Abstract
We present the quantum theory of superresolution for discrete subwavelength structures. It allows to formulate, in particular, the standard quantum limit of superresolution achieved for illumination of the structure by light in coherent state. Our theory is based on discrete prolate spheroidal sequences and functions which are the proper basis set of the problem. We demonstrate that the superresolution factor is much higher for discrete structures than for continuous objects for the same signal-to-noise ratio. This result is a clear illustration of the crucial role of a priori information in superresolution problems.
Highlights
In this paper we present the quantum theory of superresolution specially developed for imaging of discrete subwavelength structures
We show that the proper basis functions for description of this problem are the discrete prolate spheroidal sequences and functions introduced by Slepian [11] and some other authors [12]
The superresolution factor for imaging discrete structures can be evaluated in terms of the point-spread function (PSF) similar to the continuous case [5]
Summary
Let us mention that the question of superresolution of discrete optical images and sampled signals in general has been discussed in the literature In this paper we present the quantum theory of superresolution specially developed for imaging of discrete subwavelength structures. We shall demonstrate that due to the discrete nature of this problem one can obtain significantly higher superresolution factor than in the continuous case for the same signal-to-noise ratio.
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