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DOE OSTI2023

An Investigation of Time Distributions for Task Primitives to Support the HUNTER Dynamic Human Reliability Analysis

As an effort to support data collection for dynamic human reliability analysis (HRA), this study investigates time distributions for task primitives defined in the Goals, Operators, Methods, and Selection rules (GOMS)–Human Reliability Analysis (HRA) method. GOMS-HRA was developed to provide cognition-based time and human error probability information for dynamic HRA calculation in the Human Unimodel for Nuclear Technology to Enhance Reliability (HUNTER) framework. HUNTER is a framework to support the dynamic modelling of human error in conjunction with other modelling tools. In this paper, we investigate time distributions using experimental data collected from the Simplified Human Error Experimental Program (SHEEP) study, which suggests an HRA data collection framework to complement full-scope simulator research as well as collect input data for dynamic HRA using simplified simulators such as the Rancor Microworld Simulator. In this study, time required for GOMS-HRA task primitives to satisfy thirteen statistical distributions is investigated. Then, the time distributions from student operators and professional operators are compared and discussed. As a result, this study identified several time distributions on five GOMS-HRA task primitives at a statistically significant level. According to analyses to date, a greater number of significant time distributions was found in abnormal or emergency operating procedures rather than standard operating procedures. In the future, it is expected that the result of this study can provide objective reference on elapsed time data for task primitives as well as help to realistically simulate scenarios within dynamic HRA.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2024

Applying queueing theory to evaluate wait-time-savings of triage algorithms

Abstract In the past decade, artificial intelligence (AI) algorithms have made promising impacts in many areas of healthcare. One application is AI-enabled prioritization software known as computer-aided triage and notification (CADt). This type of software as a medical device is intended to prioritize reviews of radiological images with time-sensitive findings, thus shortening the waiting time for patients with these findings. While many CADt devices have been deployed into clinical workflows and have been shown to improve patient treatment and clinical outcomes, quantitative methods to evaluate the wait-time-savings from their deployment are not yet available. In this paper, we apply queueing theory methods to evaluate the wait-time-savings of a CADt by calculating the average waiting time per patient image without and with a CADt device being deployed. We study two workflow models with one or multiple radiologists (servers) for a range of AI diagnostic performances, radiologist’s reading rates, and patient image (customer) arrival rates. To evaluate the time-saving performance of a CADt, we use the difference in the mean waiting time between the diseased patient images in the with-CADt scenario and that in the without-CADt scenario as our performance metric. As part of this effort, we have developed and also share a software tool to simulate the radiology workflow around medical image interpretation, to verify theoretical results, and to provide confidence intervals for the performance metric we defined. We show quantitatively that a CADt triage device is more effective in a busy, short-staffed reading setting, which is consistent with our clinical intuition and simulation results. Although this work is motivated by the need for evaluating CADt devices, the evaluation methodology presented in this paper can be applied to assess the time-saving performance of other types of algorithms that prioritize a subset of customers based on binary outputs.

Thompson, Yee Lam Elim (ORCID:0000000196537707)↗

DOE OSTI2021

The effects of low- Z shielding on uranium isotope discrimination using the time-emission profiles of long-lived delayed neutrons

Characteristic radiation signals can often be obscured or distorted by relatively small amounts of shielding, as is the case for highly-enriched uranium (HEU). Methods that can detect and identify special nuclear material (SNM) even in the presence of shielding are therefore of high value in many nuclear security and nonproliferation applications. It has been previously shown that the buildup and decay time profiles of long-lived delayed neutron emission from induced fission are unique and can be used to successfully discriminate between uranium isotopes and infer enrichment without the need for a calibration standard. Because the long-lived delayed neutron precursors exhibit decay times on the order of tens of seconds, their time profiles are not sensitive to the delays associated with scattering or diffusion in shielding materials, which occur on much shorter time scales. The use of capture-based neutron detectors can also mitigate the effects of shielding, because unlike recoil-based detectors, they do not have a low-energy detection threshold, so that neutrons that lose their energy in the shielding are still detectable. In this work, the effects of low-Z shielding on the discrimination of uranium isotopes using delayed neutron time profile measurements are investigated for the first time. Furthermore, the delayed neutron buildup and decay time profiles of polyethylene-shielded HEU and depleted uranium objects are measured using two different capture-gated detector designs. The recorded profiles show good agreement with the shapes predicted from six-group delayed neutron models even with the shielding in place, and the enrichment of the HEU and DU objects was estimated accurately to within 5%. While this method shows potential for discriminating and characterizing extreme cases of enrichment when a moderate amount of shielding is present, simulation results suggest that significant limitations exist for intermediate enrichment levels due to distortions to the delayed neutron time profile caused by neutron reflection in the shielding.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2020

