Self-calibration strategies for reducing systematic slope measurement errors of autocollimators in deflectometric profilometry.

Deflectometric profilometers are used to precisely measure the form of beam shaping optics of synchrotrons and X-ray free-electron lasers. They often utilize autocollimators which measure slope by evaluating the displacement of a reticle image on a detector. Based on our privileged access to the raw image data of an autocollimator, novel strategies to reduce the systematic measurement errors by using a set of overlapping images of the reticle obtained at different positions on the detector are discussed. It is demonstrated that imaging properties such as, for example, geometrical distortions and vignetting, can be extracted from this redundant set of images without recourse to external calibration facilities. This approach is based on the fact that the properties of the reticle itself do not change - all changes in the reticle image are due to the imaging process. Firstly, by combining interpolation and correlation, it is possible to determine the shift of a reticle image relative to a reference image with minimal error propagation. Secondly, the intensity of the reticle image is analysed as a function of its position on the CCD and a vignetting correction is calculated. Thirdly, the size of the reticle image is analysed as a function of its position and an imaging distortion correction is derived. It is demonstrated that, for different measurement ranges and aperture diameters of the autocollimator, reductions in the systematic errors of up to a factor of four to five can be achieved without recourse to external measurements.

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. The use of diaboloids becomes especially interesting for the new low-emittance storage rings because the reduction of aberration becomes essential for such small sources. The validity of the toroidal and other mirror surfaces approximating the diaboloid, and the effect of the mirror magnification, are discussed.

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. The element here replaces the toroid, and in such a system provides completely aberration free, point-to-point imaging of rays from the on-axis source point. We present an analytic solution for the mirror shape in its laboratory coordinate system with zero slope at the centre, and approximate solutions, based on bending an oblique circular cone and a bent right circular cylinder, that may facilitate fabrication and metrology.

Performance optimization of a bendable parabolic cylinder collimating X-ray mirror for the ALS micro-XAS beamline 10.3.2.

The Advanced Light Source (ALS) beamline (BL) 10.3.2 is an apparatus for X-ray microprobe spectroscopy and diffraction experiments, operating in the energy range 2.4-17 keV. The performance of the beamline, namely the spatial and energy resolutions of the measurements, depends significantly on the collimation quality of light incident on the monochromator. In the BL 10.3.2 end-station, the synchrotron source is imaged 1:1 onto a set of roll slits which form a virtual source. The light from this source is collimated in the vertical direction by a bendable parabolic cylinder mirror. Details are presented of the mirror design, which allows for precision assembly, alignment and shaping of the mirror, as well as for extending of the mirror operating lifetime by a factor of ∼10. Assembly, mirror optimal shaping and preliminary alignment were performed ex situ in the ALS X-ray Optics Laboratory (XROL). Using an original method for optimal ex situ characterization and setting of bendable X-ray optics developed at the XROL, a root-mean-square (RMS) residual surface slope error of 0.31 µrad with respect to the desired parabola, and an RMS residual height error of less than 3 nm were achieved. Once in place at the beamline, deviations from the designed optical geometry (e.g. due to the tolerances for setting the distance to the virtual source, the grazing incidence angle, the transverse position) and/or mirror shape (e.g. due to a heat load deformation) may appear. Due to the errors, on installation the energy spread from the monochromator is typically a few electron-volts. Here, a new technique developed and successfully implemented for at-wavelength (in situ) fine optimal tuning of the mirror, enabling us to reduce the collimation-induced energy spread to ∼0.05 eV, is described.

High-order multilayer coated blazed gratings for high resolution soft x-ray spectroscopy.

