X‐ray near‐field speckle‐based phase‐sensing approaches provide efficient means of characterizing optical elements. Presented here is a theoretical review of several of these speckle methods within the framework of optical characterization, and a generalization of the concept is provided. As is also demonstrated experimentally in a parallel paper [Berujon, Cojocaru, Piault, Celestre, Roth, Barrett & Ziegler (2020), J. Synchrotron Rad.27, (this issue)], the methods theoretically developed here can be applied to different beams and optics and within a variety of situations where at‐wavelength metrology is desired. By understanding the differences between the various processing methods, it is possible to find and implement the most suitable approach for each metrology scenario.
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. A latest-generation X-ray nanofocusing beamline for coherent applications (ID16A at the ESRF) has been chosen to study in detail the issues related to highly demagnifying synchrotron sources and exploiting the beam coherence. The performance of the beamline is studied for two storage rings: the old ESRF-1 (emittance 4000 pm) and the new ESRF-EBS (emittance 150 pm). In addition to traditional results in terms of flux and beam sizes, an innovative study on the partial coherence properties based on the propagation of coherent modes is presented. The different algorithms and methodologies are implemented in the software suite OASYS. These are discussed with emphasis placed upon the their benefits and limitations of each.
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 parallel paper [Berujon, Cojocaru, Piault, Celestre, Roth, Barrett & Ziegler (2020), J. Synchrotron Rad.27, 284–292] reviewed theoretically some of the available processing schemes for X‐ray wavefront sensing based on random modulation. Shown here are experimental applications of the technique for characterizing both refractive and reflective optical components. These fast and accurate X‐ray at‐wavelength metrology methods can assist the manufacture of X‐ray optics that transport X‐ray beams with a minimum amount of wavefront distortion. It is also recalled how such methods can facilitate online optimization of active optics.
We introduce a new X-ray speckle-vector tracking method for phase imaging, which is based on the wavelet transform. Theoretical and experimental results show that this method, which is called wavelet-transform-based speckle-vector tracking (WSVT), has stronger noise robustness and higher efficiency compared with the cross-correlation-based method. In addition, the WSVT method has the controllable noise reduction and can be applied with fewer scan steps. These unique features make the WSVT method suitable for measurements of large image sizes and phase shifts, possibly under low-flux conditions, and has the potential to broaden the applications of speckle tracking to new areas requiring faster phase imaging and real-time wavefront sensing, diagnostics, and characterization.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.