Classical discrete time crystals

The spontaneous breaking of time-translation symmetry in periodically driven quantum systems leads to a new phase of matter: the discrete time crystal (DTC). This phase exhibits collective subharmonic oscillations that depend upon an interplay of non-equilibrium driving, many-body interactions and the breakdown of ergodicity. However, subharmonic responses are also a well-known feature of classical dynamical systems ranging from predator–prey models to Faraday waves and a.c.-driven charge density waves. This raises the question of whether these classical phenomena display the same rigidity characteristic of a quantum DTC. In this work, we explore this question in the context of periodically driven Hamiltonian dynamics coupled to a finite-temperature bath, which provides both friction and, crucially, noise. Focusing on one-dimensional chains, where in equilibrium any transition would be forbidden at finite temperature, we provide evidence that the combination of noise and interactions drives a sharp, first-order dynamical phase transition between a discrete time-translation invariant phase and an activated classical discrete time crystal (CDTC) in which time-translation symmetry is broken out to exponentially long timescales. Power-law correlations are present along a first-order line, which terminates at a critical point. We analyse the transition by mapping it to the locked-to-sliding transition of a d.c.-driven charge density wave. To conclude, building upon results from the field of probabilistic cellular automata, we conjecture the existence of classical time crystals with true long-range order, where time-translation symmetry is broken out to infinite times.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

TDCOSMO VIII. A key test of systematics in the hierarchical method of time-delay cosmography

The largest source of systematic errors in the time-delay cosmography method likely arises from the lens model mass distribution, where an inaccurate choice of model could in principle bias the value of $H$ 0 . A Bayesian hierarchical framework has been proposed which combines lens systems with kinematic data, constraining the mass profile shape at a population level. The framework has been previously validated using a small sample of lensing galaxies drawn from hydro-simulations. The goal of this work is to expand the validation to a more general set of lenses consistent with observed systems, as well as confirm the capacity of the method to combine two lens populations: one which has time delay information and one which lacks time delays and has systematically different image radii. For this purpose, we generated samples of analytic lens mass distributions made of baryons+dark matter and fit the subsequent mock images with standard power-law models. Corresponding kinematics data were also emulated. The hierarchical framework applied to an ensemble of time-delay lenses allowed us to correct the $H$ 0 bias associated with model choice to find $H$ 0 within 1.5σ of the fiducial value. We then combined this set with a sample of corresponding lens systems which have no time delays and have a source at lower $z$, resulting in a systematically smaller image radius relative to their effective radius. The hierarchical framework has successfully accounted for this effect, recovering a value of $H$ 0 which is both more precise (σ ~ 2%) and more accurate (0.7% median offset) than the time-delay set alone. This result confirms that non-time-delay lenses can nonetheless contribute valuable constraining power to the determination of $H$ 0 via their kinematic constraints, assuming they come from the same global population as the time-delay set.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

Automated Signal Timing Plan Reconstruction Using High-Resolution Event-Based Controller Data for Digital Twins

