Optical depths for the magnification and positions of multiple quasar images created by a cosmological distribution of isolated elliptical potential wells are computed. Introducing a core radius into a singular potential well can reduce the optical depth for multiple imaging by a large factor. Strong lenses predominantly produce three images (of which two are opposed) at low magnification and five images at high magnification when amplification bias may become important. In practice, amplification bias is important only for bright (B < 18 mag) quasars. In most instances one image is deamplified by the core. Marginal lenses produce mainly three comparatively bright images, but with relatively small probability. As an application, we estimate a probability ∼10⁻⁶ that a given galaxy at zL ∼ 0.04 will lens a background quasar (e.g., 2237 + 0305).
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Kochanek et al. (1987) studied this question.