E-PVT: enhanced position-velocity-time scheduler for computer-controlled optical finishing with comprehensive considerations of dynamics constraints, continuity and efficiency.

Deterministic computer-controlled optical finishing is an essential approach for achieving high-quality optical surfaces. Its determinism and convergence rely heavily on precise and smooth motion control to guide the machine tool over an optical surface to correct residual errors. One widely supported and smooth motion control model is position-velocity-time (PVT), which employs piecewise cubic polynomials to describe positions. Our prior research introduced a PVT-based velocity scheduling method, demonstrating sub-nanometer level convergence in ion beam figuring (IBF) processes. However, three challenges remained. Firstly, this method relies on quadratic programming, resulting in computational intensiveness for dense tool paths. Secondly, the dynamics constraints and velocity and acceleration continuities are not comprehensively considered, limiting the full potential of PVT-based control. Thirdly, no compensation mechanism existed when dynamics constraints are exceeded. In this study, in response to these challenges, we proposed the Enhanced PVT (E-PVT) method, reducing the time complexity from O(n3) to O(n) while fully addressing dynamics constraints and continuities. A novel compensation method utilizing particle swarm optimization was proposed to address situations where dynamics constraints might be exceeded while maintaining the overall processing efficiency. Validation through simulation and experimentation confirmed the improved performance of E-PVT.

Two-step retrace error calibration removing tilt ambiguity in coherence scanning interferometry.

In interferometry measurement, the retrace error often limits its high-precision metrology applications. Retrace error calibration with tilted flats can give a relation between the retrace error and the introduced tilt angles, but there is still an ambiguity between the introduced tilt angles and the tilt terms in the created retrace error. We propose a novel, to the best of our knowledge, two-step calibration method to resolve this tilt ambiguity. It involves additional measurements of spherical mirror(s) with known curvature(s). The experiment shows that the curvature deviation due to the tilt ambiguity can be significantly reduced after applying the proposed method.

Hybrid height and slope figuring method for grazing-incidence reflective optics.

Grazing-incidence reflective optics are commonly used in synchrotron radiation and free-electron laser facilities to transport and focus the emitted X-ray beams. To preserve the imaging capability at the diffraction limit, the fabrication of these optics requires precise control of both the residual height and slope errors. However, all the surface figuring methods are height based, lacking the explicit control of surface slopes. Although our preliminary work demonstrated a one-dimensional (1D) slope-based figuring model, its 2D extension is not straightforward. In this study, a novel 2D slope-based figuring method is proposed, which employs an alternating objective optimization on the slopes in the x- and y-directions directly. An analytical simulation revealed that the slope-based method achieved smaller residual slope errors than the height-based method, while the height-based method achieved smaller residual height errors than the slope-based method. Therefore, a hybrid height and slope figuring method was proposed to further enable explicit control of both the height and slopes according to the final mirror specifications. An experiment to finish an elliptical-cylindrical mirror using the hybrid method with ion beam figuring was then performed. Both the residual height and slope errors converged below the specified threshold values, which verified the feasibility and effectiveness of the proposed ideas.

Study of interface reaction in a B4C/Cr mirror at elevated temperature using soft X-ray reflectivity.

Boron carbide is a prominent material for high-brilliance synchrotron optics as it remains stable up to very high temperatures. The present study shows a significant change taking place at 550°C in the buried interface region formed between the Cr adhesive layer and the native oxide layer present on the silicon substrate. An in situ annealing study is carried out at the Indus-1 Reflectivity beamline from room temperature to 550°C (100°C steps). The studied sample is a mirror-like boron carbide thin film of 400 Šthickness deposited with an adhesive layer of 20 ŠCr on a silicon substrate. The corresponding changes in the film structure are recorded using angle-dependent soft X-ray reflectivity measurements carried out in the region of the boron K-edge after each annealing temperature. Analyses performed using the Parratt recursive formalism reveal that the top boron carbide layer remains intact but interface reactions take place in the buried Cr-SiO2 region. After 300°C the Cr layer diffuses towards the substrate. At higher temperatures of 500°C and 550°C the Cr reacts with the native oxide layer and tends to form a low-density compound of chromium oxysilicide (CrSiOx). Depth profiling of Si and Cr distributions obtained from secondary ion mass spectroscopy measurements corroborate the layer model obtained from the soft X-ray reflectivity analyses. Details of the interface reaction taking place near the substrate region of boron carbide/Cr sample are discussed.

AMX - the highly automated macromolecular crystallography (17-ID-1) beamline at the NSLS-II.

