Variability of microlensing light curves I. Autocorrelation method and the calculation of the correlated deflection probability.

The recently observed microlensing variations in the gravitational lens system 2237+0305 has renewed the interest in gravitational microlensing. Most theoretical investigations of microlensing are based on a numerical scheme called ray-shooting. We present here a new method for calculating the autocorrelation function of microlensing light curves and the magnification fluctuations, following in part a method presented by Deguchi & Watson (1987). In the present paper, we outline the method and investigate in detail its major ingredient, the probability distribution for the difference of the deflection angles of two light rays with fixed separation in the lens plane, the so-called correlated deflection probability. The application to the calculation of autocorrelation functions and magnification fluctuations, in particular the application to the system 2237+0305, is presented in a forthcoming paper.