Systematic Calibration Errors Research Articles

Laser-tracker-based reference measurement for geometric calibration of phase-measuring deflectometry with active display registration

Abstract. Phase-measuring deflectometry (PMD) with active display registration (ADR) is a ray-optics-based technique for the shape measurement of specular surfaces. To obtain quantitative results, the relative position of the cameras of the PMD–ADR setup needs to be determined by geometric calibration. Geometric calibration can be performed by inserting a planar mirror into the setup that brings all camera fields of view to overlap on an active pattern display. The mirror is tilted to multiple positions and each time the cameras capture the displayed images, which yields sufficient data to obtain the relative camera positions and the positions of the mirror. In this article, we give a more detailed description of PMD–ADR and its calibration. We also implement a laser-tracker-based reference method to measure the mirror positions and use its result to expose systematic errors in the geometric calibration.

A Systematic Calibration Modeling Method for Redundant INS with Multi-Sensors Non-Orthogonal Configuration.

Because of the non-orthogonal configuration of multi-sensors, the redundant inertial navigation system (INS) has a more complex error model compared with the traditional orthogonal INS, and the complexity of sensors configuration also increases the difficulty of error separation. Based on sufficient analysis of the error principle of redundant IMUs, a generalized high-accuracy calibration modeling method which is suitable for filtering method systematic calibration is summarized in this paper, and it has been applied to an RIMU prototype consisting of four ring laser gyros (RLGs) and four quartz accelerometers. Through the rotational excitation of the three-axis turntable in the laboratory, the high-precision filtering method systematic calibration of the RIMU is achieved, and static navigation and dynamic vehicle test experiments are also carried out. The experimental results reflect that the positioning accuracy can be obviously improved by using this new systematic calibration error model and the validity of this modeling method is also verified.

Telluric absorption lines in the ALMA spectra of η Car

ABSTRACT The massive binary system formed by η Car and an unknown companion is a strong source at millimetre and submillimetre wavelengths. Close to the stars, continuum bremsstrahlung and radio recombination lines originate in the massive ionized wind of η Car and in several compact sources of high density plasma. Molecular lines are also detected at these wavelengths, some of them are seen in absorption towards the continuum emission region, many of them revealed by ALMA observations. However, because the ALMA atmospheric calibration is performed in a low spectral resolution mode, telluric lines can still be present in some high-resolution spectra of scientific products, which could lead to a false identification of molecules. In this work, we explore three different sets of ALMA archive data of η Car, including high resolution (0.065 arcsec × 0.043 arcsec) observations recently published by our group, to verify which of these absorption lines are real and discuss their origin. We conclude that some of them truly originate in clouds close to the binary system, while others are artefacts of a faulty elimination of telluric lines during ALMA calibration procedure. We found that these absorption lines are not present in the phase calibrators because they are much weaker than η Car, where the absorption line appears because the high intensity continuum enhances the small individual systematic calibration errors.

Photometric Recalibration of the SDSS Stripe 82 to a Few Millimagnitude Precision with the Stellar Color Regression Method and Gaia EDR3

Abstract By combining spectroscopic data from the LAMOST DR7, Sloan Digital Sky Survey (SDSS) DR12, and corrected photometric data from the Gaia EDR3, we apply the stellar color regression (SCR) method to recalibrate the SDSS Stripe 82 standard stars catalog of Ivezić et al. With a total number of about 30,000 spectroscopically targeted stars, we have mapped out the relatively large and strongly correlated photometric zero-point errors present in the catalog, ∼2.5% in the u band and ∼1% in the griz bands. Our study also confirms some small but significant magnitude dependence errors in the z band for some charge-coupled devices. Various tests show that we have achieved an internal precision of about 5 mmag in the u band and about 2 mmag in the griz bands, which is about five times better than previous results. We also apply the method to the latest version of the catalog (v4.2), and find modest systematic calibration errors of up to ∼1% along the R.A. direction and smaller errors along the decl. direction. The results demonstrate the power of the SCR method when combining spectroscopic data and Gaia photometry in breaking the 1% precision barrier of ground-based photometric surveys. Our work paves the way for the recalibration of the whole SDSS photometric survey and has important implications for the calibration of future surveys. Future implementations and improvements of the SCR method under different situations are also discussed.

