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Abstract
In the application of Frieden's impulse-generating filter to super-resolution, the characteristics of the point response as well as those of the filter are seen to depend on the extent of the restricted field. Here curves are presented that show how the filter and its diffraction pattern change with field extent, and the behaviour of some pertinent figures of merit is examined under various conditions. For a given field extent it is found that (1) the resolution gain eventually increases linearly with the order M to which the point response approximates the delta function, (2) the filter transmission ratio exhibits a maximum for a certain value of M and eventually settles to the levels characteristic of the Zernike polynomials and (3) the Strehl central-irradiance ratio and the encircled-energy ratio for the restricted field drop without limit once M exceeds the superresolution threshold. The trade-off between resolution gain, central irradiance and field extent is also investigated.