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 lens figure errors retrieved by deep learning from several beam intensity images.

The phase problem in the context of focusing synchrotron beams with X-ray lenses is addressed. The feasibility of retrieving the surface error of a lens system by using only the intensity of the propagated beam at several distances is demonstrated. A neural network, trained with a few thousand simulations using random errors, can predict accurately the lens error profile that accounts for all aberrations.

X-ray beam quality after a mirror reflection: Experimental and simulated results for a toroidal mirror in a 4 generation storage-ring beamline.

Background: The surface errors found in X-ray mirrors constitute a limiting factor for preserving beam quality. This is particularly important when the X-ray beam has low emittance and a significant coherence fraction, like in newly upgraded synchrotron storage rings.

Methods: We studied the fringes observed in the image of an undulator-produced X-ray beam reflected by a high-quality toroidal mirror.

Off-axis representation of hyperbolic mirror shapes for X-ray beamlines.

Mirror-centered, closed-form expressions for hyperbolic surfaces used in X-ray beamlines have been derived. Hyperbolic mirrors create a virtual focus or source point and can be used to lengthen or shorten the effective focal distance of a compound optical system. The derivations here express off-axis segments of a hyperbolic surface in terms of the real and virtual focal distances and the incident glancing angle at the center of the mirror.

Tilting refractive x-ray lenses for fine-tuning of their focal length.

In this work, we measure and model tilted x-ray refractive lenses to investigate their effects on an x-ray beam. The modelling is benchmarked against at-wavelength metrology obtained with x-ray speckle vector tracking experiments (XSVT) at the BM05 beamline at the ESRF-EBS light source, showing very good agreement. This validation permits us to explore possible applications of tilted x-ray lenses in optical design.

A fast and lightweight tool for partially coherent beamline simulations in fourth-generation storage rings based on coherent mode decomposition.

A new algorithm to perform coherent mode decomposition of undulator radiation is proposed. It is based on separating the horizontal and vertical directions, reducing the problem by working with one-dimension wavefronts. The validity conditions of this approximation are discussed.

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.

Thermal optimization of a high-heat-load double-multilayer monochromator.

Finite-element analysis is used to study the thermal deformation of a multilayer mirror due to the heat load from the undulator beam at a low-emittance synchrotron source, specifically the ESRF-EBS upgrade beamline EBSL-2. The energy bandwidth of the double-multilayer monochromator is larger than that of the relevant undulator harmonic, such that a considerable portion of the heat load is reflected. Consequently, the absorbed power is non-uniformly distributed on the surface.

Simulations of applications using diaboloid mirrors.

The diaboloid is a reflecting surface that converts a spherical wave to a cylindrical wave. This complex surface may find application in new Advanced Light Source bending-magnet beamlines or in other beamlines that now use toroidal optics for astigmatic focusing. Here, the numerical implementation of diaboloid mirrors is described, and the benefit of this mirror in beamlines exploiting diffraction-limited storage rings is studied by ray tracing.

Diaboloidal mirrors: algebraic solution and surface shape approximations.

A new type of optical element that can focus a cylindrical wave to a point focus (or vice versa) is analytically described. Such waves are, for example, produced in a beamline where light is collimated in one direction and then doubly focused by a single optic. A classical example in X-ray optics is the collimated two-crystal monochromator, with toroidal mirror refocusing.

Design simulations of a horizontally deflecting high-heat-load monochromator.

The performance of a liquid-nitrogen-cooled high-heat-load monochromator with a horizontal scattering plane has been analysed, aiming to preserve the high quality of the X-ray beam in the vertical plane for downstream optics. Using finite-element analysis, height profiles of the crystal surface for various heat loads and the corresponding slope errors in the meridional and sagittal planes were calculated. Then the angular distortions of the reflected beam in both meridional and sagittal planes were calculated analytically and also modelled by ray tracing, revealing a good agreement of the two approaches.

Compensation of heat load deformations using adaptive optics for the ALS upgrade: a wave optics study.

A realistic wave optics simulation method has been developed to study how wavefront distortions originating from heat load deformations can be corrected using adaptive X-ray optics. Several planned soft X-ray and tender X-ray insertion-device beamlines in the Advanced Light Source upgrade rely on a common design principle. A flat, first mirror intercepts the white beam; vertical focusing is provided by a variable-line-space monochromator; and horizontal focusing comes from a single, pre-figured, adaptive mirror.

A cantilevered liquid-nitrogen-cooled silicon mirror for the Advanced Light Source Upgrade.

This paper presents a novel cantilevered liquid-nitrogen-cooled silicon mirror design for the first optic in a new soft X-ray beamline that is being developed as part of the Advanced Light Source Upgrade (ALS-U) (Lawrence Berkeley National Laboratory, USA). The beamline is optimized for photon energies between 400 and 1400 eV with full polarization control. Calculations indicate that, without correction, this design will achieve a Strehl ratio greater than 0.

A ray-tracing algorithm for ab initio calculation of thermal load in undulator-based synchrotron beamlines.