A grand challenge in soft x-ray spectroscopy is to drive the resolving power of monochromators and spectrometers from the 10(4) achieved routinely today to well above 10(5). This need is driven mainly by the requirements of a new technique that is set to have enormous impact in condensed matter physics, Resonant Inelastic X-ray Scattering (RIXS). Unlike x-ray absorption spectroscopy, RIXS is not limited by an energy resolution dictated by the core-hole lifetime in the excitation process. Using much higher resolving power than used for normal x-ray absorption spectroscopy enables access to the energy scale of soft excitations in matter. These excitations such as magnons and phonons drive the collective phenomena seen in correlated electronic materials such as high temperature superconductors. RIXS opens a new path to study these excitations at a level of detail not formerly possible. However, as the process involves resonant excitation at an energy of around 1 keV, and the energy scale of the excitations one would like to see are at the meV level, to fully utilize the technique requires the development of monochromators and spectrometers with one to two orders of magnitude higher energy resolution than has been conventionally possible. Here we investigate the detailed diffraction characteristics of multilayer blazed gratings. These elements offer potentially revolutionary performance as the dispersive element in ultra-high resolution x-ray spectroscopy. In doing so, we have established a roadmap for the complete optimization of the grating design. Traditionally 1st order gratings are used in the soft x-ray region, but we show that as in the optical domain, one can work in very high spectral orders and thus dramatically improve resolution without significant loss in efficiency.

Development and calibration of mirrors and gratings for the soft x-ray materials science beamline at the Linac Coherent Light Source free-electron laser.

This work discusses the development and calibration of the x-ray reflective and diffractive elements for the Soft X-ray Materials Science (SXR) beamline of the Linac Coherent Light Source (LCLS) free-electron laser (FEL), designed for operation in the 500 to 2000 eV region. The surface topography of three Si mirror substrates and two Si diffraction grating substrates was examined by atomic force microscopy (AFM) and optical profilometry. The figure of the mirror substrates was also verified via surface slope measurements with a long trace profiler. A boron carbide (B4C) coating especially optimized for the LCLS FEL conditions was deposited on all SXR mirrors and gratings. Coating thickness uniformity of 0.14 nm root mean square (rms) across clear apertures extending to 205 mm length was demonstrated for all elements, as required to preserve the coherent wavefront of the LCLS source. The reflective performance of the mirrors and the diffraction efficiency of the gratings were calibrated at beamline 6.3.2 at the Advanced Light Source synchrotron. To verify the integrity of the nanometer-scale grating structure, the grating topography was examined by AFM before and after coating. This is to our knowledge the first time B4C-coated diffraction gratings are demonstrated for operation in the soft x-ray region.

High-efficiency 5000 lines/mm multilayer-coated blazed grating for extreme ultraviolet wavelengths.

Volume x-ray gratings consisting of a multilayer coating deposited on a blazed substrate can diffract with very high efficiency, even in high orders if diffraction conditions in-plane (grating) and out-of-plane (Bragg multilayer) are met simultaneously. This remarkable property, however, depends critically on the ability to create a structure with near atomic perfection. In this Letter we report on a method to produce these structures. We report measurements that show, for a 5000l/mm grating diffracting in the third order, a diffraction efficiency of 37.6% at a wavelength of 13.6nm. This work now shows a direct route to achieving high diffraction efficiency in high order at wavelengths throughout the soft x-ray energy range.

Super-resolution surface slope metrology of x-ray mirrors.

