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At least 451 records · Page 25

Safeguards-Informed Hybrid Imagery Dataset [Poster]

Deep Learning computer vision models require many thousands of properly labelled images for training, which is especially challenging for safeguards and nonproliferation, given that safeguards-relevant images are typically rare due to the sensitivity and limited availability of the technologies. Creating relevant images through real-world staging is costly and limiting in scope. Expert-labeling is expensive, time consuming, and error prone. We aim to develop a data set of both realworld and synthetic images that are relevant to the nuclear safeguards domain that can be used to support multiple data science research questions. In the process of developing this data, we aim to develop a novel workflow to validate synthetic images using machine learning explainability methods, testing among multiple computer vision algorithms, and iterative synthetic data rendering. We will deliver one million images – both real-world and synthetically rendered – of two types uranium storage and transportation containers with labelled ground truth and associated adversarial examples.

97 MATHEMATICS AND COMPUTING↗

The Uranium-Containing and Thorium-Containing Anions Studied by Photoelectron Spectroscopy

An in-depth knowledge of actinide chemistry is fundamental to many aspects of nuclear science and technology, including the synthesis and processing of materials and the remediation of waste disposal sites. Among the actinides, the chemical bonding behaviors of actinium and thorium resemble those of the transition metals; the 5f-electrons of protactinium, uranium, neptunium, and plutonium often play important roles in their bonding; and among the still heavier elements, their bonding tends to mimic the lanthanide elements in terms of electron shielding and their f-electron contributions. Bonding that involves 5f-electrons, however, is especially important, in part because of the significance of uranium and plutonium, but also because these elements are among the few where f-electron participation in bonding is relatively common. This work focused on studying uranium-containing and thorium-containing anions in the gas phase using negative ion photoelectron spectroscopy. Since this technique directly probed valence electrons, it was uniquely positioned to address open questions regarding molecular bonding and electron configurations. A particularly important issue concerned how bonding in actinide-containing molecules was affected by modifications to their actinide atoms’ environment, i.e., due to their interaction with ligands. A closely related question was how actinide atoms’ suborbitals were qualitatively reordered and their energies quantitatively shifted as a result of their ligated environments. These were especially relevant issues in regard to uranium due to it having multiple possible oxidation states (OS) and the potential for 5f electron participation in bonding. The effects of ligands on oxidation states and 5f-orbital energies in uranium bonding was expected to be pronounced. Both ligands and excess electrons were seen as probes of actinide atoms within actinide-containing molecules. Our strategy for advancing knowledge of chemical bonding in the actinide-containing species utilized the synergy between experiments and theory, where in some cases experimental results validated theory and where in others computational results assisted in interpreting experiments. Calculations on actinide systems are terrifically challenging due to large spin-orbit interactions, relativistic effects, and just the sheer number of electrons involved. Even in the simplest species, e.g., U and U2, the most sophisticated, modern calculations carried out by the most experienced theorists often only approximate experimentally-measured values, such as electron affinities. For theory to provide confident predictions that can be used to solve real problems it needed an iterative and ultimately corrective mechanism by which its methods can develop further. Experiments can be used to identify when theory has failed; whereupon the subsequent process of using the experiment-theory interplay can be used to find the cause of the failure. Upon fixing it in one case, different test species can be proposed and studied by the experiment-theory