  Estimating the angular separation between two incoherently radiating
monochromatic point sources is a canonical toy problem to quantify spatial
resolution in imaging. In recent work, Tsang {\em et al.} showed, using a
Fisher Information analysis, that Rayleigh's resolution limit is just an
artifact of the conventional wisdom of intensity measurement in the image
plane. They showed that the optimal sensitivity of estimating the angle is only
a function of the total photons collected during the camera's integration time
but entirely independent of the angular separation itself no matter how small
it is, and found the information-optimal mode basis, intensity detection in
which achieves the aforesaid performance. We extend the above analysis, which
was done for a Gaussian point spread function (PSF) to a hard-aperture pupil
proving the information optimality of image-plane sinc-Bessel modes, and
generalize the result further to an arbitrary PSF. We obtain new
counterintuitive insights on energy vs. information content in spatial modes,
and extend the Fisher Information analysis to exact calculations of minimum
mean squared error, both for Gaussian and hard aperture pupils.