We present experimental, analytical, and numerical methods developed for reconstruction (deconvolution) of one-dimensional (1D) surface slope profiles over the spatial frequency range where the raw data are significantly perturbed due to the limited resolution of the measurement instrument. We characterize the spatial resolution properties of a profiler with the instrument's transfer function (ITF). To precisely measure the ITF, we apply a recently developed method utilizing test surfaces with 1D linear chirped height profiles of constant slope amplitude. Based on the results of the ITF calibration, we determine parameters of an analytical model for the ITF that is used in the original reconstruction software. Here, we treat surface slope metrology data obtained with the Optical Surface Measuring System (OSMS), using as a sensor an electronic autocollimator (AC) ELCOMAT-3000. The spatial resolution of the OSMS is limited by the size of the AC light-beam-collimating aperture. For the purposes of this investigation, the OSMS is equipped with a circular aperture with a diameter of 2.5 mm. This is a typical arrangement of most AC-based slope profilers developed for surface slope metrology of state-of-the-art x-ray mirrors. Using the example of surface slope metrology of two state-of-the-art elliptically shaped x-ray focusing mirrors, we demonstrate that the developed data reconstruction procedure allows us to significantly improve the accuracy of surface slope metrology with the OSMS over the spatial wavelength range from ∼1.6 mm to 7 mm. Thus, the amplitude of the quasi-periodic error characteristic of the deterministic polishing process used appears to be higher by a factor of ∼2 than is apparent from the rough metrology data. Underestimation of the surface slope errors in this spatial wavelength range can lead to serious errors in the expected performance of x-ray mirrors in synchrotron beamlines, especially at modern light sources utilizing coherent x rays, where the perturbations can lead to increased speckle-like intensity variation.

An ultrahigh-resolution soft x-ray microscope for quantitative analysis of chemically heterogeneous nanomaterials.

The analysis of chemical states and morphology in nanomaterials is central to many areas of science. We address this need with an ultrahigh-resolution scanning transmission soft x-ray microscope. Our instrument provides multiple analysis tools in a compact assembly and can achieve few-nanometer spatial resolution and high chemical sensitivity via x-ray ptychography and conventional scanning microscopy. A novel scanning mechanism, coupled to advanced x-ray detectors, a high-brightness x-ray source, and high-performance computing for analysis provide a revolutionary step forward in terms of imaging speed and resolution. We present x-ray microscopy with 8-nm full-period spatial resolution and use this capability in conjunction with operando sample environments and cryogenic imaging, which are now routinely available. Our multimodal approach will find wide use across many fields of science and facilitate correlative analysis of materials with other types of probes.

Optimization of the size and shape of the scanning aperture in autocollimator-based deflectometric profilometers.

Deflectometric profilometers based on industrial electronic autocollimators (ACs), as the ELCOMAT-3000, have become indispensable tools for precision form measurements of optical surfaces. A growing number of labs at synchrotron and free electron laser x-ray facilities are going for BESSY-II NOM-like versions of the AC-based profilometers. These tools have proven capable of characterizing state-of-the-art aspherical x-ray optics with an accuracy on the level of 100 nrad (root-mean-square) over the spatial frequency range limited by the size of the aperture used in the profilometer. Typically, a round aperture with a diameter of about 2.5 mm is used. Previous investigations have shown that with the optimally aligned 2.5-mm aperture, the spatial resolution of a NOM-like profilometer corresponding to the first zero-crossing of the optical transform function (OTF) is ∼1.2 mm. In this paper, we investigate the performance of an AC ELCOMAT-3000 for a slope profilometer with different aperture sizes and shapes. The results of angular calibration of the AC equipped with circular and rectangular apertures placed at different distances from the AC are discussed. The calibration was performed at the Physikalisch-Technische Bundesanstalt using the original experimental arrangements, also discussed in the paper. The OTF measurements with the specially developed test sample with chirped surface slope profiles were performed at the Advanced Light Source X-Ray Optics Laboratory (XROL) in application to a new optical surface measuring system under development at the XROL. In the OTF measurements, we have shown that application of a rectangular aperture with dimensions of 1.5 mm × 3 mm improves the spatial resolution in the tangential direction by a factor of ∼1.4 compared to that of the standard circular aperture of 2.5-mm diameter. We believe that the results of our investigations are crucial for reaching fundamental metrological limits in deflectometric profilometry utilizing state-of-the-art electronic autocollimators.

Environmental influences on autocollimator-based angle and form metrology.