The highly automated macromolecular crystallography beamline AMX/17-ID-1 is an undulator-based high-intensity (>5 × 1012 photons s-1), micro-focus (7 µm × 5 µm), low-divergence (1 mrad × 0.35 mrad) energy-tunable (5-18 keV) beamline at the NSLS-II, Brookhaven National Laboratory, Upton, NY, USA. It is one of the three life science beamlines constructed by the NIH under the ABBIX project and it shares sector 17-ID with the FMX beamline, the frontier micro-focus macromolecular crystallography beamline. AMX saw first light in March 2016 and started general user operation in February 2017. At AMX, emphasis has been placed on high throughput, high capacity, and automation to enable data collection from the most challenging projects using an intense micro-focus beam. Here, the current state and capabilities of the beamline are reported, and the different macromolecular crystallography experiments that are routinely performed at AMX/17-ID-1 as well as some plans for the near future are presented.

Simulation of X-ray Hartmann wavefront sensing with the Synchrotron Radiation Workshop.

X-ray wavefront measurement is an important beam diagnostic tool, especially for the diffraction-limited X-ray beam. These in situ diagnostics give a better understanding of beam imperfections, and they enable feedback for possible corrections and/or optical alignment improvements. Hartmann wavefront sensing is one of the promising techniques to perform in situ X-ray wavefront measurements. In this work, a simulation tool of the X-ray Hartmann Wavefront Sensor (HWS) is developed under the Synchrotron Radiation Workshop (SRW) framework. Using this new simulation capability, one can take advantage of the full SRW package to simulate Hartmann wavefront sensing with the beam traveling from the X-ray source to the sample through different X-ray optical components. This SRW HWS simulation tool can help to optimize the wavefront sensor parameters for a specific X-ray energy range. It can also simulate an in situ wavefront measurement experiment with a particular beamline optical layout and predict the expected results of the wavefront measurement under different beamline configurations.

Multi-tool optimization for computer controlled optical surfacing.

With the rapid development of precision technologies, the demand of high-precision optical surfaces has drastically increased. These optical surfaces are mainly fabricated with computer controlled optical surfacing (CCOS). In a CCOS process, a target surface removal profile is achieved by scheduling the dwell time for a set of machine tools. The optimized dwell time should be positive and smooth to ensure convergence to the target while considering CNC dynamics. The total run time of each machine tool is also expected to be balanced to improve the overall processing efficiency. In the past few decades, dwell time optimization for a single machine tool has been extensively developed. While the methods are applicable to multi-tool scenarios, they fail to consider the overall contributions of multiple tools simultaneously. In this paper, we conduct a systematic study on the strategies for multi-tool dwell time optimization and propose an innovative method for simultaneously scheduling dwell time for multiple tools for the first time. First, the influential factors to the positiveness and smoothness of dwell time solutions for a single machine tool are analyzed. The compensation strategies that minimize the residual while considering the CNC dynamics limit are then proposed. Afterwards, these strategies are extended to the proposed multi-tool optimization that further balances the run time of machine tools. Finally, the superiority of each strategy is carefully studied via simulation and experiment. The experiment is performed by bonnet polishing a 60 mm × 60 mm mirror with three tools of different diameters (i.e., 12 mm, 8 mm, and 5 mm). The figure error of the mirror is reduced from 45.42 nm to 11.18 nm root mean square in 13.28 min. Moreover, the measured polishing result well coincides with the estimation, which proves the effectiveness of the proposed method.

Special Issue "EUV and X-ray Wavefront Sensing".

X-ray optics are extensively used in synchrotron radiation and free-electron laser facilities, as well as in table-top laboratory sources [...].

FMX - the Frontier Microfocusing Macromolecular Crystallography Beamline at the National Synchrotron Light Source II.