From Cosmicflows distance moduli to unbiased distances and peculiar velocities

ABSTRACTSurveys of galaxy distances and radial peculiar velocities can be used to reconstruct the large-scale structure. Other than systematic errors in the zero-point calibration of the galaxy distances the main source of uncertainties of such data is errors on the distance moduli, assumed here to be Gaussian and thus turning into lognormal errors on distances and velocities. Naively treated, this leads to spurious nearby outflow and strong infall at larger distances. The lognormal bias is corrected here and tested against mock data extracted from a ΛCDM simulation, designed to statistically follow the grouped Cosmicflows-3 (CF3) data. Considering a subsample of data points, all of which have the same true distances or the same redshifts, the lognormal bias arises because the means of the distributions of observed distances and velocities are skewed off the means of the true distances and velocities. However, the medians are invariant under the lognormal transformation. This invariance allows the Gaussianization of the distances and velocities and the removal of the lognormal bias. This bias Gaussianization correction (BGc) algorithm is tested against mock CF3 catalogues. The test consists of a comparison of the BGc estimated with the simulated distances and velocities and of an examination of the Wiener filter reconstruction from the BGc data. Indeed, the BGc eliminates the lognormal bias. The estimation of Hubble’s constant (H0) is also tested. The residual of the BGc-estimated H0 from the simulated values is $-0.6\pm 0.7{\, \rm km \ s^{-1}\, Mpc^{-1}}$, and is dominated by the cosmic variance. The BGc correction of the actual CF3 data yields $H_0=75.8\pm 1.1{\, \rm km \ s^{-1}\, Mpc^{-1}}$.

Distorted pinhole camera modeling and calibration.

Camera modeling and calibration are essential tasks in modern optics. Conventionally, the pinhole model is adopted with a further extension for lens distortion. However, pinhole and distortion models are mutually dependent; thus, the standard approach induces systematic camera calibration errors. This research presents a unifying distorted pinhole camera model that includes a telecentric, distortion-free pinhole, and radial lens distortion as particular cases. An iterative calibration method based on the derived distorted pinhole model is proposed, and experimental evaluation by calibrating a camera with high radial distortion is performed. The calibration results are compared with the standard and fisheye models using a well-known commercial camera calibrator software. The proposed method outperforms the standard model and achieves accuracy comparable to the fisheye model, and the proposed approach is a versatile and accurate tool for diverse optical metrology applications.

Vanishing Cantilever Calibration Error with Magic Ratio Atomic Force Microscopy

AbstractAn analysis is presented of the error propagation through a simplified contact model for atomic force microscopy (AFM) static force spectroscopy, one that is meant to be intuitive and pedagogically informative rather than maximally realistic. It is shown that an important dimensionless ratio appears in several critical locations in the closed form error equation, and that under common calibration methods there exists a ``magic'' ratio where an important class of systematic calibration errors cancel out completely. This argument is extended to more complex contact models and the presence of a magic ratio is demonstrated using real data. A method is shown to identify and operate at optimal conditions in commercial AFMs. Targeting this magic ratio provides a simple, comprehensive guideline for cantilever selection, system calibration, and imaging parameter selection.

KiDS+VIKING-450 and DES-Y1 combined: Cosmology with cosmic shear

We present a combined tomographic weak gravitational lensing analysis of the Kilo Degree Survey (KV450) and the Dark Energy Survey (DES-Y1). We homogenize the analysis of these two public cosmic shear datasets by adopting consistent priors and modeling of nonlinear scales, and determine new redshift distributions for DES-Y1 based on deep public spectroscopic surveys. Adopting these revised redshifts results in a 0.8σreduction in the DES-inferred value forS​8, which decreases to a 0.5σreduction when including a systematic redshift calibration error model from mock DES data based on the MICE2 simulation. The combined KV450+DES-Y1 constraint onS8= 0.762−0.024+0.025is in tension with thePlanck2018 constraint from the cosmic microwave background at the level of 2.5σ. This result highlights the importance of developing methods to provide accurate redshift calibration for current and future weak-lensing surveys.

FORUM Earth Explorer 9: Characteristics of Level 2 Products and Synergies with IASI-NG

FORUM (Far-infrared Outgoing Radiation Understanding and Monitoring) has been approved to be the ninth Earth Explorer mission of the European Space Agency. The mission is scheduled for launch on a Polar satellite in the 2025–2026 time frame. The core FORUM instrument is a Fourier Transform Spectrometer measuring, with very high accuracy, the upwelling spectral radiance, from 100 to 1600 cm − 1 (from 100 to 6.25 microns in wavelength), thus covering the Far-Infrared (FIR), and a Mid-Infrared (MIR) portion of the spectrum emitted by the Earth. FORUM will fly in loose formation with the MetOp-SG-1A satellite, hosting the Infrared Atmospheric Sounding Interferometer – New Generation (IASI-NG). IASI-NG will measure only the MIR part of the upwelling atmospheric spectrum, from 645 to 2760 cm − 1 (from 15.5 to 3.62 microns in wavelength), thus, the matching FORUM measurements will supply the missing FIR complement. Together, the two missions will provide, for the first time, a spectrally resolved measurement of the full Earth emitted thermal spectrum. The calibrated spectral radiance will be, on its own, the main product of the FORUM mission, however, the radiances will also be processed up to Level 2, to determine the vertical profile of water vapour, surface spectral emissivity and cloud parameters in the case of cloudy atmospheres. In this paper we assess the performance of the FORUM Level 2 products based on clear-sky simulated retrievals and we study how the FORUM and IASI-NG matching measurements can be fused in a synergistic retrieval scheme, to provide improved Level 2 products. Considering only the measurement noise and the systematic calibration error components, we find the following figures for the synergistic FORUM and IASI-NG retrieval products. In the upper troposphere/lower stratosphere region, individual water vapour profiles can be retrieved with 1 km vertical sampling and an error ranging from 10% to 15%. In the range from 300 to 600 cm − 1 , surface spectral emissivity can be retrieved with an absolute error as small as 0.001 in dry Polar atmospheres. Ice cloud parameters such as ice water path and cloud top height can be retrieved with errors smaller than 10% and 1 km, respectively, for ice water path values ranging from 0.2 to 60 g/m 2 .

