Power spectrum of radiation from a Gaussian source microlensed by a point mass: analytic results

Gravitational lensing deals with general-relativistic effects in the propagation of electromagnetic radiation. We consider wavelength-dependent contributions in case of a (micro)lensing of an extended Gaussian source by a point mass under standard assumptions about the incoherent emission of different source elements. Analytical expressions for the power spectrum of a microlensed radiation, which are effective in case of a large source, are obtained. If the source center, the mass, and an observer are on a straight line, the power spectrum is found in a closed form in terms of a hypergeometric function. In the case of general locations of the lens and the source, the result is presented in the form of a series. Approximate analytic expressions for the power spectrum in the case of a large source and high frequencies are obtained.