  Theoretical investigations into the deflection angle caused by microlenses
offer a direct path to uncovering principles of the cosmological microlensing
effect. This work specifically concentrates on the the probability density
function (PDF) of the light deflection angle induced by microlenses. We have
made several significant improvements to the widely used formula from Katz et
al. First, we update the coefficient from 3.05 to 1.454, resulting in a better
fit between the theoretical PDF and our simulation results. Second, we
developed an elegant fitting formula for the PDF that can replace its integral
representation within a certain accuracy, which is numerically divergent unless
arbitrary upper limits are chosen. Third, to facilitate further theoretical
work in this area, we have identified a more suitable Gaussian approximation
for the fitting formula.
