Localization measures for high-aperture wavefields based on pupil moments

A variety of different measures for the localization of high-aperture scalar wavefields, based on the moments of the pupil, are compared. These are applied to particular examples such as Gaussian beams in the complex focus model, and aplanatic and Herschel focusing systems. These measures can be used to investigate focusing properties of different optical systems, and the use of apodizers and super-resolving masks. The optimum apodizer for achieving minimum axial second moment width is investigated.