Impact of Cross-Axis Projection Error of Optically Pumped Magnetometers on Calibration Accuracy of OPM-MEG Systems.
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The filterscope diagnostic on DIII-D utilizes photomultiplier tubes to measure visible light emission from the plasma. The system has undergone a substantial upgrade since previous attempts to cross-calibrate the filterscope with other spectroscopic diagnostics were unsuccessful. The optics now utilize a dichroic mirror to initially split the light at nearly 99% transmission or reflectance for light below or above 550 nm. This allows the system to measure D α emission without degrading visible light emission from the plasma for wavelengths below 550 nm (to measure D β , D γ , W–I, C-III, etc.). Additional optimization of the optical components and calibration techniques reduce the error in the signal up to 10% in some channels compared to previous methods. Cross-calibration measurements with two other high resolution spectroscopic diagnostics now show excellent agreement for the first time. This expands the capabilities of the filterscope system allowing measurement of divertor detachment, emission profiles, edge-localized mode behavior, and plasma–wall interactions. Additionally, it enables direct comparisons against calculations from boundary plasma simulations. These were not possible before.
High-accuracy metrology is vitally important in manufacturing ultra-high-quality free-form mirrors designed to manipulate X-ray light with nanometer-scale wavelengths. The current capabilities and possibility for improvements in X-ray mirror manufacturing are limited by inherent imperfections of the integrated metrology tools. In the case of Fizeau interferometry, metrology tools are currently calibrated with super-polished flat test-standard/reference mirrors. This is acceptable for measuring slightly curved X-ray optics. However, for even moderately curved aspherical X-ray mirrors the flat-reference calibration is not sufficiently accurate and stitching Fizeau interferometer-based surface metrology is used to mitigate the problem. But still, the retrace and aberration errors, as well as the limited spatial resolution, described with the instrument transfer function (ITF), can be transferred into the optical surface topography of X-ray mirrors obtained in stitching metrology. For ITF calibration, we have developed an original technique, based on test standards structured as two-dimensional (2D) highly-randomized (HR) binary pseudo-random arrays (BPRAs). The technique employs the unique properties of the HR BPRA patterns in the spatial frequency domain., i.e. the inherent 2D power spectral density of the HR BPRA pattern has a deterministic white-noise-like character that allows direct determination of the ITF with uniform sensitivity over the entire spatial frequency range and field-of-view of an instrument. Here, we explore technological, metrological, and analytical aspects essential for calibration of the retrace and aberration errors of Fizeau interferometers using different types of tilted test samples, including a super-polished reference mirror for the re-trace calibration and the uniformly redundant array (URA) BPRA standards for the geometrical distortion (aberration) calibration. While the first method was previously demonstrated by researchers at DIAMOND Light Source, a method based on the URA BPRA is described and demonstrated here for the first time. We outline the design and fabrication process used in fabrication of URA BPRA test standards, and present the results of application of the URA BPRA standards demonstrating the high efficacy of our approach to geometrical distortion calibration of Fizeau interferometers. We also discuss the possible sources of unexpected peculiarities of the systematic errors, including an astigmatic character of the retrace error, observed with Fizeau interferometers at the Advanced Light Source X-Ray Optics Laboratory.
High-accuracy surface metrology is vitally important in manufacturing ultra-high-quality free-form mirrors designed to manipulate x-ray light with nanometer-scale wavelengths. The current and potential capabilities of x˗ray mirror manufacturing are limited by inherent imperfections of the integrated metrology tools. Metrology tools are currently calibrated with super-polished flat test-standard/reference mirrors. This is acceptable for fabrication of slightly curved x-ray optics. However, for even moderately curved aspherical x-ray mirrors the flat-reference calibration is not sufficiently accurate. For micro-stitching interferometry developed for surface measurements with curved x-ray mirrors, the tool aberration errors are known to be transferred into the optical surface topography of x-ray mirrors. Our approach to improving metrology is to thoroughly calibrate the measuring tool and apply the results of the calibration to deconvolution of the measured data. Here we explore the application of a recently developed technique for calibrating the instrument transfer function (ITF) of 3D optical surface profilers to metrology with significantly curved x-ray optics. The technique, based on test standards patterned with two-dimensional (2D) binary pseudo-random arrays (BPRAs), employs the unique properties of the BPRA patterns in the spatial frequency domain. The inherent 2D power spectral density of the pattern has a deterministic white-noise-like character that allows direct determination of the ITF with uniform sensitivity over the entire spatial frequency range and field of view of an instrument. The high efficacy of the technique has been previously demonstrated in application to metrology with flat and slightly curved optics. Here, we concentrate on development of an efficient fabrication process for production of highly randomized (HR) BPRA test standards on flat and 500-mm spherical optical substrates. We also compare and discuss the results of the ITF calibration of an interferometric microscope when using the HR BPRA standards on flat and curved substrates.
