At-wavelength Metrology Research Articles

At-wavelength metrology of an X-ray mirror using a downstream wavefront modulator.

At-wavelength metrology of X-ray optics plays a crucial role in evaluating the performance of optics under actual beamline operating conditions, enabling insitu diagnostics and optimization. Techniques utilizing a wavefront random modulator have gained increasing attention in recent years. However, accurately mapping the measured wavefront slope to a curved X-ray mirror surface when the modulator is downstream of the mirror has posed a challenge. To address this problem, an iterative method has been developed in this study. The results demonstrate a significant improvement compared with conventional approaches and agree with offline measurements obtained from optical metrology. We believe that the proposed method enhances the accuracy of at-wavelength metrology techniques, and empowers them to play a greater role in beamline operation and optics fabrication.

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. We conclude that while tilting 2D lenses does not seem interesting from the point of view of aberration-free focusing, tilting 1D lenses around their focusing direction can be used for smoothly fine-tuning their focal length. We demonstrate experimentally this continuous change in the apparent lens radius of curvature R: a reduction up to a factor of two and beyond is achieved and possible applications in beamline optical design are proposed.

Two-dimensional speckle technique for slope error measurements of weakly focusing reflective X-ray optics.

Speckle-based at-wavelength metrology techniques now play an important role in X-ray wavefront measurements. However, for reflective X-ray optics, the majority of existing speckle-based methods fail to provide reliable 2D information about the optical surface being characterized. Compared with the 1D information typically output from speckled-based methods, a 2D map is more informative for understanding the overall quality of the optic being tested. In this paper, we propose a method for in situ 2D absolute metrology of weakly focusing X-ray mirrors. Importantly, the angular misalignment of the mirror can be easily corrected with the proposed 2D processing procedure. We hope the speckle pattern data processing method presented here will help to extend this technique to wider applications in the synchrotron radiation and X-ray free-electron laser communities.

Rapid aberration correction for diffractive X-ray optics by additive manufacturing.

Diffraction-limited hard X-ray optics are key components for high-resolution microscopy, in particular for upcoming synchrotron radiation sources with ultra-low emittance. Diffractive optics like multilayer Laue lenses (MLL) have the potential to reach unprecedented numerical apertures (NA) when used in a crossed geometry of two one-dimensionally focusing lenses. However, minuscule fluctuations in the manufacturing process and technical limitations for high NA X-ray lenses can prevent a diffraction-limited performance. We present a method to overcome these challenges with a tailor-made refractive phase plate. With at-wavelength metrology and a rapid prototyping approach we demonstrate aberration correction for a crossed pair of MLL, improving the Strehl ratio from 0.41(2) to 0.81(4) at a numerical aperture of 3.3 × 10-3. This highly adaptable aberration-correction scheme provides an important tool for diffraction-limited hard X-ray focusing.

Real-time X-ray phase-contrast imaging using SPINNet—a speckle-based phase-contrast imaging neural network

X-ray phase-contrast imaging has become indispensable for visualizing samples with low absorption contrast. In this regard, speckle-based techniques have shown significant advantages in spatial resolution, phase sensitivity, and implementation flexibility compared with traditional methods. However, the computational cost associated with data inversion has hindered their wider adoption. By exploiting the power of deep learning, we developed a speckle-based phase-contrast imaging neural network (SPINNet) that significantly improves the imaging quality and boosts the phase retrieval speed by at least 2 orders of magnitude compared to existing methods. To achieve this performance, we combined SPINNet with a coded-mask-based technique, an enhanced version of the speckle-based method. Using this scheme, we demonstrate the simultaneous reconstruction of absorption and phase images on the order of 100 ms, where a traditional correlation-based analysis would take several minutes even with a cluster. In addition to significant improvement in speed, our experimental results show that the imaging and phase retrieval quality of SPINNet outperform existing single-shot speckle-based methods. Furthermore, we successfully demonstrate SPINNet application in x-ray optics metrology and 3D x-ray phase-contrast tomography. Our result shows that SPINNet could enable many applications requiring high-resolution and fast data acquisition and processing, such as in situ and in operando 2D and 3D phase-contrast imaging and real-time at-wavelength metrology and wavefront sensing.

Aberration characterization of x-ray optics using multi-modal ptychography and a partially coherent source

Ptychography is a scanning coherent diffraction imaging technique that provides high-resolution imaging and complete spatial information of the complex probe and object transmission function. The wavefront error caused by aberrated optics has previously been recovered using ptychography when a highly coherent source is used, but has not been demonstrated with partial coherence due to the multi-modal probe required. Here, we demonstrate that partial coherence can be accounted for in ptychographic reconstructions using the multi-modal approach and assuming that decoherence arises from either the probe or the object. This equivalence recovers coherent (or single state) reconstructions of both the probe and the object even in the presence of partial coherence. We demonstrate this experimentally by using hard x-ray ptychography with a partially coherent source to image a Siemens star test object and to also recover the wavefront error from an aberrated beryllium compound refractive lens. The source properties and resolving capabilities are analyzed, and the wavefront error results are compared with another at-wavelength metrology technique. Our work demonstrates the capability of ptychography to provide high-resolution imaging and optics characterization even in the presence of partial coherence.

