Impact of Cross-Axis Projection Error of Optically Pumped Magnetometers on Calibration Accuracy of OPM-MEG Systems.
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Star selection and bias error eliminating calibrations for five onboard optical measurements used to determine spacecraft trajectories
The Timed Doppler Interferometer (TIDI) will accurately and precisely determine the global vector MLTI (Mesosphere and Lower Thermosphere) wind, temperature, and density profiles. It will measure characteristics of the gravity wave and planetary wave spectra. The tidal characteristics of temperature, density, and wind in the MLTI will be determined. The neutral and ion winds will be measured to characterize the electrodynamical behavior of the MLTI. Oxygen and O2 abundances and nocticulent cloud activity will be measured. This review goes into the calibration and error sources, optical design, mechanisms design, detector design, electronics design, microprocessor and flight software design, and quality assurance and parts.
In couple of years we expect the launch of the CALIPSO lidar spaceborne mission designed to observe aerosols and clouds. CALIPSO will collect profiles of the lidar attenuated backscattering coefficients in two spectral wavelengths (0.53 and 1.06 microns). Observations are provided along the track of the satellite around the globe from pole to pole. The attenuated backscattering coefficients are sensitive to the vertical distribution of aerosol particles, their shape and size. However the information is insufficient to be mapped into unique aerosol physical properties and vertical distribution. Infinite number of physical solutions can reconstruct the same two wavelength backscattered profile measured from space. CALIPSO will fly in formation with the Aqua satellite and the MODIS spectro-radiometer on board. Spectral radiances measured by MODIS in six channels between 0.55 and 2.13 microns simultaneously with the CALIPSO observations can constrain the solutions and resolve this ambiguity, albeit under some assumptions. In this paper we describe the inversion method and apply it to aircraft lidar and MODIS data collected over a dust storm off the coast of West Africa during the SHADE experiment. It is shown that the product of the single scattering albedo, omega, and the phase function, P, for backscattering can be retrieved from the synergism between measurements avoiding a priori hypotheses required for inverting lidar measurements alone. The resultant value of (omega)P(180 deg.) = 0.016/sr are significantly different from what is expected using Mie theory, but are in good agreement with recent results obtained from lidar observations of dust episodes. The inversion is robust in the presence of noise of 10% and 20% in the lidar signal in the 0.53 and 1.06 pm channels respectively. Calibration errors of the lidar of 5 to 10% can cause an error in optical thickness of 20 to 40% respectively in the tested cases. The lidar calibration errors cause degradation in the ability to fit the MODIS data. Therefore the MODIS measurements can be used to identify the calibration problem and correct for it. The CALIPSO-MODIS measurements of the profiles of fine and coarse aerosols, together with CALIPSO measurements of clouds vertical distribution, is expected to be critically important in understanding aerosol transport across continents and political boundaries, and to study aerosol-cloud interaction and its effect on precipitation and global forcing of climate.
Mariner 9 data analysis showed a good performance of the Mars probe planetary approach navigation systems and a good agreement between measured and predicted probe-approach characteristics. It was found that all operations were completed on time and that the calibration of the instruments and the observation of a greater-than-planned number of stars resulted in a higher-than-expected measurement accuracy. The key instruments of the Mariner were TV cameras taking pictures of Phobos and Deimos against a background of stars, calibrated sun and star sensors, and a scan platform. The error models used for optical navigation system elements, the calibration of the scan platform and of the TV cameras, and the image detection and location techniques are discussed in detail.
A breadboard is under development to demonstrate the calibration of spectral errors in microarcsecond stellar interferometers. Analysis shows that thermally and mechanically stable hardware in addition to careful optical design can reduce the wavelength dependent error to tens of nanometers. Calibration of the hardware can further reduce the error to the level of picometers. The results of thermal, mechanical and optical analysis supporting the breadboard design will be shown.
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.
A new technique was developed for the weighting of data from satellite tracking systems in order to obtain an optimum least-squares solution and an error calibration for the solution parameters. Data sets from optical, electronic, and laser systems on 17 satellites in GEM-T1 Goddard Earth Model-T1 (GEM-T1) were employed toward application of this technique for gravity field parameters. Also GEM-T2 (31 satellites) was recently computed as a direct application of the method and is summarized. The method employs subset solutions of the data associated with the complete solution to agree with their error estimates. With the adjusted weights the process provides for an automatic calibration of the error estimates for the solution parameters. The data weights derived are generally much smaller than corresponding weights obtained from nominal values of observation accuracy or residuals. Independent tests show significant improvement for solutions with optimal weighting. The technique is general and may be applied to orbit parameters, station coordinates, or other parameters than the gravity model.
The Palomar Adaptive Optics System actively corrects for changing aberrations in light due to atmospheric turbulence. However, the underlying internal static error is unknown and uncorrected by this process. The dedicated wavefront sensor device necessarily lies along a different path than the science camera, and, therefore, doesn't measure the true errors along the path leading to the final detected imagery. This is a standard problem in adaptive optics (AO) called "non-common path error." The Autonomous Phase Retrieval Calibration (APRC) software suite performs automated sensing and correction iterations to calibrate the Palomar AO system to levels that were previously unreachable.
A new technique was developed for the weighting of data from satellite tracking systems in order to obtain an optimum least squares solution and an error calibration for the solution parameters. Data sets from optical, electronic, and laser systems on 17 satellites in GEM-T1 (Goddard Earth Model, 36x36 spherical harmonic field) were employed toward application of this technique for gravity field parameters. Also, GEM-T2 (31 satellites) was recently computed as a direct application of the method and is summarized here. The method employs subset solutions of the data associated with the complete solution and uses an algorithm to adjust the data weights by requiring the differences of parameters between solutions to agree with their error estimates. With the adjusted weights the process provides for an automatic calibration of the error estimates for the solution parameters. The data weights derived are generally much smaller than corresponding weights obtained from nominal values of observation accuracy or residuals. Independent tests show significant improvement for solutions with optimal weighting as compared to the nominal weighting. The technique is general and may be applied to orbit parameters, station coordinates, or other parameters than the gravity model.