In this work we extend the active learning emulators for two-body scattering in coordinate space with error estimation, recently developed by Maldonado et al. [Phys. Rev. C 112, 024002], to coupled-channel scattering in momentum space. Our full-order model (FOM) solver is based on the Lippmann-Schwinger integral equation for the scattering t-matrix as opposed to the radial Schrödinger equation. We use (Petrov-)Galerkin projections and high-fidelity calculations at a few snapshots across the parameter space of the interaction to construct efficient reduced-order models (ROMs), trained by a greedy algorithm for locally optimal snapshot selection. Both the FOM solver and the corresponding ROMs are implemented efficiently in Python using Google's JAX library. We present results for emulating scattering phase shifts in coupled and uncoupled channels and cross sections, and assess the accuracy of the developed ROMs and their computational speedup factors. We also develop emulator error estimation for both the t-matrix and the total cross section. The software framework for reproducing and extending our results is publicly available. Together with our recent advances in developing active-learning emulators for three-body scattering, these emulator frameworks set the stage for full Bayesian calibrations of chiral nuclear interactions and optical models against scattering data with quantified emulator errors.
ABSTRACT For the past decade, SALT2 has been the most common model used to fit Type Ia supernova (SN Ia) light curves for dark energy analyses. Recently, the SALT3 model was released, which upgraded a number of model features but has not yet been used for measurements of dark energy. Here, we evaluate the impact of switching from SALT2 to SALT3 for a SN cosmology analysis. We train SALT2 and SALT3 on an identical training sample of 1083 well-calibrated Type Ia supernovae, ensuring that any differences found come from the underlying model framework. We publicly release the results of this training (the SALT ‘surfaces’). We then run a cosmology analysis on the public Dark Energy Survey 3-Yr Supernova data sample (DES-SN3YR), and on realistic simulations of those data. We provide the first estimate of the SN + CMB systematic uncertainty arising from the choice of SALT model framework (i.e. SALT2 versus SALT3), Δw = + 0.001 ± 0.005 – a negligible effect at the current level of dark energy analyses. We also find that the updated surfaces are less sensitive to photometric calibration uncertainties than previous SALT2 surfaces, with the average spectral energy density dispersion reduced by a factor of two over optical wavelengths. This offers an opportunity to reduce the contribution of calibration errors to SN cosmology uncertainty budgets.
Deflectometric profilometers are used to precisely measure the form of beam shaping optics of synchrotrons and X-ray free-electron lasers. They often utilize autocollimators which measure slope by evaluating the displacement of a reticle image on a detector. Based on our privileged access to the raw image data of an autocollimator, novel strategies to reduce the systematic measurement errors by using a set of overlapping images of the reticle obtained at different positions on the detector are discussed. It is demonstrated that imaging properties such as, for example, geometrical distortions and vignetting, can be extracted from this redundant set of images without recourse to external calibration facilities. This approach is based on the fact that the properties of the reticle itself do not change – all changes in the reticle image are due to the imaging process. Firstly, by combining interpolation and correlation, it is possible to determine the shift of a reticle image relative to a reference image with minimal error propagation. Secondly, the intensity of the reticle image is analysed as a function of its position on the CCD and a vignetting correction is calculated. Thirdly, the size of the reticle image is analysed as a function of its position and an imaging distortion correction is derived. It is demonstrated that, for different measurement ranges and aperture diameters of the autocollimator, reductions in the systematic errors of up to a factor of four to five can be achieved without recourse to external measurements.
Two-colour pyrometry (2CP) has been used over several decades to study engine-relevant combustion processes, but results are generally regarded as qualitative or semi-quantitative. In many current 2CP systems, large measurement errors are introduced by parallax because the two measured wavelengths are not from the same line of sight. Here this work presents a spatially-resolved 2CP system with the objective of quantifying and reducing measurement uncertainty. An optical setup that eliminates parallax in 2CP is used together with pixel-by-pixel calibration of the camera sensor to increase measurement accuracy. Primary uncertainty terms are identified, and an error propagation analysis is performed to compute uncertainties in the final results of soot temperature, soot concentration parameter, KL, and soot mass. These methodologies are applied to investigate an auto-igniting fuel spray in a constant pressure flow rig at diesel-like conditions of high ambient pressure and temperature. Results show bias uncertainty of around 200 K (≈10%) for temperature and about 40%–60% for KL. High uncertainty was found to occur on the diffusion flame front where both optical thickness and soot concentrations are small. However, these uncertain measurement zones with relatively low soot concentrations contribute minimally to the total soot mass present in the reacting jet during the temporal evolution of the flame.