Investigation of the stripe patterns from X-ray reflection optics.

X-ray beams reflected from a single layer or multilayer coating are widely used for X-ray tomography, holography, and X-ray phase contrast imaging. However, the observed irregular stripe patterns from either unfocused or defocused beams often cause disturbing artifacts and seriously deteriorate the image quality. In this work, we investigate the origin of these irregular fine structures using the wave optics theory. The connection to similar results obtained by the geometric optics theory is also presented. The proposed relation between the second derivative of the wavefront and the irregular structures was then verified by conducting at-wavelength metrology with the speckle-based wavefront sensing technique. This work will not only help to understand the formation of these irregular structures but also provide the basis for manufacturing future 'stripe-free' refection optics.

X-ray optics and beam characterization using random modulation: theory

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.

X-ray optics and beam characterization using random modulation: experiments.

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.

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 ofthe figures of merit.

Absolute metrology method of the x-ray mirror with speckle scanning technique.

As an important characterization method for beamline optics, at-wavelength metrology technology based on wavefront measurements has been developed for many years. However, the previous studies on at-wavelength metrology of reflective mirrors is limited to the indirect method. So, the accurate surface information of the mirror under test would normally be inaccessible because of lack of experimental deconvolution between the mirror and any backgrounds from upstream optics. In this study, an absolute metrology method is developed based on the speckle scanning technique. Using this method, the surface profile of the mirror can be extracted exactly from the mixed information of the entire upstream beamline. At the same time, data acquisition time can also be significantly reduced by the processing algorithm introduced in this study without sacrificing the angular sensitivity.

Optimized alignment of X-ray mirrors with an automated speckle-based metrology tool.

X-ray mirrors are widely used in beamlines and laboratories as focusing or collimating optics. As well as the highly accurate processes used to fabricate them, optimized alignment of X-ray mirrors also plays an important role in achieving an ideal X-ray beam. Currently, knife-edge scans are the most often used method for aligning X-ray mirrors, which can characterize the focal size and tune the alignment iteratively. However, knife-edge scanning provides only one-dimensional information and this method suffers from being time-consuming and requiring a high-resolution piezo translation stage. Here we describe a straightforward and non-iterative method for mirror alignment by measuring the relationship between the tilt aberration and the misaligned pitch angle, which is retrieved by an at-wavelength metrology technique using a randomly shaped wavefront modulator. Software and a graphical user interface have been developed to automate the alignment process. Combining the user-friendly interface and the flexibility of the at-wavelength metrology technique, we believe the proposed method and software can benefit researchers working at synchrotron facilities and on laboratory sources.

Auto-alignment of X-ray focusing mirrors with speckle-based at-wavelength metrology.

Significant improvements have been made in the fabrication of diffraction-limited X-ray optics used to pursue an aberration-free wavefront. Alignment of these optics plays a crucial role in the resultant beam quality. Here, we present a simple and fast alignment method based on imaging X-ray near-field speckle patterns, with experimental demonstration using a pair of Kirkpatrick-Baez mirrors. The proposed technique has the potential to be an alternative to conventional methods. It loosens the stringent demand for high-resolution scanning stages compared to conventional knife-edge scan and, hence, can be applied to nano-focusing optics. The flexibility and straightforward implementation of the method allow it to be applied to a wide range of experiments at synchrotron facilities and laboratory-based sources.

State of the Art of X-ray Speckle-Based Phase-Contrast and Dark-Field Imaging

In the past few years, X-ray phase-contrast and dark-field imaging have evolved to be invaluable tools for non-destructive sample visualisation, delivering information inaccessible by conventional absorption imaging. X-ray phase-sensing techniques are furthermore increasingly used for at-wavelength metrology and optics characterisation. One of the latest additions to the group of differential phase-contrast methods is the X-ray speckle-based technique. It has drawn significant attention due to its simple and flexible experimental arrangement, cost-effectiveness and multimodal character, amongst others. Since its first demonstration at highly brilliant synchrotron sources, the method has seen rapid development, including the translation to polychromatic laboratory sources and extension to higher-energy X-rays. Recently, different advanced acquisition schemes have been proposed to tackle some of the main limitations of previous implementations. Current applications of the speckle-based method range from optics characterisation and wavefront measurement to biomedical imaging and materials science. This review provides an overview of the state of the art of the X-ray speckle-based technique. Its basic principles and different experimental implementations as well as the the latest advances and applications are illustrated. In the end, an outlook for anticipated future developments of this promising technique is given.

Efficient high-order suppression system for a metrology beamline.