Transportation digital twins are essential tools for evaluating emerging technologies such as connected and automated vehicles, adaptive traffic signal control, and mobility optimization strategies. Realistic digital twins require accurate emulation of real-world signal controllers and detailed signal timing plans. However, signal timing plans are often unavailable or difficult to access, forcing researchers and modelers to rely on assumed fixed timings or halt their analysis. To overcome this challenge, we present a method that directly estimates signal timing plan parameters using high-resolution, event-based data from traffic signal controllers. The proposed method extracts key parameters, including cycle length, offset, phase sequence, coordinated phases, phase-specific minimum and maximum green durations, vehicle extensions, and splits under coordination. A rule-based deterministic signal timing reconstruction algorithm based on traffic signal operation rules, such as those outlined in the Signal Timing Manual, is developed and validated. We evaluate this method, which uses high-resolution controller event logs and verified signal timing plans, on 94 signalized intersections in Nashville, Tennessee, demonstrating their ability to generate accurate, simulation-ready signal timing plans for tools such as SUMO and Vissim.

Saroj, Abhilasha [ORNL] (ORCID:0000000191178063)↗

DOE OSTI2023

Time dependent model for non-inductive ECH X-I current ramp-up for SHPD tokamak facility

Non-inductive (NI) plasma current start-up and ramp-up is an important research topic for spherical tokamak (ST) based reactors and fusion pilot plant (FPP). For a compact FPP, the OH flux availability is highly restricted due to its compact geometry. Efficient fundamental extraordinary mode (X-I) electron cyclotron heating (ECH) current start-up and ramp-up regime was identified for a reactor-like high toroidal magnetic field range which has more than a hundred times higher current drive efficiency compared to more conventional ECH methods for the relevant start-up temperature range. High current drive efficiency is possible due to the strong X-I fundamental ECH interaction only with unidirectional passing electrons constrained by the wave accessibility conditions. Here, we extend the X-I electron cyclotron current drive (ECCD) investigation to a time dependent model to simulate the non-inductive current ramp-up to 10 MA for the Sustained High-Power Density (SHPD) facility. As the X-I ECCD driven current I EC rises, due to the back EMF driven negative current, the net plasma current Ip rises more slowly with the current resistive time scale. For tokamak confinement time (both L-mode and H-Mode) which tends to rise with I p , a positive feedback results and even with constant applied ECH power, T e0 , I EC , and I p can continue to rise to very high values. However, in a realistic situation, the T e0 rise should saturate due to a number of factors such as enhanced core radiation and increased power loss at high temperature. To simulate this effect, we adopt a maximum T e0 model which would limit the temperature rise to certain T e0 . With this model, we investigated the current ramp-up for various ECH power levels and the maximum T e0 of 15, 20, and 25 keV. We find that while the power required is reduced with increasing T e0 limit due to increased current drive efficiency, the time to reach 10 MA tends to go up due to the reduced plasma resistivity for the higher T e0 limit. We also find for a given Te0 limit, the time to reach 10 MA tends to be reduced by increasing the applied ECH power by over driving the current ramp-up where I EC is driven at significantly higher level than 10 MA. While the current ramp-up time may not be an issue for the steady-state reactor systems, if it is desirable to minimize the current ramp-up time, it is prudent to have a sufficient ECH power for current over-drive and have some T e0 limiting tools such as impurity seeding for enhanced radiation. In conclusion, a well-controlled NI ECH start-up also has a potential of improving the tokamak start-up reliability and avoid run-away electrons while the NI off-axis current drive could enhance MHD stability and plasma performance improvements.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Introducing a Markov chain-based time calibration procedure for multi-channel particle detectors: application to the SuperFGD and ToF detectors of the T2K experiment