A fast and accurate beam-based alignment (BBA) method for harmonic sextupoles has been devel oped at NSLS-II using Linear Optics from Closed Orbit Modulation (LOCOM). The approach excites the beam with simultaneous sine-wave signals at two fast correctors, chosen with an appropriate phase advance to span the full betatron phase space. This strategy suppresses systematic errors from hysteresis, while additional errors from orbit drift and power-supply calibration are minimized by the short measurement time (a few minutes) and reliance solely on beam-based current-to-field conver sion of the sextupoles, with hysteresis explicitly included. Simulations indicate that Linear Optics from Closed Orbits (LOCO) combined with 0.5 mm local orbit bumps can resolve relative sextupole field offsets (∆k₂) with precision better than 10% of k₂, reflecting to beam-based alignment (BBA) accuracy finer than 50 µm. Moreover, employing machine-learning-optimized local orbit bumps en hances sextupole-induced quadrupole signals in a deterministic manner and maintains orbit stability under large sextupole strength variations (±40%). The proposed method is experimentally validated through proof-of-principle measurements at NSLS-II, demonstrating its potential as a fast, precise, and robust tool for harmonic sextupole alignment.
The Cosmology Large Angular Scale Surveyor (CLASS) is a telescope array that observes the cosmic microwave background (CMB) over ∼75% of the sky from the Atacama Desert, Chile, at frequency bands centered near 40, 90, 150, and 220 GHz. CLASS measures the large angular scale CMB polarization to constrain the tensor-to-scalar ratio and the optical depth to last scattering. This paper presents the optical characterization of the 90 GHz telescope. Observations of the Moon establish the pointing while dedicated observations of Jupiter are used for beam calibration. The standard deviations of the pointing error in azimuth, elevation, and boresight angle are 1$^{'}_.$3, 2$^{'}_.$1, and 2$^{'}_.$0, respectively, over the first 3 yr of observations. This corresponds to a pointing uncertainty ∼7% of the beam’s full width at half-maximum (FWHM). The effective azimuthally symmetrized instrument 1D beam estimated at 90 GHz has an FWHM of 0$^°_.$620 ± 0$^°_.$003 and a solid angle of 138.7 ± 0.6(stats.) ± 1.1(sys.) μsr integrated to a radius of 4°. The corresponding beam window function drops to $b^2_ℓ$ = 0.93, 0.71, 0.14 at ℓ = 30, 100, 300, respectively. Far-sidelobes are studied using detector-centered intensity maps of the Moon and measured to be at a level of 10 −3 or below relative to the peak. The polarization angle of Tau A estimated from preliminary survey maps is 149°.6 ± 0°.2(stats.) in equatorial coordinates. The instrumental temperature-to-polarization (T → P) leakage fraction, inferred from per-detector demodulated Jupiter scan data, has a monopole component at the level of 1.7 × 10 −3 , a dipole component with an amplitude of 4.3 × 10 −3 , with no evidence of quadrupolar leakage.
In this paper, we propose a method to estimate the position, orientation, and gain of a magnetic field sensor using a set of (large) electromagnetic coils. We apply the method for calibrating an array of optically pumped magnetometers (OPMs) for magnetoencephalography (MEG). We first measure the magnetic fields of the coils at multiple known positions using a well-calibrated triaxial magnetometer, and model these discreetly sampled fields using vector spherical harmonics (VSH) functions. We then localize and calibrate an OPM by minimizing the sum of squared errors between the model signals and the OPM responses to the coil fields. We show that by using homogeneous and first-order gradient fields, the OPM sensor parameters (gain, position, and orientation) can be obtained from a set of linear equations with pseudo-inverses of two matrices. The currents that should be applied to the coils for approximating these low-order field components can be determined based on the VSH models. Computationally simple initial estimates of the OPM sensor parameters follow. As a first test of the method, we placed a fluxgate magnetometer at multiple positions and estimated the RMS position, orientation, and gain errors of the method to be 1.0 mm, 0.2°, and 0.8%, respectively. Lastly, we calibrated a 48-channel OPM array. The accuracy of the OPM calibration was tested by using the OPM array to localize magnetic dipoles in a phantom, which resulted in an average dipole position error of 3.3 mm. The results demonstrate the feasibility of using electromagnetic coils to calibrate and localize OPMs for MEG.