Two new macromolecular crystallography (MX) beamlines at the National Synchrotron Light Source II, FMX and AMX, opened for general user operation in February 2017 [Schneider et al. (2013). J. Phys. Conf. Ser. 425, 012003; Fuchs et al. (2014). J. Phys. Conf. Ser. 493, 012021; Fuchs et al. (2016). AIP Conf. Proc. SRI2015, 1741, 030006]. FMX, the micro-focusing Frontier MX beamline in sector 17-ID-2 at NSLS-II, covers a 5-30 keV photon energy range and delivers a flux of 4.0 × 1012 photons s-1 at 1 Šinto a 1 µm × 1.5 µm to 10 µm × 10 µm (V × H) variable focus, expected to reach 5 × 1012 photons s-1 at final storage-ring current. This flux density surpasses most MX beamlines by nearly two orders of magnitude. The high brightness and microbeam capability of FMX are focused on solving difficult crystallographic challenges. The beamline's flexible design supports a wide range of structure determination methods - serial crystallography on micrometre-sized crystals, raster optimization of diffraction from inhomogeneous crystals, high-resolution data collection from large-unit-cell crystals, room-temperature data collection for crystals that are difficult to freeze and for studying conformational dynamics, and fully automated data collection for sample-screening and ligand-binding studies. FMX's high dose rate reduces data collection times for applications like serial crystallography to minutes rather than hours. With associated sample lifetimes as short as a few milliseconds, new rapid sample-delivery methods have been implemented, such as an ultra-high-speed high-precision piezo scanner goniometer [Gao et al. (2018). J. Synchrotron Rad. 25, 1362-1370], new microcrystal-optimized micromesh well sample holders [Guo et al. (2018). IUCrJ, 5, 238-246] and highly viscous media injectors [Weierstall et al. (2014). Nat. Commun. 5, 3309]. The new beamline pushes the frontier of synchrotron crystallography and enables users to determine structures from difficult-to-crystallize targets like membrane proteins, using previously intractable crystals of a few micrometres in size, and to obtain quality structures from irregular larger crystals.

RISE: robust iterative surface extension for sub-nanometer X-ray mirror fabrication.

Precision optics have been widely required in many advanced technological applications. X-ray mirrors, as an example, serve as the key optical components at synchrotron radiation and free electron laser facilities. They are rectangular silicon or glass substrates where a rectangular Clear Aperture (CA) needs to be polished to sub-nanometer Root Mean Squared (RMS) to keep the imaging capability of the incoming X-ray wavefront at the diffraction limit. The convolutional polishing model requires a CA to be extended with extra data, from which the dwell time is calculated via deconvolution. However, since deconvolution is very sensitive to boundary errors and noise, the existing surface extension methods can hardly fulfill the sub-nanometer requirement. On one hand, the figure errors in a CA were improperly modeled during the extension, leading to continuity issues along the boundary. On the other hand, uncorrectable high-frequency errors and noise were also extended. In this study, we propose a novel Robust Iterative Surface Extension (RISE) method that resolves these problems with a data fitting strategy. RISE models the figure errors in a CA with orthogonal polynomials and ensures that only correctable errors are fit and extended. Combined with boundary conditions, an iterative refinement of dwell time is then proposed to compensate the errors brought by the extension and deconvolution, which drastically reduces the estimated figure error residuals in a CA while the increase of total dwell time is negligible. To our best knowledge, RISE is the first data fitting-based surface extension method and is the first to optimize dwell time based on iterative extension. An experimental verification of RISE is given by fabricating two elliptic cylinders (10 mm × 80 mm CAs) starting from a sphere with a radius of curvature around 173 m using ion beam figuring. The figure errors in the two CAs greatly improved from 204.96 nm RMS and 190.28 nm RMS to 0.62 nm RMS and 0.71 nm RMS, respectively, which proves that RISE is an effective method for sub-nanometer level X-ray mirror fabrication.

Universal dwell time optimization for deterministic optics fabrication.

Computer-Controlled Optical Surfacing (CCOS) has been greatly developed and widely used for precision optical fabrication in the past three decades. It relies on robust dwell time solutions to determine how long the polishing tools must dwell at certain points over the surfaces to achieve the expected forms. However, as dwell time calculations are modeled as ill-posed deconvolution, it is always non-trivial to reach a reliable solution that 1) is non-negative, since CCOS systems are not capable of adding materials, 2) minimizes the residual in the clear aperture 3) minimizes the total dwell time to guarantee the stability and efficiency of CCOS processes, 4) can be flexibly adapted to different tool paths, 5) the parameter tuning of the algorithm is simple, and 6) the computational cost is reasonable. In this study, we propose a novel Universal Dwell time Optimization (UDO) model that universally satisfies these criteria. First, the matrix-based discretization of the convolutional polishing model is employed so that dwell time can be flexibly calculated for arbitrary dwell points. Second, UDO simplifies the inverse deconvolution as a forward scalar optimization for the first time, which drastically increases the solution stability and the computational efficiency. Finally, the dwell time solution is improved by a robust iterative refinement and a total dwell time reduction scheme. The superiority and general applicability of the proposed algorithm are verified on the simulations of different CCOS processes. A real application of UDO in improving a synchrotron X-ray mirror using Ion Beam Figuring (IBF) is then demonstrated. The simulation indicates that the estimated residual in the 92.3 mm × 15.7 mm CA can be reduced from 6.32 nm Root Mean Square (RMS) to 0.20 nm RMS in 3.37 min. After one IBF process, the measured residual in the CA converges to 0.19 nm RMS, which coincides with the simulation.

