This PDF file contains the front matter associated with SPIE Proceedings Volume 9209 including the Title Page, Copyright information, Table of Contents, Introduction, and Conference Committee listing.

A full wave propagation of X-rays from source to sample at a storage ring beamline requires simulation of the electron beam source and optical elements in the beamline. The finite emittance source causes the appearance of partial coherence in the wave field. Consequently, the wavefront cannot be treated exactly with fully coherent wave propagation or fully incoherent ray tracing. We have used the wavefront code Synchrotron Radiation Workshop (SRW) to perform partially coherent wavefront propagation using a parallel computing cluster at the Diamond Light Source. Measured mirror profiles have been used to correct the wavefront for surface errors.

European X-ray Free Electron Laser (XFEL) in Hamburg will be most powerful FEL source in the world. It will deliver coherent X-ray pulses with femtosecond duration and high repetition rate up to 4.5 MHz. For beam conditioning all the end stations at European XFEL will be using focusing optics, the grazing incidence KB mirrors or/and Compound Refraction Lenses (CRLs). For precise design and specification of optical components, one faces problems that require full-scale wavefront simulations, taking into account optics imperfections and diffraction effects on apertures. We present application examples of wavefront simulations for various focusing optics schemes at the European XFEL, such as extreme focusing with long KB mirrors, concurrent impact of diffraction on the apertures of the mirrors cutting the beam and quality of the mirror surfaces. status of software framework for start to end simulation for single particle imaging experiments is also described.

The ESRF Upgrade includes construction of long beamlines to use routinely nano-beams. This requires a very high demagnification of the ESRF source, which makes beamline optics design a fundamental concept for the future availability of bright and small stable beam. A summary of recent simulations for Upgrade beamlines is presented, including transfocators, bent crystals and graded multilayers. Some examples of particular calculations are described. In parallel to the Upgrade Programme, an ambitious project for the upgrade and integration of existing software and development of new toolbox is been carried out, with particular interest in beam polarization and partial coherence.

Recent updates in the “Synchrotron Radiation Workshop” physical optics computer code, including the transition to the Open Source development format, the results of the on-going collaborative development efforts in the area of X-ray optics, in particular grazing incidence mirrors, gratings and crystal monochromators, and in other areas, as well as some simulation activities for storage ring and X-ray free-electron laser sources are reported. Future development plans are discussed.

The current status of the software package PHASE for the propagation of coherent light pulses along a synchrotron radiation beamline is presented. PHASE is based on an asymptotic expansion of the Fresnel-Kirchhoff integral (stationary phase approximation) which is usually truncated at the 2nd order. The limits of this approximation as well as possible extensions to higher orders are discussed. The accuracy is benchmarked against a direct integration of the Fresnel-Kirchhoff integral. Long range slope errors of optical elements can be included by means of 8th order polynomials in the optical element coordinates w and l. Only recently, a method for the description of short range slope errors has been implemented. The accuracy of this method is evaluated and examples for realistic slope errors are given. PHASE can be run either from a built-in graphical user interface or from any script language. The latter method provides substantial flexibility. Optical elements including apertures can be combined. Complete wave packages can be propagated, as well. Fourier propagators are included in the package, thus, the user may choose between a variety of propagators. Several means to speed up the computation time were tested - among them are the parallelization in a multi core environment and the parallelization on a cluster.

A hybrid method combining ray-tracing and wavefront propagation was recently developed for X-ray optics simulation and beamline design optimization. One major application of the hybrid method is its ability to assess the effects of figure errors on the performance of focusing mirrors. In the present work, focusing profiles of mirrors with different figure errors are simulated using three available wave optics methods: the hybrid code based on the Fourier optics approach, the stationary phase approximation and a technique based on the direct Fresnel-Kirchhoff diffraction integral. The advantages and limitations of each wave optics method are discussed. We also present simulations performed using the figure errors of an elliptical cylinder mirror measured at APS using microstitching interferometry. These results show that the hybrid method provides accurate and quick evaluation of the expected mirror performance making it a useful tool for designing diffraction-limited focusing beamlines.