The tilt of a Raman laser beam is a major systematic error in precision gravity measurement using atom interferometry. The conventional approach to evaluating this tilt error involves modulating the direction of the Raman laser beam and conducting time-consuming gravity measurements to identify the error minimum. In this work, we demonstrate a method to expediently determine the tilt of the Raman laser beam by transforming the tilt angle measurement into characterization of parallelism, which integrates the optical method of aligning the laser direction, commonly used in freely falling corner-cube gravimeters, into an atom gravimeter. A position-sensing detector (PSD) is utilized to quantitatively characterize the parallelism between the test beam and the reference beam, thus measuring the tilt precisely and rapidly. After carefully positioning the PSD and calibrating the relationship between the distance measured by the PSD and the tilt angle measured by the tiltmeter, we achieved a statistical uncertainty of less than 30 µrad in the tilt measurement. Furthermore, we compared the results obtained through this optical method with those from the conventional tilt modulation method for gravity measurement. The comparison validates that our optical method can achieve tilt determination with an accuracy level of better than 200 µrad, corresponding to a systematic error of 20 µGal in g measurement. This work has practical implications for real-world applications of atom gravimeters.
We present a probabilistic framework tailored for solar energy applications referred to as the Weather Research and Forecasting-Solar ensemble prediction system (WRF-Solar EPS). WRF-Solar EPS has been developed by introducing stochastic perturbations into the most relevant physical variables for solar irradiance predictions. In this study, we comprehensively discuss the impact of the stochastic perturbations of WRF-Solar EPS on solar irradiance forecasting compared to a deterministic WRF-Solar prediction (WRF-Solar DET), a stochastic ensemble using the stochastic kinetic energy backscatter scheme (SKEBS), and a WRF-Solar multi-physics ensemble (WRF-Solar PHYS). The performances of the four forecasts are evaluated using irradiance retrievals from the National Solar Radiation Database (NSRDB) over the contiguous United States. We focus on the predictability of the day-ahead solar irradiance forecasts during the year of 2018. The results show that the ensemble forecasts improve the quality of the forecasts, compared to the deterministic prediction system, by accounting for the uncertainty derived by the ensemble members. However, the three ensemble systems are under-dispersive, producing unreliable and overconfident forecasts due to a lack of calibration. In particular, WRF-Solar EPS produces less optically thick clouds than the other forecasts, which explains the larger positive bias in WRF-Solar EPS (31.7 W/m 2 ) than in the other models (22.7–23.6 W/m 2 ). This study confirms that the WRF-Solar EPS reduced the forecast error by 7.5% in terms of the mean absolute error (MAE) compared to WRF-Solar DET, and provides in-depth comparisons of forecast abilities with the conventional scientific probabilistic approaches (i.e., SKEBS and a multi-physics ensemble). Guidelines for improving the performance of WRF-Solar EPS in the future are provided.
For cosmic microwave background (CMB) polarization observations, calibration of detector polarization angles is essential. We have developed a fully remote controlled calibration system with a sparse wire grid that reflects linearly polarized light along the wire direction. The new feature is a remote-controlled system for regular calibration, which has not been possible in sparse wire grid calibrators in past experiments. The remote control can be achieved by two electric linear actuators that load or unload the sparse wire grid into a position centered on the optical axis of a telescope between the calibration time and CMB observation. Furthermore, the sparse wire grid can be rotated by using a motor. A rotary encoder and a gravity sensor are installed on the sparse wire grid to monitor the wire direction. They allow us to achieve detector polarization angle calibration with an expected systematic error of 0.08°. The calibration system will be installed in small-aperture telescopes at Simons Observatory.
Measurements of laser absorption in high-temperature, underdense plasmas produced at the Omega Laser Facility are made using two near-field imaging detectors that diagnose the spatial profile and energy of the port P9 beam before and after it transmits through the plasma. The incident beam is sampled using a partial reflection from a full-aperture, (30 cm-diam) uncoated wedge pickoff located before the target chamber vacuum window and final focus lens assembly. A concave mirror reduces the reflected beam size, allowing it to be recorded directly using a charged-coupled device (CCD) camera. The P9 transmitted beam diagnostic (P9TBD) characterizes the transmitted light by terminating the expanded beam on a semi-transparent diffuser and imaging the illuminated surface using a lens and CCD camera. The P9TBD samples a numerical aperture twice as large as the input beam, allowing the energy of transmitted beams with moderate levels of beam spray to be measured accurately. Calibration shots with no plasma provide a path to infer absorption without absolute photometric calibration of either detector. Lastly, the cross-calibration between the two detectors was measured to remain stable at ±200 ppm, enabling measurements of total beam absorption below 1% with ±0.07% error.
