Open AccessDuality between noise and spatial resolution in linear systems
Author(s) -
T. E. Gureyev,
Yakov Nesterets,
Frank de Hoog,
Gerd Schmalz,
Sheridan C Mayo,
Sara Mohammadi,
Giuliana Tromba
Publication year - 2014
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.22.009087
Subject(s) - point spread function , optics , scaling , image resolution , linear system , optical transfer function , invariant (physics) , noise (video) , physics , convolution (computer science) , quantum noise , mathematical analysis , mathematics , computer science , quantum , quantum mechanics , geometry , image (mathematics) , artificial intelligence , artificial neural network
It is shown that in a broad class of linear systems, including general linear shift-invariant systems, the spatial resolution and the noise satisfy a duality relationship, resembling the uncertainty principle in quantum mechanics. The product of the spatial resolution and the standard deviation of output noise in such systems represents a type of phase-space volume that is invariant with respect to linear scaling of the point-spread function, and it cannot be made smaller than a certain positive absolute lower limit. A corresponding intrinsic "quality" characteristic is introduced and then evaluated for the cases of some popular imaging systems, including computed tomography, generic image convolution and phase-contrast imaging. It is shown that in the latter case the spatial resolution and the noise can sometimes be decoupled, potentially leading to a substantial increase in the imaging quality.