An appropriate Green’s function is constructed by use of the eigenfunctions of the Helmholtz equation for spherical geometry such that it vanishes on the sphere. The diffracted amplitude is expressed as an integral on the surface of the sphere that involves only the amplitude distribution in the aperture. In terms of the Laplace coefficients, the integral reduces to a product relation that allows us to define the transfer function of free space. The normal derivative of the Green’s function plays the role of the impulse response of the diffraction problem.
A. S. Marathay, "Diffraction of light from an aperture on a spherical surface," J. Opt. Soc. Am. 65, 909-913 (1975)