High-spectral-resolution lidar (HSRL) systems provide vertical profiles of optical depth, backscatter cross-section, depolarization, and backscatter phase function. All HSRL measurements are calibrated by reference to molecular scattering, which is measured at each point in the lidar profile. Like the Raman lidar (RL), but unlike simple backscatter lidars such as the micropulse lidar (MPL), this enables the HSRL to measure backscatter cross-sections and optical depths without prior assumptions about the scattering properties of the atmosphere. The depolarization observations allow robust discrimination between ice and water clouds. Rigorous error estimates can be computed for all measurements. A very narrow angular field of view reduces multiple scattering contributions. The small field of view, coupled with a narrow optical bandwidth, nearly eliminates noise due to scattered sunlight. The laser transmitter is a diode-pumped, frequency-doubled Nd:YAG laser. Narrow-band, single-frequency operation is provided by injection seeding with a single-frequency, cw-diode-pumped diode laser. The main laser cavity is maintained in resonance with the seed laser by adjusting the cavity length to minimize the time between the Q-switch trigger and the emission of the laser pulse. The emission wavelength is tuned via temperature control of the seed laser crystal and is locked to line #1109 of the iodine absorption spectra. Locking is accomplished by minimizing the transmission through a 2-cm-long iodine absorption cell. Use of a high-repetition-rate laser and expansion of the transmitted beam through a 400-mm telescope reduces the transmitted energy density to eye-safe levels. It is possible to look directly into the output beam without hazard. The receiver and transmitter use the same afocal telescope, simplifying the maintenance of stable alignment of the transmitter and receiver although the angular FOV is only 100 μrad. The small FOV and the 4-kHz repetition rate also limit the near-field signal strength, making it possible to record continuous profiles that start at an altitude of ~100 m and extend to 30 km using photon counting detectors. The small FOV also suppresses multiple scattering contributions.
Abstract In this research, we propose an Error Separation Technique (EST) based on optical fiber sensors for on-machine straightness error measurement. Two fiber optic Fabry–Pérot interferometers have been developed serving as two displacement sensors. The displacement distance is computed according to the reflected spectrum from interferometers, which can achieve a sub-micrometer resolution. The two-point method has been employed to separate the straightness error of the slides and the profile error of a fine-polished standard block. The spacing distance between two interferometers is determined by the diameter of optical fibers so that the EST's resolution has the potential to reach the sub-millimeter scale. In the experiment, the straightness error has been measured on a commercially available computer numerical control machine tool, and the measurement has been conducted on its x-axis. The spacing distance between two optical fiber sensors is 1.5 mm which equals the EST's resolution along the machine tool's x-axis. The separated profile error of the measured standard block is around 30 µm which has been verified by a high precision Coordinate Measurement Machine (CMM). The magnitude of the separated straightness error is around 40 µm. This technique is flexible and simple to be conducted, which can contribute to the micro-machine tool calibration and other straightness error applications.
A novel flow cell allowing for multiple optical spectroscopy measurements on flowing molten salts was designed, and demonstrative calibrations of impurities in aqueous samples were performed. Online compositional measurements of molten salts are of high interest to monitor the state of relevant solar and nuclear systems. Here, the Spectroscopic Configuration for Optical Real-Time Characterization of High-Temperature (SCORCH) fluids cell was designed to meet this need by providing optical access to a high-temperature molten salt sample stream without physical contact between the sample and window materials. Laser-induced breakdown spectroscopy (LIBS) was utilized to quantify Li, Cr, Fe, Ni, Sr, and Pr at concentrations ranging nominally from 0 to 315 mmol L −1 . Laser power, frequency, and plasma position were optimized to mitigate challenges associated with sample splashing. Univariate calibration models were built with R 2 > 0.98, percent root mean square error of cross-validation (%RMSECV) as low as 2.7%, and limits of quantification (LOQs) down to 4.1 mmol L −1 . Simultaneously, absorbance calibrations were developed for the applicable analytes (Cr, Ni, and Pr) using Beer’s law with a pathlength of 4.41 ± 0.10 mm. These models provide excellent quantification performance with R 2 > 0.999, %RMSECV as low as 0.6%, and LODs down to 0.08 mmol L −1 . Although these calibrations were performed for each spectroscopic technique separately, the two methods may be combined in the future through multivariate modeling and sensor fusion to provide more robust models with the benefits of both techniques (e.g., absorbance: oxidation state concentrations, LIBS: elemental concentration). Additionally, optimized spectrometers may be deployed to enhance sensitivity.