combination to determine whether the problem has been corrected. Thus, experiments not only measure the values of molecular properties, they also provide navigational 3 beacons that keep computations off the reefs in an otherwise dark sea with few reference points. Experimental measurements in the actinide field are not only important, they are in actuality essential to computational progress. While it was not always possible to compare the theoreticallydetermined quantity of interest directly with the same experimentally-measured observable, it was usually possible to compare consequential properties that are both calculable and measurable. In the work completed here electron affinities and electronic state spacings were often sensitive consequential parameters. Reasonable agreement between measured and computational values signaled that a calculation that was very likely to be on-track. We had established collaborative relationships with five computational groups, all of which have expertise in computational actinide chemistry. Their PI’s are L. Cheng, D. Dixon, L. Gagliardi, K. Peterson, and B. Vlaisavljevich. Our close interaction with our theory partners led to us suggesting systems to them and them to us. This reciprocal interaction between our experimental and their computational results was among the most important strengths of this work and was a thread woven throughout. Even though anion photoelectron spectroscopic studies are conducted on anions, much of the information that they provide, pertains to the electronic structure of the neutral counterparts of those anions; among these are electron affinities and electronically excited state spacings. Our experimental tools included several specialized ion sources for forming the anionic species of interest, a mass spectrometer for identifying and mass-selecting them, and an anion photoelectron spectrometer for determining their electron affinities (EA) and characterizing the electronic states of the selected anions’ neutral counterparts. Anion photoelectron spectroscopy is conducted by crossing a mass-selected beam of anions with a fixed-frequency laser beam and energy-analyzing the resultant photodetached electrons. The photodetachment process is governed by the energyconserving relationship: hν = EBE + EKE, where hν is the photon’s energy, EBE is the electron binding (photodetachment transition) energy, and EKE is the electron’s kinetic energy. In our apparatus mass-selection is accomplished via time-of-flight mass spectrometry (TOF-MS), electron energy analysis is achieved with either a magnetic bottle or by velocity mapped imaging. Photodetachment of electrons from anions is implemented via either Nd:YAG or excimer lasers. The photodetachment transition energy, i.e., the EBE, between the ground vibrational and electronic state of an anion and the ground vibrational and electronic state of that anion’s neutral counterpart is the adiabatic electron affinity (EA) of that neutral molecule. Likewise, photodetachment transitions between the ground vibrational and electronic state of an anion and the various electronically-excited states of that anion’s corresponding neutral map the electronic spectrum of that neutral species, i.e., the spectral spacings in the photoelectron spectrum are a mirror image of the neutral’s electronic spectrum. It was, of course, crucial to be able to form the anionic species of interest. There, we had a particularly broad field of anion sources from which to choose. These included several variants of pulsed laser vaporization (LV), laser photoemission, infrared desorption plus photoemission, pulsed arc discharge (PACIS), electrospray ionization (ESI), and Rydberg electron transfer (RET). Each of these anion sources were readily combined with, i.e., connected to, the anion photoelectron spectroscopic portion of our apparatus as described above. Among the sources that utilize lasers, visible light for LV sources as well as IR for desorption sources are provided by Nd:YAG lasers. Ultraviolet photons are provided by both Nd:YAG and excimer lasers, whereas the excitation wavelengths for RET experiments come from two Nd:YAG-pumped dye lasers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Data Collection and Analysis Challenges and Mitigation Strategies for Quantitative Human Factors Research Studies in Nuclear Power Plant Modernization