We present an open source python based ray tracing tool that offers several useful features in graphical presentation, material properties, advanced calculations of synchrotron sources, implementation of diffractive and refractive elements, complex (also closed) surfaces and multiprocessing. The package has many usage examples which are supplied together with the code and visualized on its web page. We exemplify the present version by modeling (i) a curved crystal analyzer, (ii) a quarter wave plate, (iii) Bragg-Fresnel optics and (iv) multiple reflective and non-sequential optics (polycapillary). The present version implements the use of OpenCL framework that executes calculations on both CPUs and GPUs. Currently, the calculations of an undulator source on a GPU show a gain of about two orders of magnitude in computing time. The development version is successful in modelling the wavefront propagation. Two examples of diffraction on a plane mirror and a plane blazed grating are given for a beam with a finite energy band.

We will present examples of applying the X-ray tracing software package McXtrace to different kinds of X-ray scattering experiments. In particular we will be focusing on time-resolved type experiments. Simulations of full scale experiments are particularly useful for this kind, especially when they are performed at an FEL-facility. Beamtime here is extremely scarce and the delay between experiment and publication is notoriously long. A major cause for the delay is the general complexity of the experiments performed. A complexity which arises from the pulsed state of the source. As an example, consider a pump-and-probe type experiment. In order to get the wanted signal from the sample the X-ray pulse from the FEL source needs to overlap in space and time with the pumping pulse inside the sample. This is made more difficult by several effects: The sample response may be dependent of the polarisation of the pumping and/or probing pulse. There may be significant time-jitter in the pulse arrival times. The composition of the sample may vary depending on local sample geometry and be modified by the probing pulse. Many of the samples considered are in a liquid state and thus have a variable geometry. ...to name some of the issues encountered. Generally more than one or all of these effects are present at once. Simulations can in these cases be used to identify distinct footprints of such distortions and thus give the experimenter a means of deconvoluting them from the signal. We will present a study of this kind along with the newest developments of the McXtrace software package.

MASH stands for Macros for the Automation of SHadow". It allows to run a set of ray-tracing simulations, for a range of photon energies for example, fully automatically. Undulator gaps, crystal angles etc. are tuned automatically. Important output parameters, such as photon flux, photon irradiance, focal spot size, bandwidth, etc. are then directly provided as function of photon energy. A photon energy scan is probably the most commonly requested one, but any parameter or set of parameters can be scanned through as well. Heat load calculations with finite element analysis providing temperatures, stress and deformations (Comsol) are fully integrated. The deformations can be fed back into the ray-tracing process simply by activating a switch. MASH tries to hide program internals such as le names, calls to pre-processors etc., so that the user (nearly) only needs to provide the optical setup. It comes with a web interface, which allows to run it remotely on a central computation server. Hence, no local installation or licenses are required, just a web browser and access to the local network. Numerous tools are provided to look at the ray-tracing results in the web-browser. The results can be also downloaded for local analysis. All files are human readable text files that can be easily imported into third-party programs for further processing. All set parameters are stored in a single human-readable file in XML format.

One of the problems often encountered in X-ray mirror manufacturing is setting proper manufacturing tolerances to guarantee an angular resolution - often expressed in terms of Point Spread Function (PSF) - as needed by the specific science goal. To do this, we need an accurate metrological apparatus, covering a very broad range of spatial frequencies, and an affordable method to compute the PSF from the metrology dataset. In the past years, a wealth of methods, based on either geometrical optics or the perturbation theory in smooth surface limit, have been proposed to respectively treat long-period profile errors or high-frequency surface roughness. However, the separation between these spectral ranges is difficult do define exactly, and it is also unclear how to affordably combine the PSFs, computed with different methods in different spectral ranges, into a PSF expectation at a given X-ray energy. For this reason, we have proposed a method entirely based on the Huygens-Fresnel principle to compute the diffracted field of real Wolter-I optics, including measured defects over a wide range of spatial frequencies. Owing to the shallow angles at play, the computation can be simplified limiting the computation to the longitudinal profiles, neglecting completely the effect of roundness errors. Other authors had already proposed similar approaches in the past, but only in far-field approximation, therefore they could not be applied to the case of Wolter-I optics, in which two reflections occur in sequence within a short range. The method we suggest is versatile, as it can be applied to multiple reflection systems, at any X-ray energy, and regardless of the nominal shape of the mirrors in the optical system. The method has been implemented in the WISE code, successfully used to explain the measured PSFs of multilayer-coated optics for astronomic use, and of a K-B optical system in use at the FERMI free electron laser.