Deflectometric profilometers are indispensable tools for the precision form measurement of beam-shaping optics of synchrotrons and x-ray free electron lasers. They are used in metrology labs for x-ray optics worldwide and are crucial for providing measurement accuracy dictated by the form tolerances for modern state-of-the-art x-ray optics. Deflectometric profilometers use surface slope (angle) to assess form, and they utilize commercial autocollimators for the contactless slope measurement. In this contribution, we discuss the influences of environmental parameters, such as temperature and air pressure, including their gradients, on high-accuracy metrology with autocollimators in profilometers. They can cause substantial systematic errors in form measurement, especially in the case of large and strongly curved optical surfaces of high dynamic range. Relative angle and form measuring errors of the order of 10-4 are to be expected. We characterize environmental influences by extended theoretical and experimental investigations and derive strategies for correcting them. We also discuss the possibility to minimize the contributions of some errors by the application of sophisticated experimental arrangements and methods. This work aims at approaching fundamental limits in autocollimator-based slope and form metrology.

Ex situ metrology and data analysis for optimization of beamline performance of aspherical pre-shaped x-ray mirrors at the advanced light source.

Super high quality aspherical x-ray mirrors with a residual slope error of ∼100 nrad (root-mean-square) and a height error of ∼1-2 nm (peak-to-valley), and even lower, are now available from a number of the most advanced vendors utilizing deterministic polishing techniques. The mirror specification for the fabrication is based on the simulations of the desired performance of the mirror in the beamline optical system and is normally given with the acceptable level of deviation of the mirror figure and finish from the desired ideal shape. For example, in the case of aspherical x-ray mirrors designed for the Advanced Light Source (ALS) QERLIN beamline, the ideal shape is defined with the beamline application (conjugate) parameters and their tolerances. In this paper, we first discuss an original procedure and dedicated software developed at the ALS X-Ray Optics Laboratory (XROL) for optimization of beamline performance of pre-shaped hyperbolic and elliptical mirrors. The optimization is based on results of ex situ surface slope metrology and consists in minimization of the mirror shape error by determining the conjugate parameters of the best-fit ideal shape within the specified tolerances. We describe novel optical metrology instrumentation, measuring techniques, and analytical methods used at the XROL for acquisition of surface slope data and optimization of the optic's beamline performance. The high efficacy of the developed experimental methods and data analysis procedures is demonstrated in results of measurements with and performance optimization of hyperbolic and elliptical cylinder mirrors designed and fabricated for the ALS QERLIN beamline.

Modular soft x-ray spectrometer for applications in energy sciences and quantum materials.

Over the past decade, the advances in grating-based soft X-ray spectrometers have revolutionized the soft X-ray spectroscopies in materials research. However, these novel spectrometers are mostly dedicated designs, which cannot be easily adopted for applications with diverging demands. Here we present a versatile spectrometer design concept based on the Hettrick-Underwood optical scheme that uses modular mechanical components. The spectrometer's optics chamber can be used with gratings operated in either inside or outside orders, and the detector assembly can be reconfigured accordingly. The spectrometer can be designed to have high spectral resolution, exceeding 10 000 resolving power when using small source (∼1µm) and detector pixels (∼5µm) with high line density gratings (∼3000 lines/mm), or high throughput at moderate resolution. We report two such spectrometers with slightly different design goals and optical parameters in this paper. We show that the spectrometer with high throughput and large energy window is particularly useful for studying the sustainable energy materials. We demonstrate that the extensive resonant inelastic X-ray scattering (RIXS) map of battery cathode material LiNi1/3Co1/3Mn1/3O2 can be produced in few hours using such a spectrometer. Unlike analyzing only a handful of RIXS spectra taken at selected excitation photon energies across the elemental absorption edges to determine various spectral features like the localized dd excitations and non-resonant fluorescence emissions, these features can be easily identified in the RIXS maps. Studying such RIXS maps could reveal novel transition metal redox in battery compounds that are sometimes hard to be unambiguously identified in X-ray absorption and emission spectra. We propose that this modular spectrometer design can serve as the platform for further customization to meet specific scientific demands.