The United States (U.S.) Department of Energy (DOE) Light Water Reactor Sustainability (LWRS) program Plant Modernization Pathway is conducting targeted research and development (R&D) to address aging and reliability concerns with the legacy instrumentation and control and related information systems of the U.S. LWR fleet. In this effort, the application of human factors engineering (HFE) provides an important role in ensuring new digital plant technologies enable broad innovation and business improvement with continued operational safety. Evaluation is a key activity in HFE, which often occurs iteratively through the system design lifecycle. While qualitative methods are important in collecting information of how users perform tasks through observations, quantitative methods are equally important in assessing system design based on performance. In collecting and analyzing this quantitative data, there are notable challenges in the nuclear HFE domain that may threaten the validity and reliability of the inferences made in these studies. Notable challenges include small sample size and limited resources, large error variance and small effect size, an “adding test features to losing degrees of freedom” dilemma, non-normal distribution, and heterogeneity of variance. The results in control room usability studies are often statistically non-significant, which makes it hard to interpret. This work discusses these challenges across different scientific viewpoints and provides real-world examples of these challenges in practice. Collectively, the objective of this work is to position these challenges to the larger data science community as a means of identifying future opportunities to address these issues.

99 GENERAL AND MISCELLANEOUS↗

Ringing Artifact Reduction Method for Ultrasound Reconstruction Using Multi-Agent Consensus Equilibrium

Non-destructive characterization of multi-layered structures that can be accessed from only a single side is important for applications such as well-bore integrity inspection. Existing methods related to Synthetic Aperture Focusing Technique (SAFT) rapidly produce acceptable results but with significant artifacts. Recently, ultrasound model-based iterative reconstruction (UMBIR) approaches have shown significant improvements over SAFT. However, even these methods produce ringing artifacts due to the high fractional-bandwidth of the excitation signal.In this paper, we propose a ringing artifact reduction method for ultrasound image reconstruction that uses a multi-agent consensus equilibrium (RARE-MACE) framework. Our approach integrates a physics-based forward model that accounts for the propagation of a collimated ultrasonic beam in multi-layered media, a spatially varying image prior, and a denoiser designed to suppress the ringing artifacts that are characteristic of reconstructions from high-fractional bandwidth ultrasound sensor data. We test our method on simulated and experimental measurements and show substantial improvements in image quality compared to SAFT and UMBIR.

Alanazi, Abdulrahman M↗

Subtask 1.5 – CO2 Injection Monitoring with an Optimized Scalable, Automated, Semipermanent Seismic Array

The scalable, automated, semipermanent seismic array (SASSA) method is a flexible and relatively cost-effective surface geophysical method for regular time-lapse monitoring of the movement of injected carbon dioxide (CO2) in a reservoir for CO2 enhanced oil recovery (EOR) or geologic CO2 storage operations. It has the advantages of a low-environmental-footprint while monitoring regions of a reservoir from the surface without the need for a regular grid distribution of receivers. Automated data collection is possible. As only time-lapse amplitude changes at the reservoir level due to CO2 movement within the reservoir are monitored, the turnaround time to deliver results from the SASSA method can be short, without the need for long, time-consuming data-processing workflows. As data is collected and processed, incremental information can be provided to the field operator. The Energy & Environmental Research Center (EERC) conducted a SASSA field test from September 2018 to November 2020 in a portion of the Bell Creek Field in Montana, which implemented new CO2 EOR field activities during the study period. Lessons learned from a proof-of-concept study were incorporated to improve the data quality of the SASSA method and demonstrate the viability of the technology. The EERC implemented several enhancements to improve data quality, including 1) an iterative survey design, which allowed placing the receivers in strategic locations where the movement of the CO2 in the reservoir could be tracked with minimum interference by the cultural noise in the study area; 2) the use of powerful seismic sources in the form of surface orbital vibrators, and 3) data acquisition during optimal periods. History-matched reservoir simulation was performed to predict gas saturation and pressure response induced by CO2 injection in the study area. The results were compared with the SASSA-measured responses to CO2 injection as a partial validation technique. A match between the two methods was observed for most of the SASSA points predicted to have intersected a CO2 saturation change. The validated results provide confidence that the SASSA method can be used independently as a CO2 saturation monitoring technique. As data are collected and processed, incremental information can be provided to the field operator. The critical components of the SASSA workflow for a successful application of the method are the following: Iterative survey design with information about CO2 injection activities from the oilfield operator. A detailed CO2 injection plan is the key driver to select the strategic monitoring location of the SASSA sensors. After this information is incorporated in the initial distribution of sources and receivers in the study area, high-resolution satellite images are used to identify ground locations not affected by cultural noise sources, such as power lines, pipelines/flow lines, or roadways. In the next iteration of the survey design, a scouting trip to the study area is needed to understand more details of the noise sources identified in the previous step and the intensity of the field activities that can also generate noise during the monitoring. Integrating the information from the scouting trip into the survey design to select the optimum source and receiver locations is the final step. Noise attenuation. The variety of noise types during seismic monitoring of an oil field is enormous. Tailored noise characterization and processing at a node-by-node level can enhance the performance and sensitivity of the SASSA technique. Future advancements that could improve the efficiency and application of the SASSA technology include: Gaining a better understanding of the noise field produced by the seismic source to aid the choice of receiver location. Surface noise from the source can overwhelm the small signal changes due to CO2 that the SASSA method measures. Improved data-processing workflow to automatically analyze and adapt to dynamic noise conditions associated with industrial settings. This subtask was funded through the EERC–DOE Joint Program on Research and Development for Fossil Energy-Related Resources Cooperative Agreement No. DE- FE0024233.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

A Second Moment Method for k -Eigenvalue Acceleration with Continuous Diffusion and Discontinuous Transport Discretizations

