Formulation of perfect-crystal diffraction from Takagi-Taupin equations: numerical implementation in the crystalpy library.

The Takagi-Taupin equations are solved in their simplest form (zero deformation) to obtain the Bragg-diffracted and transmitted complex amplitudes. The case of plane-parallel crystal plates is discussed using a matrix model. The equations are implemented in an open-source Python library crystalpy adapted for numerical applications such as crystal reflectivity calculations and ray tracing.

X-ray focusing by bent crystals: focal positions as predicted by the crystal lens equation and the dynamical diffraction theory.

The location of the beam focus when monochromatic X-ray radiation is diffracted by a thin bent crystal is predicted by the `crystal lens equation'. This equation is derived in a general form valid for Bragg and Laue geometries. It has little utility for diffraction in Laue geometry.

Translative lens-based full-field coherent X-ray imaging.

A full-field coherent imaging approach suitable for hard X-rays based on a classical (i.e. Galilean) X-ray microscope is described.

Gauging low-dose X-ray phase-contrast imaging at a single and large propagation distance.

The interactions of a beam of hard and spatio-temporally coherent X-rays with a soft-matter sample primarily induce a transverse distribution of exit phase variations δϕ (retardations or advancements in pieces of the wave front exiting the object compared to the incoming wave front) whose free-space propagation over a distance z gives rise to intensity contrast gz. For single-distance image detection and |δϕ| ≪ 1 all-order-in-z phase-intensity contrast transfer is linear in δϕ. Here we show that ideal coherence implies a decay of the (shot-)noise-to-signal ratio in gz and of the associated phase noise as z(-1/2) and z(-1), respectively.

Optimized x-ray multilayer mirrors for single nanometer focusing.

We present numerical simulations optimizing the layer shapes of curved focusing x-ray multilayer mirrors deployed at synchrotron radiation facilities using a wave-optical model. The confocal elliptical shapes of the inner layers are corrected for refraction based on the modified Bragg law. Simulated wave amplitudes are further propagated to the focal region, promising nanometer focusing.

Wave-optical theory of nanofocusing x-ray multilayer mirrors.

We have derived a wave-optical model of curved nanofocusing x-ray multilayer mirrors used at synchrotron radiation sources, using a Takagi-Taupin-like approach. In a first approximation, the individual layers are assumed to be confocal elliptical. This assumption leads to a convenient spatial description in elliptical coordinates.

Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography.

A well-known problem in x-ray microcomputed tomography is low sensitivity. Phase contrast imaging offers an increase of sensitivity of up to a factor of 10(3) in the hard x-ray region, which makes it possible to image soft tissue and small density variations. If a sufficiently coherent x-ray beam, such as that obtained from a third generation synchrotron, is used, phase contrast can be obtained by simply moving the detector downstream of the imaged object.

Mixed transfer function and transport of intensity approach for phase retrieval in the Fresnel region.

We present a method for phase retrieval in propagation-based x-ray imaging, based on the contrast transfer and transport of intensity equation approaches. We show that the contrast transfer model does not coincide with the transport of intensity in the limit of small propagation distances, and we derive a new model that alleviates this problem. Using this model, we devise an algorithm to retrieve the phase from slowly varying samples that is valid beyond the limit of small distances.

The partial Talbot effect and its use in measuring the coherence of synchrotron X-rays.

The Talbot effect is the self-imaging, at distances D multiple of D(R), of the intensity downstream of a periodic object. Earlier work with hard synchrotron radiation X-rays showed the variation with D of the fundamental Fourier component of intensity to be a good measurement of beam coherence. Any higher-order Fourier coefficients I (D, m > 1) would be periodic with a reduced period D(Rm) = D(R)/m for an ideally coherent incident beam (partial Talbot effect).