Inter-channel mis-synchronisation can be a limiting factor to the time resolution of high performance timing detectors with multiple readout channels and independent electronics units. In these systems, time calibration methods employed must be able to efficiently correct for minimal mis-synchronisation between channels and achieve the best detector performance. We present an iterative time calibration method based on Markov Chains, suitable for detector systems with multiple readout channels. Starting from correlated hit pairs alone, and without requiring an external reference time measurement, the method solves for fixed per-channel offsets, with precision limited only by the intrinsic single-channel resolution. A mathematical proof that the method is able to find the correct time offsets to be assigned to each detector channel in order to achieve inter-channel synchronisation is given, and it is shown that the number of iterations to reach convergence within the desired precision is controllable with a single parameter. Numerical studies are used to confirm unbiased recovery of true offsets. Finally, the application of the calibration method to the Super Fine-Grained Detector (SuperFGD) and the Time of Flight (TOF) detector at the upgraded T2K near detector (ND280) shows good improvement in overall timing resolution, demonstrating the effectiveness in a real-world scenario and scalability.

calibration and fitting methods↗

DOE OSTI2024

Real-time confinement regime detection in fusion plasmas with convolutional neural networks and high-bandwidth edge fluctuation measurements

Abstract A real-time detection of the plasma confinement regime can enable new advanced plasma control capabilities for both the access to and sustainment of enhanced confinement regimes in fusion devices. For example, a real-time indication of the confinement regime can facilitate transition to the high-performing wide-pedestal (WP) quiescent H-mode, or avoid unwanted transitions to lower confinement regimes that may induce plasma termination. To demonstrate real-time confinement regime detection, we use the 2D beam emission spectroscopy (BES) diagnostic system to capture localized density fluctuations of long wavelength turbulent modes in the edge region at a 1 MHz sampling rate. BES data from 330 discharges in either L-mode, H-mode, quiescent H (QH)-mode, or WP QH-mode were collected from the DIII-D tokamak and curated to develop a high-quality database to train a deep-learning classification model for real-time confinement detection. We utilize the 6×8 spatial configuration with a time window of 1024 µ s and recast the input to obtain spectral-like features via fast Fourier transform preprocessing. We employ a shallow 3D convolutional neural network for the multivariate time-series classification task and utilize a softmax in the final dense layer to retrieve a probability distribution over the different confinement regimes. Our model classifies the global confinement state on 44 unseen test discharges with an average F 1 score of 0.94, using only ∼1 ms snippets of BES data at a time. This activity demonstrates the feasibility for real-time data analysis of fluctuation diagnostics in future devices such as ITER, where the need for reliable and advanced plasma control is urgent.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Hydrodynamization times of a holographic fluid far from equilibrium

Here we investigate several hydrodynamization times for an ensemble of different far-from-equilibrium solutions of the strongly coupled $\mathscr{N}$ = 4 supersymmetric Yang-Mills plasma undergoing Bjorken flow. For the ensemble of initial data analyzed in the present work, we find that, with typical tolerances between 3% to 5%, the average hydrodynamization time associated with the late time convergence of the pressure anisotropy to the corresponding Borel resummed hydrodynamic attractor is approximately equal to the average hydrodynamization time associated with the Navier-Stokes result, while both are shorter than the average hydrodynamization time associated with second-order hydrodynamics. On the other hand, we find that the entropy density of the different solutions coalesces to second-order hydrodynamics long before entering in the Navier-Stokes regime. A clear hierarchy between the different average hydrodynamization times of the Bjorken expanding fluid is established for the set of analyzed initial data, comprising also some solutions which, whilst satisfying the dominant and the weak energy conditions at the initial time, evolve such as to transiently violate one or both conditions when the fluid is still far from equilibrium. In particular, solutions violating the weak energy condition are generally found to take a longer time to enter in the hydrodynamic regime than the other solutions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Absolutely Stable Time Crystals at Finite Temperature

Here, we show that locally interacting, periodically driven (Floquet) Hamiltonian dynamics coupled to a Langevin bath support finite-temperature discrete time crystals (DTCs) with an infinite autocorrelation time. By contrast to both prethermal and many-body localized DTCs, the time crystalline order we uncover is stable to arbitrary perturbations, including those that break the time translation symmetry of the underlying drive. Our approach utilizes a general mapping from probabilistic cellular automata to open classical Floquet systems undergoing continuous-time Langevin dynamics. Applying this mapping to a variant of the Toom cellular automaton, which we dub the "π-Toom time crystal," leads to a 2D Floquet Hamiltonian with a finite-temperature DTC phase transition. We provide numerical evidence for the existence of this transition, and analyze the statistics of the finite temperature fluctuations. Finally, we discuss how general results from the field of probabilistic cellular automata imply the existence of discrete time crystals (with an infinite autocorrelation time) in all dimensions, d ≥ 1.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

