The idea behind this paper is relatively easy to get. Traditionally, x-ray imaging is examined using the 'light as particle' method of thinking. It works, and the math is easy. But nobody really examines x-ray imaging from the 'light as a wave' point of view. Recently though, there have been a number of articles looking at phase imaging for x-ray systems. This article (Wu X, Liu H, "Clinical implementation of x-ray phase-contrast imaging: Theoretical foundations and design considerations", Med Phys 30, 2169-2179 (2003)) is one of them.
It's a topic that I've been peripherally interested for a while. I've always wondered what x-ray imaging physics might look like formulated from the 'light as wave' perspective.
One thing I found interesting was that the refractive portion of the refractive index for tissue (δ, Eq 1 & 2) was much larger than the absorptive portion (β, Eq 1), the implication being that it ought to be relatively easy to do phase based imaging.
One of the interesting things in this paper is that the authors extend the theory of phase contrast imaging to real-world x-ray machines as opposed to specialized micro-focus x-ray units or monochromatic x-rays from a synchrotron (Section II.C) and end up predicting things that previous treatments did not (A Pogany, D Gao, S Wilkins, "Contrast and resolution in imaging with a microfocus x-ray source", Rev Sci Instrum 68, 2774-2782 (1997). Mammography machines fit the resolution requirements for observing phase contrast, but an x-ray tube with a smaller focal spot is needed. Still, the requirements aren't something you find in a run-of the mill x-ray unit. However, the fact that phase contrast imaging can be done with polychromatic beams is exciting.
Theory is tested by simulating a mammography imaging system to find optimal values for source-object and object/detector distances. Experiments also illustrate the exciting prospects of phase contrast imaging in mammography (Section IV).
A well written paper, with some very interesting and promising results. Some of the more complicated math has been glossed over, but details can be found in another paper by the same authors.