAVITATIONAL LENS SURVEYS .1. SELECTION FUNCTIONS AND AMBIGUOUS CANDIDATES

Our analysis of the four optical surveys for gravitational lenses shows that only one more lens is expected among the unidentified image pairs found in the surveys. The best candidates and the estimated likelihood that they are lenses are 0011-012 at 36%, 2355-019 at 26%, DW 0400+258 at 18%, and 1318+111 at 10% and potentially 0205 - 379 at 69% because its companion is identified as a star only by its red color. The distributions of unidentified candidates from Crampton et al. (1992) and the ESO/Liege Survey in both separation from the quasar and magnitude are consistent with the expected distribution of Galactic stars. Stars are a important source of background contamination in lens surveys, and stellar companions to quasars become more common than lensed images at the confusion limit of approximately 2.5 (1.2) mag fainter than 17 (19) V mag quasars. Cross-comparisons of candidates in the four surveys show that point-spread function asymmetries are an unreliable means of identifying lens candidates for statistical purposes because they have a very high false positive rate. These candidates must be excluded from statistical analyses of lens surveys. We estimate the completeness of the surveys is near 80% for lenses produced by E and SO galaxies and near 70% for spiral galaxies. We use the incidence of quasar-quasar pairs in the sample to estimate that the quasar-quasar correlation length is between 1 h-1(1 + z)-1 Mpc less than or similar r0 less than or similar 18 h-1 (1 + z)-1 Mpc, consistent with other measurements of quasar clustering.