Secure Time Synchronization in Power Grids and Network HIL Synchrophasor Testing

Reliable and secure time synchronization underpins the monitoring and control functions of modern power grids. As GPS-based timing infrastructures grow more susceptible to spoofing and jamming, their vulnerabilities pose escalating risks to grid stability. This work investigates a secure, resilient timing framework that can serve as an alternative or redundant source for power grids, with a particular focus on synchrophasorbased applications. A candidate timing system architecture is evaluated to guarantee trustworthy time dissemination, even in degraded conditions. A network hardware-in-the-loop testing of two synchrophasors validates the concepts, demonstrating enhanced timing integrity, improved detection of timing anomalies, and sustained observability during adverse timing events.

Wu, Ori [ORNL] (ORCID:0000000326723410)↗

DOE OSTI2020

Accelerating Parallel Applications in Cloud Platforms via Adaptive Time-Slice Control

Cloud platforms can provide flexible and cost-effective environments for parallel applications. However, the resource over-commitment issues, i.e., cloud providers often provide much more executable virtual CPUs than available physical CPUs, still impede the synchronization operations of parallel applications, causing severe performance degradation. Existing methods optimize parallel applications by promoting the priorities of involved VMs. They cannot fully explore the performance of parallel applications, because they ignore the time-slice requirements of different phases of parallel applications. Furthermore, non-parallel applications experience unsatisfied performance because of low scheduling priorities. Given empirical analysis on time-slices of virtual machines (VMs), we find that shortening time-slices can mitigate synchronization overhead which incurs during communication phases, while over-short time-slices cause frequent cache misses in computation phases. Accordingly, we propose an Adaptive Time-slice Control (ATC) mechanism. ATC first detects the phases of parallel applications based on lock latency or cache misses. Then, ATC shortens time-slices during communication phases and prolongs time-slices during computation phases for parallel applications, and sets a uniform time-slice for non-parallel applications. Finally, we evaluate ATC using seven well-known benchmarks with 25+ applications. Experiments show that ATC obtains 1.5-75x performance gain for running parallel applications than state-of-the-art solutions, with nearly unaffected impact on non-parallel applications.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

White Rabbit Time Synchronization for Radiation Detector Readout Electronics

As radiation detector arrays in nuclear physics applications become larger and physically more separated, the time synchronization and trigger distribution between many channels of detector readout electronics become more challenging. Clocks and triggers are traditionally distributed through dedicated cabling, but newer methods such as the IEEE 1588 Precision Time Protocol and White Rabbit allow clock synchronization through the exchange of timing messages over Ethernet. Consequently, we report here the use of White Rabbit in a new detector readout module, the Pixie-Net XL. Herein, the White Rabbit core, data capture from multiple digitizing channels, and subsequent pulse processing for pulse height and constant fraction timing are implemented in a Kintex 7 FPGA. The detector data records include White Rabbit time stamps and are transmitted to storage through the White Rabbit core's gigabit Ethernet data path or a slower diagnostic/control link using an embedded Zynq processor. The performance is characterized by time-of-flight style measurements and by time correlation of high energy background events from cosmic showers in detectors separated by longer distances. Software for the Zynq processor can implement "software triggering", for example to limit recording of data to events where a minimum number of channels from multiple modules detect radiation at the same time.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