The second moment method is a linear acceleration technique that couples the transport equation to a diffusion equation with transport-dependent additive closures. The resulting low-order diffusion equation can be discretized independent of the transport discretization, unlike diffusion synthetic acceleration, and is symmetric positive definite, unlike quasidiffusion. While this method has been shown to be comparable to quasidiffusion in iterative performance for fixed source and time-dependent problems, it is largely unexplored as an eigenvalue problem acceleration scheme due to the belief that the resulting inhomogeneous source makes the problem ill posed. Recently, a preliminary feasibility study was performed on the second moment method for eigenvalue problems. The results suggested comparable performance to quasidiffusion and more robust performance than diffusion synthetic acceleration. This work extends the initial study to more realistic reactor problems using state-of-the-art discretization techniques. Finally, the results in this paper show that the second moment method is more computationally efficient than its alternatives on complex reactor problems with unstructured meshes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Low synchronization Gram–Schmidt and generalized minimal residual algorithms

The Gram–Schmidt process uses orthogonal projection to construct the A = QR factorization of a matrix. When Q has linearly independent columns, the operator P = I - Q(QTQ)-1QT defines an orthogonal projection onto Q⊥. In finite precision, Q loses orthogonality as the factorization progresses. A family of approximate projections is derived with the form P = I - QTQT, with correction matrix T. When T = (QTQ)-1, and T is triangular, it is postulated that the best achievable orthogonality is $\mathcal{O}(ε)\mathcal{K}(A)$. We present new variants of modified (MGS) and classical Gram–Schmidt algorithms that require one global reduction step. An interesting form of the projector leads to a compact WY representation for MGS. In particular, the inverse compact WY MGS algorithm is equivalent to a lower triangular solve. Our main contribution is to introduce a backward normalization lag into the compact WY representation, resulting in a $\mathcal{O}(ε)\mathcal{K}[r_0, AV_m])$ stable Generalized Minimal Residual Method (GMRES) algorithm that requires only one global reduce per iteration. Finally, further improvements in performance are achieved by accelerating GMRES on GPUs.

97 MATHEMATICS AND COMPUTING↗

Boron-Based Neutron Scintillator Screen Characterization with X-Rays and Neutrons

Recent work on boron-based neutron scintillator screens suggests these screens can offer superior performance when compared to commonly used screens. Borated neutron scintillator screens perform well in terms of light output (5-6 times greater than a standard Gadox screen) and detection effi-ciency (larger than standard LiF+ZnS screens). However, previously manu-factured boron-based screens have exhibited non-uniform surface coating and a poor mixture between phosphor and converter particles. The objective of this work was to evaluate newly fabricated scintillator screens to deter-mine if enhanced fabrication methods produced a more homogeneous distribution between neutron converter and scintillation phosphor particles. Uniformity of scintillator material deposition was also inspected. This new iteration of screens appeared more uniform than previous generations with the new coating method improving surface chemistry and scintillator material homogeneity. Additionally, a new methodology for screen characterization, involving the correlation of a neutron image taken with a borated scintillator screen to X-ray computed tomography of that same screen, was demonstrated to elucidate a relationship between scintillator screen thickness and relative light output of the screen under neutron exposure. This method suggested that the ideal thickness of scintillator material was ~150 µm to maximize light output of the screen.

36 - MATERIALS SCIENCE↗

Point Adversarial Self-Mining: A Simple Method for Facial Expression Recognition

In this article, we propose a simple yet effective approach, called point adversarial self mining (PASM), to improve the recognition accuracy in facial expression recognition (FER). Unlike previous works focusing on designing specific architectures or loss functions to solve this problem, PASM boosts the network capability by simulating human learning processes: providing updated learning materials and guidance from more capable teachers. Specifically, to generate new learning materials, PASM leverages a point adversarial attack method and a trained teacher network to locate the most informative position related to the target task, generating harder learning samples to refine the network. The searched position is highly adaptive since it considers both the statistical information of each sample and the teacher network capability. Other than being provided new learning materials, the student network also receives guidance from the teacher network. After the student network finishes training, the student network changes its role and acts as a teacher, generating new learning materials and providing stronger guidance to train a better student network. Here, the adaptive learning materials generation and teacher/student update can be conducted more than one time, improving the network capability iteratively. Extensive experimental results validate the efficacy of our method over the existing state of the arts for FER.