High-quality metrology with synchrotron radiation requires in particular a very high spectral purity of the incident beam. This is usually achieved by a set of transmission filters with suitable absorption edges to suppress high-order radiation of the monochromator. The at-wavelength metrology station at a BESSY-II bending-magnet collimated plane-grating monochromator (c-PGM) beamline has recently commissioned a high-order suppression system (HiOS) based on four reflections from mirrors which can be inserted into the beam path. Two pairs of mirrors are aligned parallel so as not to disturb the original beam path and are rotated clockwise and counter-clockwise. Three sets of coatings are available for the different energy ranges and the incidence angle is freely tunable to find the optimum figure of merit for maximum suppression at maximum transmission for each photon energy required. Measured performance results of the HiOS for the EUV and XUV range are compared with simulations, and applications are discussed.

Diffraction gratings metrology and ray-tracing results for an XUV Raman spectrometer at FLASH.

The extreme-ultraviolet double-stage imaging Raman spectrometer is a permanent experimental endstation at the plane-grating monochromator beamline branch PG1 at FLASH at DESY in Hamburg, Germany. This unique instrument covers the photon energy range from 20 to 200 eV with high energy resolution of about 2 to 20 meV (design values) featuring an efficient elastic line suppression as well as effective stray light rejection. Such a design enables studies of low-energy excitations like, for example, phonons in solids close to the vicinity of the elastic line. The Raman spectrometer effectively operates with four reflective off-axial parabolic mirrors and two plane-grating units. The optics quality and their precise alignment are crucial to guarantee best performance of the instrument. Here, results on a comprehensive investigation of the quality of the spectrometer diffraction gratings are presented. The gratings have been characterized by ex situ metrology at the BESSY-II Optics Laboratory, employing slope measuring deflectometry and interferometry as well as atomic force microscopy studies. The efficiency of these key optical elements has been measured at the at-wavelength metrology laboratory using the reflectometer at the BESSY-II Optics beamline. Also, the metrology results are discussed with respect to the expected resolving power of the instrument by including them in ray-tracing studies of the instrument.

Laser-heating-based active optics for synchrotron radiation applications.

Active optics has attracted considerable interest from researchers in synchrotron radiation facilities because of its capacity for x-ray wavefront correction. Here, we report a novel and efficient technique for correcting or modulating a mirror surface profile based on laser-heating-induced thermal expansion. An experimental study of the characteristics of the surface thermal deformation response indicates that the power of a milliwatt laser yields a bump height as low as the subnanometer scale and that the variation of the spot size modulates the response function width effectively. In addition, the capacity of the laser-heating technique for free-form surface modulation is demonstrated via a one-dimensional surface correction experiment. The developed method is a promising new approach toward effective x-ray active optics coupled with at-wavelength metrology techniques.

At-wavelength metrology facility for soft X-ray reflection optics

A new Optics Beamline coupled to a versatile UHV reflectometer is successfully operating at BESSY-II. It is used to carry out at-wavelength characterization and calibration of in-house produced gratings and novel nano-optical devices as well as mirrors and multilayer systems in the UV and XUV spectral region. This paper presents most recent commissioning data of the beamline and shows their correlation with initial beamline design calculations. Special attention is paid to beamline key parameters which determine the quality of the measurements such as high-order suppression and stray light behavior. The facility is open to user operation.

Speckle-based at-wavelength metrology of X-ray mirrors with super accuracy

X-ray active mirrors, such as bimorph and mechanically bendable mirrors, are increasingly being used on beamlines at modern synchrotron source facilities to generate either focused or "tophat" beams. As well as optical tests in the metrology lab, it is becoming increasingly important to optimise and characterise active optics under actual beamline operating conditions. Recently developed X-ray speckle-based at-wavelength metrology technique has shown great potential. The technique has been established and further developed at the Diamond Light Source and is increasingly being used to optimise active mirrors. Details of the X-ray speckle-based at-wavelength metrology technique and an example of its applicability in characterising and optimising a micro-focusing bimorph X-ray mirror are presented. Importantly, an unprecedented angular sensitivity in the range of two nanoradians for measuring the slope error of an optical surface has been demonstrated. Such a super precision metrology technique will be beneficial to the manufacturers of polished mirrors and also in optimization of beam shaping during experiments.

The At-Wavelength Metrology Facility at BESSY-II

The At-Wavelength Metrology Facility at BESSY-II is dedicated to short-term characterization of novel UV, EUV and XUV optical elements, such as diffraction gratings, mirrors, multilayers and nano-optical devices like reflection zone plates. It consists of an Optics Beamline PM-1 and a Reflectometer in a clean-room hutch as a fixed end station. The bending magnet Beamline is a Plane Grating Monochromator beamline (c-PGM) equipped with an SX700 monochromator. The beamline is specially tailored for efficient high-order suppression and stray light reduction. The versatile 11-axes UHV-Reflectometer can house life-sized optical elements, which are fully adjustable and of which the reflection properties can be measured in the full incidence angular range as well as in the full azimuthal angular range to determine polarization properties.