Strategies for attaining superresolution using spectroscopic data as constraints

Abstract

In this paper, we consider the problem of attaining superresolution in the case of two point objects which are within the Rayleigh distance of each other and possess differing spectral characteristics. Furthermore, we assume that the image data is a set of intensity values as a function of both position coordinates and wavelength coordinates. If linear superposition holds, well-known linear algebraic methods of rank and eigenanalysis can be used to estimate the number of spectrally distinct objects and, in favorable cases, to estimate the spatial distribution and spectrum of each. Computer simulations of this strategy show its efficacy in detecting, spatially resolving, and spectrally identifying two impulse objects. We show that for cases where the transfer function is wavelength dependent and independent, superresolution can be attained for simulated objects within l/30th of the Rayleigh distance. ? 1985 Optical Society of America.