97 MATHEMATICS AND COMPUTING↗

Accelerating crystal structure determination with iterative AlphaFold prediction

Experimental structure determination can be accelerated with artificial intelligence (AI)-based structure-prediction methods such as AlphaFold . Here, an automatic procedure requiring only sequence information and crystallographic data is presented that uses AlphaFold predictions to produce an electron-density map and a structural model. Iterating through cycles of structure prediction is a key element of this procedure: a predicted model rebuilt in one cycle is used as a template for prediction in the next cycle. This procedure was applied to X-ray data for 215 structures released by the Protein Data Bank in a recent six-month period. In 87% of cases our procedure yielded a model with at least 50% of C α atoms matching those in the deposited models within 2 Å. Predictions from the iterative template-guided prediction procedure were more accurate than those obtained without templates. It is concluded that AlphaFold predictions obtained based on sequence information alone are usually accurate enough to solve the crystallographic phase problem with molecular replacement, and a general strategy for macromolecular structure determination that includes AI-based prediction both as a starting point and as a method of model optimization is suggested.

59 BASIC BIOLOGICAL SCIENCES↗

A DG-IMEX Method for Two-moment Neutrino Transport: Nonlinear Solvers for Neutrino–Matter Coupling

Neutrino-matter interactions play an important role in core-collapse supernova (CCSN) explosions as they contribute to both lepton number and/or four-momentum exchange between neutrinos and matter, and thus act as the agent for neutrino-driven explosions. Due to the multiscale nature of neutrino transport in CCSN simulations, an implicit treatment of neutrino-matter interactions is desired, which requires solutions of coupled nonlinear systems in each step of the time integration scheme. In this paper we design and compare nonlinear iterative solvers for implicit systems with energy coupling neutrino-matter interactions commonly used in CCSN simulations. Specifically, we consider electron neutrinos and antineutrinos, which interact with static matter configurations through the Bruenn 85 opacity set. The implicit systems arise from the discretization of a nonrelativistic two-moment model for neutrino transport, which employs the discontinuous Galerkin (DG) method for phase-space discretization and an implicit-explicit (IMEX) time integration scheme. In the context of this DG-IMEX scheme, we propose two approaches to formulate the nonlinear systems — a coupled approach and a nested approach. For each approach, the resulting systems are solved with Anderson-accelerated fixedpoint iteration and Newton’s method. The performance of these four iterative solvers has been compared on relaxation problems with various degree of collisionality, as well as proto-neutron star deleptonization problems with several matter profiles adopted from spherically symmetric CCSN simulations. Here, numerical results suggest that the nested Anderson-accelerated fixed-point solver is more efficient than other tested solvers for solving implicit nonlinear systems with energy coupling neutrino-matter interactions.

79 ASTRONOMY AND ASTROPHYSICS↗

Cas3-Mediated Genome Reduction: Demonstration in Cupriavidus Necator H16 Improves Growth on Heterotrophic and Autotrophic Carbon Sources

Genome reduction is widely used to improve microbial bioprocessing hosts by reducing the burden of inessential physiology. Rationally identifying genomic regions that are dispensable or even detrimental to bioprocessing is challenged by our inability to map genome sequence to function across complex regulation and physiology. Thus, there is a need for tools that rapidly generate reduced genome strains with improved performance in process-relevant conditions. Here, we report a Cascade-Cas3-enabled method called TRIM3 that generates large deletions by targeting a randomly integrated transposon, enabling facile generation of a genome-reduced mutant library. Mutants with improved performance were isolated following growth-coupled selection and analyzed by long-read DNA sequencing to identify deletions in their genomes. We deploy this system iteratively in the industrial host Cupriavidus necator H16 on fructose and on formate. After two rounds of TRIM3, we isolate a strain containing a total reduction of 1.4 Mb (18.4% of the genome) that grows 25% faster in a bioreactor on fructose and a strain with a total reduction of 0.5 Mb (7.3% of the genome) that grows 14% faster on formate. This work demonstrates a method for random, iterative, growth-selectable genome reduction that represents a new avenue for large-scale genome modifications and the development of improved bioprocessing hosts.