In the early 1990’s [App. Opt. 32(19), 3344-531 (1993)], Church and Takacs pointed out that the specification of surface figure and finish of x-ray mirrors must be based on their performance in the beamline optical system. In the present work, we demonstrate the limitations of specification, characterization, and performance evaluation based on the totally statistical approach, including root-mean-square (rms) roughness and residual slope variation, evaluated over the spatial frequency bandwidths that are system specific, and a more refined statistical description of the surface morphology based on the power spectral density (PSD) distribution. We show that the limitations are fatal, especially, in the case of highly collimated coherent x-ray beams, like beams from X-ray Free Electron Lasers (XFELs). The limitations arise due to the deterministic character of the surface profile data for a definite mirror, while the specific correlation properties of the surface are essential for the performance of the entire x-ray optical system. As a possible way to overcome the problem, we treat a method, suggested in [Opt. Eng. 51(4), 046501, 2012] and based on an autoregressive moving average (ARMA) modeling of the slope measurements with a limited number of parameters. The effectiveness of the approach is demonstrated with an example peculiar to the x-ray optical systems under design at the European XFEL.

We report on the implications of the design of a Soft Matter Interfaces beamline, a long energy range canted in-vacuum undulator (IVU) beamline at National Synchrotron Light Source II, based on comparison of geometrical ray-tracing and partially coherent x-ray wavefront propagation simulation software packages, namely, SHADOW and Synchrotron Radiation Workshop (SRW). For SHADOW, we employed an SRW-generated source file which simulated spectralangular distribution and apparent source characteristics of radiation produced by a 2.8 m long IVU with a 23 mm period and allowed us to realistically estimate the beam intensity at the sample positions. We highlight the necessity to use realistic mirror surface profiles with expected slope errors as opposed to “standard” built-in SHADOW surface error options. The beamline performances at three different x-ray photon energies: 20358 eV, 10778 eV, and 2101 eV, under different focusing conditions, have been studied. We compare beamline simulations performed with both software packages. In particular, we stress that the neglect of wavefront diffraction effects in geometrical ray-tracing approach results in significant discrepancies in beam spot size and beam shape, the correct assessments of which are crucial in determining the future performance of an instrument.

Up to now simulation of perfect crystal optics in the “Synchrotron Radiation Workshop” (SRW) wave-optics computer code was not available, thus hindering the accurate modelling of synchrotron radiation beamlines containing optical components with multiple-crystal arrangements, such as double-crystal monochromators and high-energy-resolution monochromators. A new module has been developed for SRW for calculating dynamical diffraction from a perfect crystal in the Bragg case. We demonstrate its successful application to the modelling of partially-coherent undulator radiation propagating through the Inelastic X-ray Scattering (IXS) beamline of the National Synchrotron Light Source II (NSLS-II) at Brookhaven National Laboratory. The IXS beamline contains a double-crystal and a multiple-crystal highenergy- resolution monochromator, as well as complex optics such as compound refractive lenses and Kirkpatrick-Baez mirrors for the X-ray beam transport and shaping, which makes it an excellent case for benchmarking the new functionalities of the updated SRW codes. As a photon-hungry experimental technique, this case study for the IXS beamline is particularly valuable as it provides an accurate evaluation of the photon flux at the sample position, using the most advanced simulation methods and taking into account parameters of the electron beam, details of undulator source, and the crystal optics.

A “source-to-sample” wavefront propagation analysis of the Electron Spectro-Microscopy (ESM) UV / soft X-ray beamline, which is under construction at the National Synchrotron Light Source II (NSLS-II) in the Brookhaven National Laboratory, has been conducted. All elements of the beamline - insertion device, mirrors, variable-line-spacing gratings and slits - are included in the simulations. Radiation intensity distributions at the sample position are displayed for representative photon energies in the UV range (20 - 100 eV) where diffraction effects are strong. The finite acceptance of the refocusing mirrors is the dominating factor limiting the spatial resolution at the sample (by ~3 μm at 20 eV). Absolute estimates of the radiation flux and energy resolution at the sample are also obtained from the electromagnetic calculations. The analysis of the propagated UV range undulator radiation at different deflection parameter values demonstrates that within the beamline angular acceptance a slightly “red-shifted” radiation provides higher flux at the sample and better energy resolution compared to the on-axis resonant radiation of the fundamental harmonic.

