X-ray phase imaging with a laboratory source using selective reflection from a mirror
Spotlight summary: Due to their universal use in diagnostic medicine, X-ray radiographs are perhaps the most widely recognized images formed at non-visible wavelengths. In this context, "x-ray imaging" is really a shorthand for "x-ray absorption imaging" - much less well known is the complementary technique of x- ray phase imaging. While phase imaging is perhaps more widely applied in the visible spectrum (e.g., in phase contrast microscopy) the same physics apply at the much shorter x-ray wavelengths. However, the sources and detectors available at x-ray wavelengths are significantly different than in the visible, and pose experimental challenges.
One simple modification of x-ray equipment to enable phase imaging involves the placement of an edge aperture in front of a detector array. Due to diffraction, gradients in the x-ray phase response of an object result in deflections of a collimated incident beam. Often however, these small changes can be washed out over the angular extent of a pixel. By using the aperture to partially obscure a fraction of each pixel, it's angular extent is decreased, meaning the angular sensitivity is increased, albeit at the cost of discarding some of the available photons. This method (employed by Olivo and coworkers) can be used to construct x-ray phase images without the use of interferometric elements.
Here Pelliccia and Paganin extend on this approach by partially obscuring the pixel with an oblique mirror rather than a simple aperture. As a result, the signal which would have otherwise been lost at the aperture is redirected on to a different region of the detector array. Spatially translating (scanning) the object then results in two complementary images: a direct image, which contains the signal falling directly on to the un-obscured fraction of a row of pixels; and the reflected image, which contains photons that struck the mirror and continued to the row of the detector which is only partially in the reflected ray path.
The authors show how simple manipulation of these two images, coupled with a little instrument calibration, can be used to produce a quantitative phase image with good contrast. Specifically, the difference between the direct and reflected images is shown to be proportional to the product of the sample attenuation and the derivative of its phase response. Conveniently, the attenuation signal is also easily found as the sum of the direct and reflected images. The paper includes a very accessible derivation of this elegant method, an experimental demonstration (a housefly is imaged using a laboratory source), and a discussion of important practical considerations such as the effects of beam divergence and pixel size. I believe it will be an interesting read both for people already familiar with x-ray phase imaging and those new to the field.
Technical Division: Optical Design and Instrumentation
ToC Category: X-ray Optics
|OCIS Codes:||(100.5070) Image processing : Phase retrieval|
|(340.7440) X-ray optics : X-ray imaging|
|(340.7470) X-ray optics : X-ray mirrors|
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