09 BIOMASS FUELS↗

Tungsten control in long pulse operation: feedback from WEST to ITER

The full W environment that is now foreseen for ITER puts strong emphasis on experimental results obtained in present devices in similar conditions. In this context, the WEST tokamak is well equipped to bring key contributions to the preparation of ITER operation, thanks to its capability to perform long pulses in dominant electron heating, torque-free scheme based on RF systems, and its ITER-grade actively cooled divertor. Recent results of interest cover the understanding of tungsten contamination and the evaluation of conditioning methods, the feedback on the current ramp-up phase, and the ageing of the ITER divertor components in L-mode attached condition. Further, new directions are being explored, in particular low divertor temperature operation that should be the normal operating regime of ITER. We also report on tungsten peaking physics, and the role of light impurity content.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Energy Exascale Computational Fluid Dynamics Simulations With the Spectral Element Method

Development and application of the open-source GPU-based fluid-thermal simulation code, NekRS, are described. Time advancement is based on an efficient kth-order accurate timesplit formulation coupled with scalable iterative solvers. Spatial discretization is based on the high-order spectral element method (SEM), which affords the use of fast, low-memory, matrix-free operator evaluation. Further, recent developments include support for nonconforming meshes using overset grids and for GPU-based Lagrangian particle tracking. Results of large-eddy simulations of atmospheric boundary layers for wind-energy applications as well as extensive nuclear energy applications are presented.

42 ENGINEERING↗

Comparison of unfolding methods using RooFitUnfold

In this study we describe RooFitUnfold, an extension of the RooFit statistical software package to treat unfolding problems, and which includes most of the unfolding methods that commonly used in particle physics. The package provides a common interface to these algorithms as well as common uniform methods to evaluate their performance in terms of bias, variance and coverage. In this paper we exploit this common interface of RooFitUnfold to compare the performance of unfolding with the Richardson–Lucy, Iterative Dynamically Stabilized, Tikhonov, Gaussian Process, bin-by-bin and inversion methods on several example problems.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

A matrix-free approach for finite-strain hyperelastic problems using geometric multigrid

This paper investigates matrix-free algorithms for problems in quasi-static finite-strain hyperelasticity. Iterative solvers with matrix-free operator evaluation have emerged as an attractive alternative to sparse matrices in the fluid dynamics and wave propagation communities because they significantly reduce the memory traffic, the limiting factor in classical finite element solvers. Specifically, we study different matrix-free realizations of the finite element tangent operator and determine whether generalized methods of incorporating complex constitutive behavior might be feasible. Furthermore, in order to improve the convergence behavior of iterative solvers, we also propose a method by which to construct level tangent operators and employ them to define a geometric multigrid preconditioner. Additionally, the performance of the matrix-free operator and the geometric multigrid preconditioner is compared to the matrix-based implementation with an algebraic multigrid (AMG) preconditioner on a single node for a representative numerical example of a heterogeneous hyperelastic material in two and three dimensions. We find that matrix-free methods for finite-strain solid mechanics are very promising, outperforming linear matrix-based schemes by two to five times, and that it is possible to develop numerically efficient implementations that are independent of the hyperelastic constitutive law.

42 ENGINEERING↗

On the emerging potential of quantum annealing hardware for combinatorial optimization

Abstract Over the past decade, the usefulness of quantum annealing hardware for combinatorial optimization has been the subject of much debate. Thus far, experimental benchmarking studies have indicated that quantum annealing hardware does not provide an irrefutable performance gain over state-of-the-art optimization methods. However, as this hardware continues to evolve, each new iteration brings improved performance and warrants further benchmarking. To that end, this work conducts an optimization performance assessment of D-Wave Systems’ Advantage Performance Update computer, which can natively solve sparse unconstrained quadratic optimization problems with over 5,000 binary decision variables and 40,000 quadratic terms. We demonstrate that classes of contrived problems exist where this quantum annealer can provide run time benefits over a collection of established classical solution methods that represent the current state-of-the-art for benchmarking quantum annealing hardware. Although this work does not present strong evidence of an irrefutable performance benefit for this emerging optimization technology, it does exhibit encouraging progress, signaling the potential impacts on practical optimization tasks in the future.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗

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.

36 MATERIALS SCIENCE↗