The OASYS suite and its powerful integration features are used to implement a ray-tracing algorithm to accurately calculate the thermal load in any component of an undulator-based synchrotron beamline. This is achieved by sampling and converting the SRW source of a given energy into a Shadow source and using the latter code to ray trace the full beamline. The accuracy of the algorithm is proved by reconstructing the full undulator radiation distribution through an aperture and comparing the result with direct calculaton of the total power using SRW.

Modelling phase imperfections in compound refractive lenses.

A framework based on physical optics for simulating the effect of imperfect compound refractive lenses (CRLs) upon an X-ray beam is described, taking into account measured phase errors obtained from at-wavelength metrology. A CRL stack is modelled, with increasing complexity, as a single thin phase element, then as a more realistic compound element including absorption and thickness effects, and finally adding realistic optical imperfections to the CRL. Coherent and partially coherent simulations using Synchrotron Radiation Workshop (SRW) are used to evaluate the different models, the effects of the phase errors and to check the validity of the design equations and suitability of the figures of merit.

A hierarchical approach for modeling X-ray beamlines: application to a coherent beamline.

Different approaches to simulate a modern X-ray beamline are considered. Several methodologies with increasing complexity are applied to discuss the relevant parameters that quantify the beamline performance. Parameters such as flux, dimensions and intensity distribution of the focused beam, and coherence properties are obtained from simple analytical calculations to sophisticated computer simulations using ray-tracing and wave optics techniques.

Understanding the instrumental profile of synchrotron radiation X-ray powder diffraction beamlines.

A Monte Carlo algorithm has been developed to calculate the instrumental profile function of a powder diffraction synchrotron beamline. Realistic models of all optical elements are implemented in a ray-tracing software. The proposed approach and the emerging paradigm have been investigated and verified for several existing X-ray powder diffraction beamlines.

ShadowOui: a new visual environment for X-ray optics and synchrotron beamline simulations.

A new computer environment to perform simulations on synchrotron experiments has been designed. It performs ray-tracing simulations using the popular ray-tracing code SHADOW. With this new application one can define, in a very easy and elegant way, one or several optical systems (beamlines) and perform calculations of the propagation of the X-ray beam through it.

DABAM: an open-source database of X-ray mirrors metrology.

An open-source database containing metrology data for X-ray mirrors is presented. It makes available metrology data (mirror heights and slopes profiles) that can be used with simulation tools for calculating the effects of optical surface errors in the performances of an optical instrument, such as a synchrotron beamline. A typical case is the degradation of the intensity profile at the focal position in a beamline due to mirror surface errors.

Aberration-free short focal length x-ray lenses.

We treat the problem of defining the ideal x-ray refractive lens design for point focusing of low emittance x-ray beams at third- and fourth-generation synchrotron sources. The task is accomplished by using Fermat's principle to define a lens shape that is completely free from geometrical aberrations. Current microfabrication resolution limits are identified, and a design that tolerates the inherent fabrication imperfections is proposed.

Thermal stress prediction in mirror and multilayer coatings.

Multilayer optics for X-rays typically consist of hundreds of periods of two types of alternating sub-layers which are coated on a silicon substrate. The thickness of the coating is well below 1 µm (tens or hundreds of nanometers). The high aspect ratio (∼10(7)) between the size of the optics and the thickness of the multilayer can lead to a huge number of elements (∼10(16)) for the numerical simulation (by finite-element analysis using ANSYS code).

A hybrid method for X-ray optics simulation: combining geometric ray-tracing and wavefront propagation.

A new method for beamline simulation combining ray-tracing and wavefront propagation is described. The `Hybrid Method' computes diffraction effects when the beam is clipped by an aperture or mirror length and can also simulate the effect of figure errors in the optical elements when diffraction is present. The effect of different spatial frequencies of figure errors on the image is compared with SHADOW results pointing to the limitations of the latter.

Benchmarking and validation of a Geant4-SHADOW Monte Carlo simulation for dose calculations in microbeam radiation therapy.

Microbeam radiation therapy (MRT) is a synchrotron-based radiotherapy modality that uses high-intensity beams of spatially fractionated radiation to treat tumours. The rapid evolution of MRT towards clinical trials demands accurate treatment planning systems (TPS), as well as independent tools for the verification of TPS calculated dose distributions in order to ensure patient safety and treatment efficacy. Monte Carlo computer simulation represents the most accurate method of dose calculation in patient geometries and is best suited for the purpose of TPS verification.

Anisotropic elasticity of silicon and its application to the modelling of X-ray optics.

The crystal lattice of single-crystal silicon gives rise to anisotropic elasticity. The stiffness and compliance coefficient matrix depend on crystal orientation and, consequently, Young's modulus, the shear modulus and Poisson's ratio as well. Computer codes (in Matlab and Python) have been developed to calculate these anisotropic elasticity parameters for a silicon crystal in any orientation.

Performance of a silicon monochromator under high heat load.

The performance of a cryogenically cooled double-crystal silicon monochromator was studied under high-heat-load conditions with total absorbed powers and power densities ranging from 8 to 780 W and from 8 to 240 W mm(-2), respectively. When the temperature of the first crystal is maintained close to the temperature of zero thermal expansion of silicon, the monochromator shows nearly ideal performance with a thermal slope error of 0.6 µrad.