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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 8 — Apr. 21, 2014
  • pp: 9087–9094

Duality between noise and spatial resolution in linear systems

Timur E. Gureyev, Yakov I. Nesterets, Frank de Hoog, Gerd Schmalz, Sheridan C. Mayo, Sara Mohammadi, and Giuliana Tromba  »View Author Affiliations

Optics Express, Vol. 22, Issue 8, pp. 9087-9094 (2014)

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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.

© 2014 Optical Society of America

OCIS Codes
(070.6110) Fourier optics and signal processing : Spatial filtering
(100.5070) Image processing : Phase retrieval
(110.0110) Imaging systems : Imaging systems
(110.4280) Imaging systems : Noise in imaging systems
(110.7440) Imaging systems : X-ray imaging
(170.6960) Medical optics and biotechnology : Tomography

ToC Category:
Imaging Systems

Original Manuscript: February 25, 2014
Revised Manuscript: March 30, 2014
Manuscript Accepted: March 30, 2014
Published: April 7, 2014

Timur E. Gureyev, Yakov I. Nesterets, Frank de Hoog, Gerd Schmalz, Sheridan C. Mayo, Sara Mohammadi, and Giuliana Tromba, "Duality between noise and spatial resolution in linear systems," Opt. Express 22, 9087-9094 (2014)

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