EUV and Hard X-ray Hartmann Wavefront Sensing for Optical Metrology, Alignment and Phase Imaging.

For more than 15 years, Imagine Optic have developed Extreme Ultra Violet (EUV) and X-ray Hartmann wavefront sensors for metrology and imaging applications. These sensors are compatible with a wide range of X-ray sources: from synchrotrons, Free Electron Lasers, laser-driven betatron and plasma-based EUV lasers to High Harmonic Generation. In this paper, we first describe the principle of a Hartmann sensor and give some key parameters to design a high-performance sensor. We also present different applications from metrology (for manual or automatic alignment of optics), to soft X-ray source optimization and X-ray imaging.

Genuine-field modeling of partially coherent X-ray imaging systems.

A genuine representation of the cross-spectral density function as a superposition of mutually uncorrelated, spatially localized modes is applied to model the propagation of spatially partially coherent light beams in X-ray optical systems. Numerical illustrations based on mode propagation with VirtualLab software are presented for imaging systems with ideal and non-ideal grazing-incidence mirrors.

Multi-pitch self-calibration measurement using a nano-accuracy surface profiler for X-ray mirror metrology.

For high accuracy X-ray mirror measurement, the analysis and corrections of minute systematic errors of the measuring instrument are required. As an X-ray mirror metrology tool, the nano-accuracy surface profiler (NSP) consists of two autocollimators (AC) serving its reference and sample beams, in which the sample-beam AC maintains a fixed distance from the mirror. In this work, the multi-pitch self-calibration method is applied to an NSP instrument to reconstruct both the mirror slope and the instrument error of the sample-beam AC through a series of x scans and pitch angle scans. It is more technically sound to apply this multi-pitch self-calibration method to a working-distance-fixed slope scanner, such as the NSP. First of all, we introduce the principle of the multi-pitch self-calibration method, discuss its ambiguities, and provide our regularization illustrated with simulations. Second, some real measurements of a spherical mirror with 10-mrad total slope are demonstrated to verify the effectiveness of the multi-pitch self-calibration technique with an NSP. Furthermore, the experimental reconstruction of the low- and high-frequency signals of the instrument error with different settings in x and pitch steps are addressed and studied in terms of repeatability, reproducibility, self-consistency, and effectiveness in compensation for single-pitch scans.

Adaptive shape control of wavefront-preserving X-ray mirrors with active cooling and heating.

This article describes the development and testing of a novel, water-cooled, active optic mirror system (called "REAL: Resistive Element Adjustable Length") that combines cooling with applied auxiliary heating, tailored to the spatial distribution of the thermal load generated by the incident beam. This technique is theoretically capable of sub-nanometer surface figure error control even at high power density. Tests conducted in an optical metrology laboratory and at synchrotron X-ray beamlines showed the ability to maintain the mirror profile to the level needed for the next generation storage rings and FEL mirrors.

Dual-tool multiplexing model of parallel computer controlled optical surfacing.

Fabrication of large optics is a time-consuming process and requires a vast investment in manpower and financial resources. Increasing the material removal rate of polishing tools and minimizing dwell time are two common ways of reducing the processing time. Indeed, the polishing efficiency can be further improved if multiple tools are used at the same time. In this Letter, we propose a dual-tool deterministic polishing model, which multiplexes the dwell time and optimizes the run parameters of two polishing tools simultaneously. The run velocities of the two tools are coordinated by boundary conditions with a velocity adjustment algorithm, and the corresponding polishing paths are studied. We demonstrate this model with a simulation of polishing one segment of the Giant Magellan Telescope, where, with the proposed dual-tool multiplexing, the processing time of an ø8.4 m mirror has been reduced by 50.54% compared with that using two tools in a sequential schedule.

Development of a position-velocity-time-modulated two-dimensional ion beam figuring system for synchrotron x-ray mirror fabrication.

