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Estimating the angular separation between two incoherently radiatingmonochromatic point sources is a canonical toy problem to quantify spatialresolution in imaging. In recent work, Tsang {\em et al.} showed, using aFisher Information analysis, that Rayleigh's resolution limit is just anartifact of the conventional wisdom of intensity measurement in the imageplane. They showed that the optimal sensitivity of estimating the angle is onlya function of the total photons collected during the camera's integration timebut entirely independent of the angular separation itself no matter how smallit is, and found the information-optimal mode basis, intensity detection inwhich achieves the aforesaid performance. We extend the above analysis, whichwas done for a Gaussian point spread function (PSF) to a hard-aperture pupilproving the information optimality of image-plane sinc-Bessel modes, andgeneralize the result further to an arbitrary PSF. We obtain newcounterintuitive insights on energy vs. information content in spatial modes,and extend the Fisher Information analysis to exact calculations of minimummean squared error, both for Gaussian and hard aperture pupils.

Fundamental limit of resolving two point sources limited by an arbitrary point spread function