Optimized mirror shape tuning using beam weightings based on distance, angle of incidence, reflectivity, and power.

For glancing-incidence optical systems, such as short-wavelength optics used for nano-focusing, incorporating physical factors in the calculations used for shape optimization can improve performance. Wavefront metrology, including the measurement of a mirror's shape or slope, is routinely used as input for mirror figure optimization on mirrors that can be bent, actuated, positioned, or aligned. Modeling shows that when the incident power distribution, distance from focus, angle of incidence, and the spatially varying reflectivity are included in the optimization, higher Strehl ratios can be achieved. Following the works of Maréchal and Mahajan, optimization of the Strehl ratio (for peak intensity with a coherently illuminated system) occurs when the expectation value of the phase error's variance is minimized. We describe an optimization procedure based on regression analysis that incorporates these physical parameters. This approach is suitable for coherently illuminated systems of nearly diffraction-limited quality. Mathematically, this work is an enhancement of the methods commonly applied for ex situ alignment based on uniform weighting of all points on the surface (or a sub-region of the surface). It follows a similar approach to the optimization of apodized and non-uniformly illuminated optical systems. Significantly, it reaches a different conclusion than a more recent approach based on minimization of focal plane ray errors.

Preface: The 5th International Workshop on X-ray Mirror Design, Fabrication, and Metrology.

Recent developments in synchrotron storage rings and free-electron laser-based x-ray sources with ever-increasing brightness and coherent flux have pushed x-ray optics requirements to new frontiers. This Special Topic gathers a set of articles derived from a subset of the key presentations of the International Workshop on X-ray Mirrors Fabrication (IWXM-2015) and Metrology held at Lawrence Berkley National Laboratory, Berkeley, California, USA, July 14-16, 2015. The workshop objective was to report on recent progress in x-ray synchrotron radiation mirrors fabrication as well as on new developments in related metrology tools and methods.

High precision tilt stage as a key element to a universal test mirror for characterization and calibration of slope measuring instruments.

The ultimate performance of surface slope metrology instrumentation, such as long trace profilers and auto-collimator based deflectometers, is limited by systematic errors that are increased when the entire angular range is used for metrology of significantly curved optics. At the ALS X-Ray Optics Laboratory, in collaboration with the HZB/BESSY-II and PTB (Germany) metrology teams, we are working on a calibration method for deflectometers, based on a concept of a universal test mirror (UTM) [V. V. Yashchuk et al., Proc. SPIE 6704, 67040A (2007)]. Potentially, the UTM method provides high performance calibration and accounts for peculiarities of the optics under test (e.g., slope distribution) and the experimental arrangement (e.g., the distance between the sensor and the optic under test). At the same time, the UTM calibration method is inherently universal, applicable to a variety of optics and experimental arrangements. In this work, we present the results of tests with a key component of the UTM system, a custom high precision tilt stage, which has been recently developed in collaboration with Physik Instrumente, GmbH. The tests have demonstrated high performance of the stage and its capability (after additional calibration) to provide angular calibration of surface slope measuring profilers over the entire instrumental dynamic range with absolute accuracy better than 30 nrad. The details of the stage design and tests are presented. We also discuss the foundation of the UTM method and calibration algorithm, as well as the possible design of a full scale UTM system.

Optimal measurement strategies for effective suppression of drift errors.

Drifting of experimental setups with change in temperature or other environmental conditions is the limiting factor of many, if not all, precision measurements. The measurement error due to a drift is, in some sense, in-between random noise and systematic error. In the general case, the error contribution of a drift cannot be averaged out using a number of measurements identically carried out over a reasonable time. In contrast to systematic errors, drifts are usually not stable enough for a precise calibration. Here a rather general method for effective suppression of the spurious effects caused by slow drifts in a large variety of instruments and experimental setups is described. An analytical derivation of an identity, describing the optimal measurement strategies suitable for suppressing the contribution of a slow drift described with a certain order polynomial function, is presented. A recursion rule as well as a general mathematical proof of the identity is given. The effectiveness of the discussed method is illustrated with an application of the derived optimal scanning strategies to precise surface slope measurements with a surface profiler.

