2.2. Systematic Searches and the Magnification Bias
While the very first lenses were found by chance (and there are still lenses found by chance from time to time; see for example Sluse et al. 2003), observational strategies were soon designed to find many more, on purpose !
Such an enterprise requires to estimate the number of lensed objects within a sample of quasars, given the selection criteria, in general a flux limit. The exercise has been done many times by many groups, following the ideas first proposed by Turner (1980). The original idea of Turner was to describe the effect of undetected lenses on the apparent evolution of quasars. As lensing amplifies the apparent luminosity of background objects, significant modifications of the observed luminosity function of quasars were suspected, in particular toward the bright end. Several ingredients are needed to carry out the calculation: (1) the spatial distribution of lenses, (2) the spatial distribution of sources, (3) a realistic mass model for the lenses in order to estimate the amplification, (4) a cosmological model and, (5) the (unlensed) luminosity function of the sources. Although none of these were precisely known in the eighties, it was quickly understood that lens statistics was a particularly sensitive function of the slope of the source luminosity function: the relative weights of the faint to bright quasar number counts give rise to the so-called "magnification bias" (see contribution by Smette, 2003 for more details). Its net effect on a flux limited sample is that the fraction of sources likely to be magnified by a given amount µ is higher for apparently bright sources than for fainter ones (see for example Schneider, Ehlers & Falco, 1992). In other words, bright sources are seen bright, because they are (more likely to be) lensed.
Based on this simple, but important finding, several surveys were started, targeting at quasars with the brightest absolute magnitude in large samples. Because at the time of the first surveys were initiated, high angular resolution was easier to achieve in the radio than in the visible, multiply imaged quasars were often the found in large radio surveys (e.g., Lawrence et al. 1986; Langston et al. 1989; Hewitt et al. 1992). The largest of these surveys so far are probably CLASS, the "Cosmic Lens All Sky Survey" and JVAS, the "Jorell Bank - VLA Astrometric Surveys" (see, among others, Patnaik et al. 1992; Myers et al. 1995; Jackson et al. 1998).
Almost in parallel with radio surveys, optical searches started and successfully yielded a significant harvest of multiply imaged quasars. Among the first ones to be discovered, were the double UM 673 (Surdej et al. 1987), the quadruple cloverleaf H 1413+117 (Magain et al. 1988), followed by some cases in the Hamburg/ESO survey for bright quasars (e.g., Wisotzki et al. 1993). The search for new cases is still ongoing, with a success rate that makes it difficult to keep track of every new discovery. Large multi-wavelengths wide field surveys are now relatively easy to carry out and the "multiband" magnification bias is studied in order to understand the effect of lensing on such data (Wyithe et al. 2003). The prospects to find many new lenses suitable for cosmological applications (e.g., in SLOAN, FIRST, GOODS, etc...) are therefore excellent. At the time of the writing of this article, several new good candidates from these surveys are under analyze.