Statistical Treatment of Fluctuations in the Gravitational Focusing of Light Due to Stellar Masses within a Gravitational Lens

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Abstract
When light from small, distant sources in the Universe is gravitationally focused by an intervening galaxy, the gravitational lens can be influenced by the granularity of the matter distribution which is caused by the stellar (or other compact) masses in the galaxy. A largely analytic, statistical calculation for a gravitational lens due to a collection of compact masses—valid for sources of finite size and for large (as well as small) "optical depths" for the lens—is developed to treat fluctuations in the light caused by such "microfocusing" effects. Previous treatments have been either numerical simulations of the Monte Carlo type or limited to single-star (i.e., low-optical-depth) effects.