With the rapid evolution of synchrotron x-ray sources, the demand for high-quality precision x-ray mirrors has greatly increased. Single nanometer shape accuracy is required to keep imaging capabilities at the diffraction limit. Ion beam figuring (IBF) has been used frequently for ultra-precision finishing of mirrors, but achieving the ultimate accuracy depends on three important points: careful alignment, accurate dwell time calculation and implementation, and accurate optical metrology. The Optical Metrology Group at National Synchrotron Light Source II has designed and built a position-velocity-time-modulated two-dimensional IBF system (PVT-IBF) with three novel characteristics: (1) a beam footprint on the mirror was used as a reference to align the coordinate systems between the metrology and the IBF hardware; (2) the robust iterative Fourier transform-based dwell time algorithm proposed by our group was applied to obtain an accurate dwell time map; and (3) the dwell time was then transformed to velocities and implemented with the PVT motion scheme. In this study, the technical aspects of the PVT-IBF systems are described in detail, followed by an experimental demonstration of the figuring results. In our first experiment, the 2D RMS in a $ 50\;{\rm mm} \times 5\;{\rm mm} $50mm×5mm clear aperture was reduced from 3.4 to 1.1 nm after one IBF run. In our second experiment, due to a 5 mm pinhole installed in front of the source, the 2D RMS in a $ 50\;{\rm mm} \times 5\;{\rm mm} $50mm×5mm clear aperture was reduced from 39.1 to 1.9 nm after three IBF runs, demonstrating that our PVT-IBF solution is an effective and deterministic figuring process.

Study on an effective one-dimensional ion-beam figuring method.

Ion-beam figuring (IBF) is a precise surface finishing technique used for the production of ultra-precision optical surfaces. In this study, we propose an effective one-dimensional IBF (1D-IBF) method approaching sub-nanometer root mean square (RMS) convergence for flat and spherical mirrors. Our process contains three key aspects. First, to minimize the misalignment of the coordinate systems between the metrology and the IBF hardware, a mirror holder is used to integrate both the sample mirror and the beam removal function (BRF) mirror. In this way, the coordinate relationship can be calculated using the measured BRF center. Second, we propose a novel constrained linear least-squares (CLLS) dwell time calculation algorithm combined with a coarse-to-fine scheme to ensure that the resultant nonnegative dwell time closely and smoothly duplicates the required removal amount. Third, considering the possible errors induced by the translation stage, we propose a dwell time slicing strategy to divide the dwell time into smaller time slices. Experiments using our approaches are performed on flat and spherical mirrors as demonstrations. Measurement results from the nano-accuracy surface profiler (NSP) show that the residual profile errors are reduced to sub-nanometer RMS for both types of mirrors while the surface roughness is not affected by the figuring process, demonstrating the effectiveness of the proposed 1D-IBF method for 1D high-precision optics fabrication.

Two-dimensional stitching interferometry for self-calibration of high-order additive systematic errors.

Stitching interferometry is performed by collecting interferometric data from overlapped sub-apertures and stitching these data together to provide a full surface map. The propagation of the systematic error in the measured subset data is one of the main error sources in stitching interferometry for accurate reconstruction of the surface topography. In this work, we propose, using the redundancy of the captured subset data, two types of two-dimensional (2D) self-calibration stitching algorithms to overcome this issue by in situ estimating the repeatable high-order additive systematic errors, especially for the application of measuring X-ray mirrors. The first algorithm, called CS short for "Calibrate, and then Stitch", calibrates the high-order terms of the reference by minimizing the de-tilted discrepancies of the overlapped subsets and then stitches the reference-subtracted subsets. The second algorithm, called SC short for "Stitch, and then Calibrate", stitches a temporarily result and then calibrates the reference from the de-tilted discrepancies of the measured subsets and the temporarily stitched result. In the implementation of 2D scans in x- and y-directions, step randomization is introduced to generate nonuniformly spaced subsets which can diminish the periodic stitching errors commonly observed in evenly spaced subsets. The regularization on low-order terms enables a highly flexible option to add the curvature and twist acquired by another system. Both numerical simulations and experiments are carried out to verify the proposed method. All the results indicate that 2D high-order repeatable additive systematic errors can be retrieved from the 2D redundant overlapped data in stitching interferometry.

Repeatability analysis of one-dimensional angular-measurement-based stitching interferometry.

Recently we presented one-dimensional Angular-measurement-based Stitching Interferometry (ASI) technique for synchrotron mirror metrology coupling an autocollimator and a white light interferometer. In this work, we conduct a further study on the measurement repeatability of this technique under different conditions, e.g. different scanning time or lengths with/without system drift. The similarity between the angle measuring stitching technique in ASI and the slope integration technique in deflectometry is addressed. The analytic expression of the height repeatability is derived while the slope noise is a zero-mean uncorrelated additive noise. In addition, we use a set of typical stationary signals from the autocollimator and the white light interferometer in a real experiment to simulate numerous virtual scans for the numerical calculation of the measurement repeatability under different measurement conditions. The simulation result predicts a link between the measurement repeatability and the scanning time with a constant speed. Moreover, it indicates that the major factor affecting the repeatability of our current ASI system is the system drift error.