Ray-tracing algorithms are used to simulate the instrumental function of a synchrotron beamline targeted to the advanced characterization of nanocrystalline materials by powder diffraction. The characteristics of the source, a bending magnet in the present case of study, and the optics influence the instrumental profile, which is a key parameter for obtaining information on the nanostructure. We combine the SHADOW simulation with the calculation of powder diffraction profiles from standard materials, into a high-level workflow environment based on the ORANGE software, allowing us to integrate data analysis fitting software with realistic information.

Until now, a treatment of dynamical diffraction from perfect crystals has been missing in the "Synchrotron Radiation Workshop" (SRW) wavefront propagation computer code despite the widespread use of crystals on X-ray synchrotron beamlines. Now a special propagator" module for calculating dynamical diffraction from a perfect crystal in the Bragg case has been written in C++, integrated into the SRW C/C++ library and made available for simulations using the Python interface of SRW. The propagator performs local processing of the frequency-domain electric field in the angular representation. A 2-D Fast Fourier Transform is used for changing the field representation from/to the coordinate representation before and after applying the crystal propagator. This ensures seamless integration of the new propagator with the existing functionalities of the SRW package, allows compatibility with existing propagators for other optical elements, and enables the simulation of complex beamlines transporting partially coherent X-rays. The code has been benchmarked by comparison with predictions made by plane-wave and spherical-wave dynamical diffraction theory. Test simulations for a selection of X-ray synchrotron beamlines are also shown.

One dimensional spatially resolved high resolution x-ray spectroscopy with spherically bent crystals and 2D pixelated detectors is an established technique on magnetic confinement fusion (MCF) experiments world wide for Doppler measurements of spatial profiles of plasma ion temperature and flow velocity. This technique is being further developed for diagnosis of High Energy Density Physics (HEDP) plasmas at laser-plasma facilities and synchrotron/x-ray free electron laser (XFEL) facilities. Useful spatial resolution (micron scale) of such small-scale plasma sources requires magnification, because of the finite pixel size of x-ray CCD detectors (13.5 μm). A von-Hamos like spectrometer using spherical crystals is capable of magnification, as well as uniform sagittal focusing across the full x-ray spectrum, and is being tested in laboratory experiments using a tungsten-target microfocus (5-10 μm) x-ray tube and 13-μm pixel x-ray CCD. A spatial resolution better than 10 μm has been demonstrated. Good spectral resolution is indicated by small differences (0.02 – 0.1 eV) of measured line widths with best available published natural line widths. Progress and status of HEDP measurements and the physics basis for these diagnostics are presented. A new type of x-ray crystal spectrometer with a convex spherically bent crystal is also reported. The status of testing of a 2D imaging microscope using matched pairs of spherical crystals with x rays will also be presented. The use of computational x-ray optics codes in development of these instrumental concepts is addressed.

Monochromatic x-ray beams improve image contrast but suffer from low intensity if produced with a flat monochromator crystal. A doubly-curved crystal makes more efficient use of the source. However, the beam shape is not conducive to imaging. A combination of a bent crystal followed by a polycapillary optic can be used to monochromatize and focus x rays to a small spot to perform monochromatic x-ray imaging with good resolution. Ray-tracing simulations have been developed which account for defects in both optics types. A comparison was made to measurements of focal spot sizes, angular divergence, and image quality parameters including resolution and contrast. Simulations support the experimental results that geometric blur is significantly reduced, and resolution enhanced, for magnification imaging with this optic combination.

X–ray phase imaging utilizes a variety of techniques to render phase information as intensity contrast and these intensity images can in some cases be processed to retrieve quantitative phase. A subset of these techniques use free space propagation to generate phase contrast and phase can be recovered by inverting differential equations governing propagation. Two techniques to generate quantitative phase reconstructions from a single phase contrast image are described in detail, along with regularization techniques to reduce the influence of noise. Lastly, a recently developed technique utilizing a binary–amplitude grid to enhance signal strength in propagation–based techniques is described.

