Information-theoretical resolution limit of a far-field subwavelength diffraction system

Abstract

A general analytical model is established to study the change in the signal-to-noise ratio (SNR) of the spatially noisy optical signal after passing through a subwavelength-aperture system. The corresponding spatial resolution limit is redefined based on Shannon's theory of information, and the expression is analytically given derived from nonparaxial vectoral diffraction theory. Contrary to the conventional wisdom, it is demonstrated both analytically and numerically that the SNR of the optical signal will increase with the propagation distance due to the presence of the subwavelength aperture and the corresponding spatial resolution could, thus, exceed the traditional Abbe-Rayleigh diffraction limit even though when the input SNR is low. The theoretical result provides perspectives for optimizing optical resolution and is general, that can be extended to other sciences, such as x-ray imaging and quantum imaging.