Abstract
X-ray phase contrast imaging is a very promising technique which may lead to significant advancements in medical imaging. One of the impediments to the clinical implementation of the technique is the general requirement to have an x-ray source of high coherence. The radiation physics group at UCL is currently developing an x-ray phase contrast imaging technique which works with laboratory x-ray sources. Validation of the system requires extensive modelling of relatively large samples of tissue. To aid this, we have undertaken a study of when geometrical optics may be employed to model the system in order to avoid the need to perform a computationally expensive wave optics calculation. In this paper, we derive the relationship between the geometrical and wave optics model for our system imaging an infinite cylinder. From this model we are able to draw conclusions regarding the general applicability of the geometrical optics approximation.
Highlights
It is hoped that x-ray Phase Contrast Imaging (XPCi) will provide a generational improvement in the effectiveness of mammography [1]
The only in vivo mammography program is in progress in Trieste, Italy, using the SYRMEP beam line [2]
This technique is known as coded aperture XPCi and has since been under continuous development within the radiation physics group at UCL
Summary
It is hoped that x-ray Phase Contrast Imaging (XPCi) will provide a generational improvement in the effectiveness of mammography [1]. An alternative XPCi technique employing laboratory sources was suggested by Olivo et al [3, 4] in 2007 This technique is known as coded aperture XPCi and has since been under continuous development within the radiation physics group at UCL (see references [5, 6, 3] for example). Keller [13] was the first to show that geometrical optics need not be limited to modelling objects with smoothly varying refractive index He showed that geometrical optics is an approximation to wave optics which can be made more accurate by the inclusion of higher order terms. In this paper we calculate higher order terms to show how the geometrical optics and wave optics solutions vary in predicting coded aperture XPCi images. We show some numerical examples and show conditions under which the geometrical optics model may be accurately employed
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