time-resolved spectroscopy fit (trspecfit) v0.01

Analyze 2D time- and energy-resolved data, such as from a pump-probe spectroscopy experiment. User can select and input different peak shapes/ functions and background types to first fit a ground state/ unperturbed spectrum. This would be similar to how standard spectroscopy data is fit. Subsequently, to describe the time domain, users can choose functions that describe the temporal dynamics of one or more spectral features, such as a peak amplitude, peak position, etc. These time dynamics functions can be added or convoluted (e.g. describing an instrument response function) with each other. Functionality to integrate implicit variables leading to distributions of certain parameters/ functions is in development. Alternatively, 2D data can be analyzed one time step at a time to get an idea of the time dynamics of the system before deploying the global 2D fit described above. Typically people write custom software for this purpose. During my PhD I've seen five internal LBL and external researchers write one-off code in different languages to analyze time- and energy-resolved spectra. While this was specifically was for a laser pump - X-ray probe spectroscopy experiment, I'm trying to write a general package for the time-resolved spectroscopy community.

Mahl, Johannes [Lawrence Berkeley National Laborat↗

DOE OSTI2023

How Time Inefficient and Uncertain are Paratransit Trips Compared to Car Trips

The Americans with Disabilities Act (ADA) stipulates that paratransit mobility be comparable to public transit. However, with just under 5% of the population relying on public transportation, transit is not a representative benchmark. To highlight this inequality, we compare trip times by paratransit to counterfactual car-based travel. Using 2.5 years of demand data from the Denver Regional Transportation District's Access-a-Ride service, we compare paratransit trip times to counterfactual car-based trips for the same origin-destination pairs, controlling for various trip characteristics. Compared to car travel, the findings indicate high variability and uncertainty associated with paratransit trip times. For the same origin-destination pairs, the mean paratransit trip time is almost twice that of the mean car travel time, with a standard deviation for paratransit trip time fourfold that of the standard deviation for car trip time. For perspective, traveling an average of 10 mi during the 7-8 a.m. morning peak can take about 16 min by car with almost no variability, while that same trip can take an average of 25 min by paratransit, with 5% of trips being outside the 95% confidence interval and thus unpredictable. Paratransit trip time inefficiency tends to be particularly worse for females; older adults; those making trips between 9 and 11 a.m.; cash-paying customers; those making shorter trips; and those traveling during inclement weather, including cold temperatures. These findings suggest a need to re-assess using public transit as a benchmark for paratransit supply as regulated by the ADA.

accessible transportation and mobility↗

DOE OSTI2023

Data-assimilated time-lapse visco-acoustic full-waveform inversion: Theory and application for injected CO 2 plume monitoring

Continuous seismic monitoring for quantifying CO 2 plume migration and detection of any potential leakages in the subsurface is essential for the security of long-term anthropogenic carbon dioxide geologic storage. Traditional time-lapse full-waveform inversion (TLFWI) methods aim to map the CO 2 distribution by estimating seismic velocity changes, but recent studies find that CO 2 -induced attenuation is an important complement to seismic velocity for tracking the CO 2 plumes and even quantifying the CO 2 saturation. We have developed a novel data-assimilated TLFWI method to construct high-resolution time-lapse velocity and attenuation changes from dense time-lapse monitoring data. This method consists of two theoretical developments: visco-acoustic full-waveform inversion (QFWI) and multiparameter hierarchical matrix-powered extended Kalman filter (mHiEKF). The method is capable of (1) posing temporal constraints to retrieve time-lapse information from dense monitoring data by using mHiEKF, (2) accurately recovering high-spatial-resolution velocity and attenuation perturbations using first-order equation system-based QFWI, and (3) providing the model uncertainty by estimating their model standard deviation. With numerical examples, we first find the effectiveness of the new QFWI on estimating accurate velocity and attenuation models simultaneously. Then, a CO 2 leakage case and a realistic Frio-II CO 2 monitoring case are presented to find the advantages and applicability of our data-assimilated QFWI method for estimating time-lapse changes using dense time-lapse monitoring surveys. Here, by assimilating time-lapse seismic monitoring data over time, our data-assimilated QFWI method can improve the resolution of velocity and attenuation changes and decrease their model uncertainties.

58 GEOSCIENCES↗

DOE OSTI2021

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.

36 MATERIALS SCIENCE↗