Determining the Lensing Fraction of SDSS Quasars: Methods and Results from the Early Data Release

We present an algorithm for selecting gravitational lens candidates from amongst Sloan Digital Sky Survey (SDSS) quasars. In median Early Data Release (EDR) conditions, the algorithm allows for the recovery of pairs of equal flux point sources down to separations of $\sim 0{\farcs}7$ or with flux ratios up to $\sim$ 10:1 at a separation of $1\farcs5$. The algorithm also recovers a wide variety of plausible quad geometries. We also present a method for determining the selection function of this algorithm through the use of simulated SDSS images and introduce a method for calibrating our simulated images through truth-testing with real SDSS data. Finally, we apply our algorithm and selection function to SDSS quasars from the EDR to get an upper bound on the lensing fraction. We find 13 candidates among 5120 z $>$ 0.6 SDSS quasars, implying an observed lensing fraction of not more than 4 $\times 10^{-3}$. There is one likely lens system in our final sample, implying an observed lensing fraction of not less than $3 \times 10^{-5}$ (95% confidence levels).