English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Signal-to-noise ratio and spatial resolution are quantitatively analysed inthe context of in-line (propagation based) X-ray phase-contrast imaging. It isknown that free-space propagation of a coherent X-ray beam from the imagedobject to the detector plane, followed by phase retrieval in accordance withPaganin's method, can increase the signal-to-noise in the resultant imageswithout deteriorating the spatial resolution. This results in violation of thenoise-resolution uncertainty principle and demonstrates "unreasonable"effectiveness of the method. On the other hand, when the process of free-spacepropagation is performed in software, using the detected intensity distributionin the object plane, it cannot reproduce the same effectiveness, due to theamplification, during free-space propagation, of photon shot noise in theobject-plane intensity. We show that the performance of Paganin's method isdetermined by just two dimensionless parameters: the Fresnel number and theratio of the phase shift to the logarithm of intensity in the object plane. Therelevant theoretical analysis is performed first, followed by computersimulations and then by a brief test using experimental images collected at asynchrotron beamline. More extensive experimental tests will be presented inthe second part of this paper.

Signal-to-noise and spatial resolution in in-line imaging. 1. Basic theory, numerical simulations and planar experimental images