A dedicated superbend x-ray microdiffraction beamline for materials, geo-, and environmental sciences at the advanced light source.

A new facility for microdiffraction strain measurements and microfluorescence mapping has been built on beamline 12.3.2 at the advanced light source of the Lawrence Berkeley National Laboratory. This beamline benefits from the hard x-radiation generated by a 6 T superconducting bending magnet (superbend). This provides a hard x-ray spectrum from 5 to 22 keV and a flux within a 1 microm spot of approximately 5x10(9) photons/s (0.1% bandwidth at 8 keV). The radiation is relayed from the superbend source to a focus in the experimental hutch by a toroidal mirror. The focus spot is tailored by two pairs of adjustable slits, which serve as secondary source point. Inside the lead hutch, a pair of Kirkpatrick-Baez (KB) mirrors placed in a vacuum tank refocuses the secondary slit source onto the sample position. A new KB-bending mechanism with active temperature stabilization allows for more reproducible and stable mirror bending and thus mirror focusing. Focus spots around 1 microm are routinely achieved and allow a variety of experiments, which have in common the need of spatial resolution. The effective spatial resolution (approximately 0.2 microm) is limited by a convolution of beam size, scan-stage resolution, and stage stability. A four-bounce monochromator consisting of two channel-cut Si(111) crystals placed between the secondary source and KB-mirrors allows for easy changes between white-beam and monochromatic experiments while maintaining a fixed beam position. High resolution stage scans are performed while recording a fluorescence emission signal or an x-ray diffraction signal coming from either a monochromatic or a white focused beam. The former allows for elemental mapping, whereas the latter is used to produce two-dimensional maps of crystal-phases, -orientation, -texture, and -strain/stress. Typically achieved strain resolution is in the order of 5x10(-5) strain units. Accurate sample positioning in the x-ray focus spot is achieved with a commercial laser-triangulation unit. A Si-drift detector serves as a high-energy-resolution (approximately 150 eV full width at half maximum) fluorescence detector. Fluorescence scans can be collected in continuous scan mode with up to 300 pixels/s scan speed. A charge coupled device area detector is utilized as diffraction detector. Diffraction can be performed in reflecting or transmitting geometry. Diffraction data are processed using XMAS, an in-house written software package for Laue and monochromatic microdiffraction analysis.

Magnetic resonance imaging with an optical atomic magnetometer.

We report an approach for the detection of magnetic resonance imaging without superconducting magnets and cryogenics: optical atomic magnetometry. This technique possesses a high sensitivity independent of the strength of the static magnetic field, extending the applicability of magnetic resonance imaging to low magnetic fields and eliminating imaging artifacts associated with high fields. By coupling with a remote-detection scheme, thereby improving the filling factor of the sample, we obtained time-resolved flow images of water with a temporal resolution of 0.1 s and spatial resolutions of 1.6 mm perpendicular to the flow and 4.5 mm along the flow. Potentially inexpensive, compact, and mobile, our technique provides a viable alternative for MRI detection with substantially enhanced sensitivity and time resolution for various situations where traditional MRI is not optimal.

Surface roughness of stainless-steel mirrors for focusing soft x rays.

We have used polished stainless steel as a mirror substrate to provide focusing of soft x rays in grazing-incidence reflection. The critical issue of the quality of the steel surface, polished and coated with gold, is discussed in detail. A comparison is made to a polished, gold-coated, electroless nickel surface, which provides a smoother finish. We used the surface height distributions, measured with an interferometric microscope and complemented by atomic-force microscope measurements, to compute power spectral densities and then to evaluate the surface roughness. The effects of roughness in reducing the specular reflectivity were verified by soft-x-ray measurements.