The propagation of X-ray waves through an optical system consisting of 33 aluminum X-ray refractive lenses is considered. For solving the problem, a finite-difference method is suggested and investigated. It is shown that very small steps of the difference grid are necessary for reliable computation of propagation of X-ray waves through the system of lenses. It is shown that the wave phase is a function very quickly increasing with distance from an optical axis, after the wave has propagated through the system of lenses. If the phase is a quickly increasing function, then the wave electric field is a quickly oscillating function. We suggest and recommend using the equation for a phase function instead of the equation for an electric field. The equation for a phase function is derived.

We demonstrate a quantitative X-ray phase contrast imaging (XPCI) technique derived from propagation dependent phase change. We assume that the absorption and phase components are correlated and solve the Transport of Intensity Equation (TIE). The experimental setup is simple compared to other XPCI techniques; the only requirements are a micro-focus X-ray source with sufficient temporal coherence and an X-ray detector of sufficient spatial resolution. This method was demonstrated in three scenarios, the first of which entails identification of an index-matched sphere. A rubber and nylon sphere were immersed in water and imaged. While the rubber sphere could be plainly seen on a radiograph, the nylon sphere was only visible in the phase reconstruction. Next, the technique was applied to differentiating liquid samples. In this scenario, three liquid samples (acetone, water, and hydrogen peroxide) were analyzed using both conventional computed tomography (CT) and phase contrast CT. While conventional CT was capable of differentiating between acetone and the other two liquids, it failed to distinguish between water and hydrogen peroxide; only phase CT was capable of differentiating all three samples. Finally, the technique was applied to CT imaging of a human artery specimen with extensive atherosclerotic plaque. This scenario demonstrated the increased sensitivity to soft tissue compared to conventional CT; it also uncovered some drawbacks of the method, which will be the target of future work. In all cases, the signal-to-noise ratio of phase contrast was greatly enhanced relative to conventional attenuation-based imaging.

Existing Computed Tomography (CT) systems require full 360 rotation projections. Using the principles of lightfield imaging, only 4 projections under ideal conditions can be sufficient when the object is illuminated with multiple-point Xray sources. The concept was presented in a previous work with synthetically sampled data from a synthetic phantom. Application to real data requires precise calibration of the physical set up. This current work presents the calibration procedures along with experimental findings for the reconstruction of a physical 3D phantom consisting of simple geometric shapes. The crucial part of this process is to determine the effective distances of the X-ray paths, which are not possible or very difficult by direct measurements. Instead, they are calculated by tracking the positions of fiducial markers under prescribed source and object movements. Iterative algorithms are used for the reconstruction. Customized backprojection is used to ensure better initial guess for the iterative algorithms to start with.

The present paper reviews the X-ray grating imaging systems at home and abroad from the aspects of technological characterizations and the newest researching focus. First, not only the imaging principles and the frameworks of the typical X-ray grating imaging system based on Talbot-Lau interferometry method, but also the algorithms of retrieving the signals of attenuation, refraction and small-angle scattering are introduced. Second, the system optimizing methods are discussed, which involves mainly the relaxing the requirement of high positioning resolution and strict circumstances for gratings and designing large field of view with high resolution. Third, two and four-dimensional grating-based X-ray imaging techniques are introduced. Moreover, the trends of X-ray grating based imaging technology are discussed, especially the multiple information fusions are tried with attenuation, refraction and scattering obtained synchronously.

In the electron beam slicing scheme^{1, 2} considered for National Synchrotron Light Source II (NSLS-II) at Brookhaven National Laboratory, when a low energy electron bunch crosses from top of a high energy storage ring electron bunch, its coulomb force will kick a short slice (slicing bunch) from the core (core bunch) of the storage ring electron bunch. The short slice bunch and the long core bunch when passing through the 3 m long U20 in-vacuum undulator will radiate X-ray pulses with pulse length ~150 fs and 30 ps respectively. To separate the satellite radiation from the core radiation, we propose a conceptual optical scheme allowing for the separation. To get reliable estimates of the separation performances, we apply the Synchrotron Radiation Workshop (SRW) physical optics computer code_{3, 4} to study the wavefront propagation. As calculations show, at 7.8 keV, the separation signal-to-noise ratio can reach 5~12 and the satellite photon flux per pulse at sample can be 5000~20000 photons/0.1%BW with x-ray pulse length 150 ~ 330 fs depending on the separation method and the crossing angle between the low energy electron bunch and the high energy storage ring bunch. Since the repetition rate of the electron beam slicing system can reach 100 kHz, the average flux per second can reach 5 x ¹⁰⁸ ` 2 x 10⁹ photons/sec/0.1%BW.

