  We calculate the quantum Fisher information (QFI) for estimating, using a
circular imaging aperture, the length of a uniformly bright incoherent line
source with a fixed mid-point and the radius of a uniformly bright incoherent
disk shaped source with a fixed center. Prolate spheroidal wavefunctions
(PSWFs) on a centered line segment and its generalized version on a centered
disk furnish the respective bases for computing the eigenstates and eigenvalues
of the one-photon density operator, from which we subsequently calculate QFI
with respect to the spatial parameters of the two sources. Zernike polynomials
provide a good set into which to project the full source wavefront, and such
classical wavefront projection data can realize quantum limited estimation
error bound in each case. We subsequently generalize our approach to analyze
sources of arbitrary brightness distributions and shapes using a certain class
of Bessel Fourier functions that are closely related to the PSWFs. We
illustrate the general approach by computing QFI for estimating the lengths of
the principal axes of a uniformly bright, centered elliptical disk.
