Periodic wrappings in coded aperture imaging

We classify all coded masks onto which cyclic difference sets can be wrapped periodically using a generalization of the Finger and Prince construction. In particular, we establish simple numerical criteria which determine whether any given mask can be wrapped periodically in this way and, for each m...

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Bibliographic Details
Published in:Nuclear instruments & methods in physics research. Section A, Accelerators, spectrometers, detectors and associated equipment Accelerators, spectrometers, detectors and associated equipment, 2014-02, Vol.738, p.132-148
Main Authors: Shutler, Paul M.E., Springham, Stuart V., Talebitaher, Alireza
Format: Article
Language:English
Subjects:
Accelerators
Classification
Coded aperture imaging
Coded mask
Coded masks
Construction
Cyclic difference set
Fingers
Hexagons
Masks
Open fraction
Signal-to-noise ratio
Singer set
Wrappings
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Summary:We classify all coded masks onto which cyclic difference sets can be wrapped periodically using a generalization of the Finger and Prince construction. In particular, we establish simple numerical criteria which determine whether any given mask can be wrapped periodically in this way and, for each mask which can, we provide explicit constructions which will produce at least one such wrapping. We show that all periodic wrappings currently reported in the literature are special cases of our explicit constructions, and we often provide simpler alternatives. Using these constructions we show that all Singer cyclic difference sets of practical size and open fraction can be wrapped exactly onto masks which are very nearly as compact and symmetrical as hexagons, without the need for pixel padding.
ISSN:0168-9002
1872-9576
DOI:10.1016/j.nima.2013.11.068