Bounds for optical transfer functions: Analytic results

This paper reviews, completes and extends the existing optics literature on bounds for optical transfer functions for both the one-dimensional case and the two-dimensional, radially symmetric case. Secondly, this paper sharpens the general bounds for the case of (symmetric) pupil functions that either decrease or increase as a function of the distance to the origin. Special attention is paid to the role in these bounds of the constant pupil function. Thirdly, this paper presents bounds for a particular form of superresolution in which a non-linear screen material is used, where the non-linearity is due to thermal effects. All results of this paper are analytic in nature and thus provide a useful completion to certain numerically computed bounds on optical transfer functions.