X-ray Bragg magnifier microscope as a linear shift invariant imaging system: image formation and phase retrieval

Abstract

We present the theoretical description of the image formation with the in-line germanium Bragg Magnifier Microscope (BMM) and the first successful phase retrieval of X-ray holograms recorded with this imaging system. The conditions under which the BMM acts as a linear shift invariant system are theoretically explained and supported by the experiment. Such an approach simplifies the mathematical treatment of the image formation and reconstruction as complicated propagation of the wavefront onto inclined planes can be avoided. Quantitative phase retrieval is demonstrated using a test sample and a proof of concept phase imaging of a spider leg is also presented.

Calculations and surface quality measurements of high-asymmetry angle x-ray crystal monochromators for advanced x-ray imaging and metrological applications

“…Four pieces of highly asymmetric germanium crystal imaging monochromators built in a Vchannel configuration were prepared by planar technology and successfully applied for high-resolution holographic imaging using synchrotron radiation sources. 15,16 One disadvantage of such a system is the finite distance between crystals magnifying in the horizontal and vertical directions which causes the effective propagation distances between the horizontal and the vertical directions to be different. 16 This problem can be solved by further development of monolithic V-shaped 17 or Z-shaped 18 monochromators, for which we are able to set the horizontal and the vertical diffractions as close together as possible while preserving the inline configuration.…”

“…15,16 One disadvantage of such a system is the finite distance between crystals magnifying in the horizontal and vertical directions which causes the effective propagation distances between the horizontal and the vertical directions to be different. 16 This problem can be solved by further development of monolithic V-shaped 17 or Z-shaped 18 monochromators, for which we are able to set the horizontal and the vertical diffractions as close together as possible while preserving the inline configuration. The very important parameter of highly asymmetric monochromators as image magnifiers is the crystal surface quality, because the long-range surface undulations 9 deteriorate the final image quality.…”

Laboratory-based multi-modal X-ray microscopy and micro-CT with Bragg magnifiers

“…To understand this point we must briefly review the principles of image formation in a Bragg Magnifier Microscope. More details can be found in [13].…”

“…More recently, thanks to advances in detection technology and crystal quality, x-ray imaging and microscopy based on x-ray Bragg magnifiers (reffered in text as Bragg Magnifier Microscope, BMM) became a reliable alternative to conventional approaches [8]. Recent results demonstrated the impressive capabilities of an BMM [9][10][11][12][13] for high resolution x-ray microscopy, holography and micro-CT (computed tomography), with synchrotron sources. In this work we report on the experimental demonstration of X-ray microscopy with Bragg Magnifier in a conventional X-ray laboratory setup.…”

Development of variable-magnification X-ray Bragg optics

“…The X-ray Bragg magnifier based on asymmetric diffraction at a nearly perfect crystal (Kohra, 1972) is a useful optical element for X-ray radiology and microscopy, and has been used at synchrotron facilities, for example, for X-ray microtomography (m-CT) (Stampanoni et al, 2002(Stampanoni et al, , 2003, analyzerbased phase-contrast imaging (Modregger et al, 2006;Hö nnicke & Cusatis, 2007;Hirano, 2011) and inline holography (Vagovič et al, 2013(Vagovič et al, , 2014. One of the most striking features of the X-ray Bragg magnifier is that it can cover a wide range of resolution from submicrometer (Kobayashi et al, 2001;Schä fer & Kö hler, 2003) up to submillimeter, thus filling the gap between X-ray microscopy and radiology.…”