A new graphic environment to drive X-ray optics simulation packages such as SHADOW and SRW is proposed. The aim is to simulate a virtual experiment, including the description of the electron beam and simulate the emitted radiation, the optics, the scattering by the sample and radiation detection. Python is chosen as common interaction language. The ingredients of the new application, a glossary of variables for optical component, the selection of visualization tools, and the integration of all these components in a high level workflow environment built on Orange are presented.

The ultrahigh energy resolution IXS spectrometer being developed at the National Synchrotron Light Source II (NSLSII) employs an innovative optical design. Its analyzer system utilizes an L-shaped laterally graded multilayer mirror in tandem with a multi-crystal arrangement. The multi-crystal arrangement explores the angular dispersion effect in extremely asymmetric Bragg reflections to achieve sub-meV energy resolution at an energy about 9.1 keV. Its angular acceptance (~ 0.1 mrad) is about two orders of magnitude lower than the spherically-bent backscattering analyzers conventionally used in other IXS spectrometers. The L-shaped laterally graded multiplayer mirror was designed to increase the angular acceptance of this new multi-crystal optics to a comparable level. It performs angular collimation of the incoming beam from about 15 mrad down to 0.1 mrad in both vertical and horizontal directions. Here we present simulations of the mirror performance and study the positioning and stability requirements in conjunction with the multicrystal energy analyzer.

Accurate physical-optics based simulation of emission, transport and use in experiments of fully- and partially-coherent X-ray radiation is essential for both designers and users of experiments at state-of-the-art light sources: low-emittance storage rings, energy-recovery linacs and free-electron lasers. To be useful for different applications, the simulations must include accurate physical models for the processes of emission, for the structures of X-ray optical elements, interaction of the radiation with samples, and propagation of scattered X-rays to a detector. Based on the “Synchrotron Radiation Workshop” (SRW) open source computer code, we are developing a simulation framework, including a graphical user interface, web interface for client-server simulations, data format for wave-optics based representation of partially-coherent X-ray radiation, and a dictionary for universal description of optical elements. Also, we are evaluating formats for sample and experimental data representation for different types of experiments and processing. The simulation framework will facilitate start-to-end simulations by different computer codes complementary to SRW, for example GENESIS and FAST codes for simulating self-amplified spontaneous emission, SHADOW and McXtrace geometrical ray-tracing codes, as well as codes for simulation of interaction of radiation with matter and data processing in experiments exploiting coherence of radiation. The development of the new framework is building on components developed for the Python-based RadTrack software, which is designed for loose coupling of multiple electron and radiation codes to enable sophisticated workflows. We are exploring opportunities for collaboration with teams pursuing similar developments at European Synchrotron Radiation Facility and the European XFEL.

We describe the new implementation in the ray-tracing code SHADOW based on a “hybrid method” developed recently. The code calculates the diffraction effects from an optical element by means of wavefront propagation, and combines the result with that from regular ray-tracing. This hybrid procedure is invoked when diffraction is present (e.g., beam clipped by an aperture or the finite size of the optics) by user demand. The code enables the simulation of mirror figure errors in the framework of wave optics. The simulation of a complete beamline based on the far-field approximation is demonstrated. The near-field propagation is also implemented for individual optics. Finally, the applicable conditions and limitations of the new code are discussed.

A recently developed technique for phase imaging using table top sources is to use multiple fine-pitch gratings. However, the strict manufacturing tolerences and precise alignment required have limited the widespread adoption of grating-based techniques. In this work, we employ a technique recently demonstrated by Bennett et al.¹ that ultilizes a single grid of much coarser pitch. Phase is extracted using Fourier processing on a single raw image taken using a focused mammography grid. The effects on the final image of varying grid, object, and detector distances, window widths, and of a variety of windowing functions, used to separate the harmonics, were investigated.