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.
The main source of error in retrieving aerosol optical thicknesses using sun photometry comes from the determination of the TOA voltages. The degradation of interference filters is the most important source of the long-term changes in the cross-calibrations. Although major improvements have been made in the design of the filters (interference filters fabricated using ion-assisted deposition), the filters remain the principal factor limiting performance of the sun photometers. Degradation of filters necessitates frequent calibration of sun photometers and frequent measurements of the filter transmission or the relative system response. The degradation of the filters mounted on the CIMEL sun photometers have been monitored since 1993 by the Aerosol Robotic Network (AERONET) project. The decay reported by Holben et al. for the first two years of a CIMEL#s operation is between 1 and 5%. Nevertheless, the filters mounted on CIMEL instruments are regularly replaced after two years of use. The cross-calibration technique consists of taking measurements concurrently with the uncalibrated and the reference sun photometers. While analyzing measurements, the quality of the calibration has to be checked, using the following considerations: (1) any cirrus clouds suspected to be masking the sun, during the calibration period, need to be reported and the corresponding data set removed; and (2) the stability of the day needs to be checked. This chapter will describe calibration techniques, facilities, and protocols used for calibrating sun photometers and sky radiometers.
Computer Generated Holograms (CGHs) have been used for some time to calibrate interferometers that require nulling optics. A typical scenario is the testing of aspheric surfaces with an interferometer placed near the paraxial center of curvature. Existing CGH technology suffers from a reduced capacity to calibrate middle and high spatial frequencies. The root cause of this shortcoming is as follows: the CGH is not placed at an image conjugate of the asphere due to limitations imposed by the geometry of the test and the allowable size of the CGH. This innovation provides a calibration system where the imaging properties in calibration can be made comparable to the test configuration. Thus, if the test is designed to have good imaging properties, then middle and high spatial frequency errors in the test system can be well calibrated. The improved imaging properties are provided by a rudimentary auxiliary optic as part of the calibration system. The auxiliary optic is simple to characterize and align to the CGH. Use of the auxiliary optic also reduces the size of the CGH required for calibration and the density of the lines required for the CGH. The resulting CGH is less expensive than the existing technology and has reduced write error and alignment error sensitivities. This CGH system is suitable for any kind of calibration using an interferometer when high spatial resolution is required. It is especially well suited for tests that include segmented optical components or large apertures.
Like all astrometric instruments, the Space Interferometry Mission (SIM) suffers from field-dependent errors requiring calibration. Diffraction effects in the delay line, polarization rotations on comer cubes, and beam walk across imperfect optics, all contribute to field-distortion that is significantly larger than is acceptable. The bulk of the systematic error is linear across the field - that is, it results in a magnification error. We show that the linear terms are inconsequential to the performance of SIM because they are inseparable from baseline length and orientation errors. One approach to calibrating the higher-order terms is to perform external' calibration; that is, SIM periodically makes differential measurements of a field of bright stars whose positions are not precisely known. We describe the requirements and constraints on the external calibration process and lay the groundwork for a specific procedure detailed in accompanying papers.
Based on the fact that the part of downward radiance that depends on the optical properties of the aerosol in the atmosphere can be extracted from the measured sky radiance, a new scheme for retrieval of the aerosol phase function and the single-scattering albedo over the ocean is developed. This retrieval algorithm is tested with simulations for several cases. It is found that the retrieved aerosol phase function and the single-scattering albedo are virtually error-free if the vertical structure of the atmosphere is known and if the sky radiance and the aerosol optical thickness can be measured accurately. The robustness of the algorithm in realistic situations, in which the measurements are contaminated by calibration errors or noise, is examined. It is found that the retrieved value of omega(0) is usually in error by less than about 10 percent, and the phase function is accurately retrieved for theta less than about 90 deg. However, as the aerosol optical thickness becomes small, e.g., less than about 0.1, errors in the sky radiance measurement can lead to serious problems with the retrieval algorithm, especially in the blue. The use of the retrieval scheme should be limited to the red and near IR when the aerosol optical thickness is small.
Segment mirror phasing, a critical step of segment mirror alignment, requires the ability to sense and correct the relative pistons between segments from up to a few hundred microns to a fraction of wavelength in order to bring the mirror system to its full diffraction capability. When sampling the aperture of a telescope, using auto-collimating flats (ACFs) is more economical. The performance of a telescope with a segmented primary mirror strongly depends on how well those primary mirror segments can be phased. One such process to phase primary mirror segments in the axial piston direction is dispersed fringe sensing (DFS). DFS technology can be used to co-phase the ACFs. DFS is essentially a signal fitting and processing operation. It is an elegant method of coarse phasing segmented mirrors. DFS performance accuracy is dependent upon careful calibration of the system as well as other factors such as internal optical alignment, system wavefront errors, and detector quality. Novel improvements to the algorithm have led to substantial enhancements in DFS performance. The Advanced Dispersed Fringe Sensing (ADFS) Algorithm is designed to reduce the sensitivity to calibration errors by determining the optimal fringe extraction line. Applying an angular extraction line dithering procedure and combining this dithering process with an error function while minimizing the phase term of the fitted signal, defines in essence the ADFS algorithm.
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.