The First VERA Astrometry Catalog

AbstractWe present the first astrometry catalog from the Japanese VLBI (very long baseline interferometer) project VERA (VLBI Exploration of Radio Astrometry). We have compiled all the astrometry results from VERA, providing accurate trigonometric-annual-parallax and proper-motion measurements. In total, 99 maser sources are listed in the VERA catalog. Among them, 21 maser sources are newly reported, while the rest of the 78 sources are referred to in previously published results or those in preparation for forthcoming papers. The accuracy in the VERA astrometry is revisited and compared with that from the other VLBI astrometry projects such as BeSSeL (The Bar and Spiral Structure Legacy) Survey and GOBELINS (the Gould’s Belt Distances Survey) with the VLBA (Very Long Baseline Array). We have confirmed that most of the astrometry results are consistent with each other, and the largest error sources are due to source structure of the maser features and their rapid variation, along with the systematic calibration errors and different analysis methods. Combined with the BeSSeL results, we estimate the up-to-date fundamental Galactic parameters of $R_{0}=7.92\pm 0.16_{\rm {stat.}}\pm 0.3_{\rm {sys.}}\:$kpc and $\Omega _{\odot }=30.17\pm 0.27_{\rm {stat.}}\pm 0.3_{\rm {sys.}}\:$km$\:$s$^{-1}\:$kpc$^{-1}$, where $R_{0}$ and $\Omega _{\odot }$ are the distance from the Sun to the Galactic center and the Sun’s angular velocity of the Galactic circular rotation, respectively.

Spectra of Ni v and Fe v in the Vacuum Ultraviolet

Abstract This work presents 97 remeasured Fe v wavelengths (1200–1600 Å) and 123 remeasured Ni v wavelengths (1200–1400 Å) with uncertainties of approximately 2 mÅ. An additional 67 remeasured Fe v wavelengths and 72 remeasured Ni v wavelengths with uncertainties greater than 2 mÅ are also reported. A systematic calibration error is also identified in the previous Ni v wavelengths and is corrected in this work. Furthermore, a new energy level optimization of Ni v is presented that includes level values as well as Ritz wavelengths. This work improves upon the available data used for observations of quadruply ionized nickel (Ni v) in white dwarf stars. This compilation is specifically targeted toward observations of the G191-B2B white dwarf spectrum that has been used to test for variations in the fine structure constant, α, in the presence of strong gravitational fields. The laboratory wavelengths for these ions were thought to be the cause of inconsistent conclusions regarding the variation limit of α as observed through the white dwarf spectrum. These inconsistencies can now be addressed with the improved laboratory data presented here.

Flow Velocity Measurement Using a Spatial Averaging Method with Two-Dimensional Flexural Ultrasonic Array Technology.

Accurate average flow velocity determination is essential for flow measurement in many industries, including automotive, chemical, and oil and gas. The ultrasonic transit-time method is common for average flow velocity measurement, but current limitations restrict measurement accuracy, including fluid dynamic effects from unavoidable phenomena such as turbulence, swirls or vortices, and systematic flow meter errors in calibration or configuration. A new spatial averaging method is proposed, based on flexural ultrasonic array transducer technology, to improve measurement accuracy and reduce the uncertainty of the measurement results. A novel two-dimensional flexural ultrasonic array transducer is developed to validate this measurement method, comprising eight individual elements, each forming distinct paths to a single ultrasonic transducer. These paths are distributed in two chordal planes, symmetric and adjacent to a diametral plane. It is demonstrated that the root-mean-square deviation of the average flow velocity, computed using the spatial averaging method with the array transducer is 2.94%, which is lower compared to that of the individual paths ranging from 3.65% to 8.87% with an average of 6.90%. This is advantageous for improving the accuracy and reducing the uncertainty of classical single-path ultrasonic flow meters, and also for conventional multi-path ultrasonic flow meters through the measurement via each flow plane with reduced uncertainty. This research will drive new developments in ultrasonic flow measurement in a wide range of industrial applications.

The Synchronous Calibration Method for the RATAN-600 using Its Two Sectors

A method of “self-calibration” of two sectors of the RATAN-600 radio telescope based on synchronous measurements of strong extragalactic sources, including variable ones, is proposed. The method gives refined corrections to the standard calibration of each of the telescope’s sector. It is based on the fact that ideal synchronous independent measurements of the same object should give the same results. Differences from the unity of the result of approximating the flux ratio synchronously measured at two sectors for a subsample of strong sources are considered as systematic calibration errors and used to calculate corrections that exclude these errors, and are applied to measurements of all sample objects in this observation cycle. The method was tested with RATAN-600 two sectors in meridian multifrequency measurements and can be used for independent pairs of any closely spaced antennas. In this case, the analog of RATAN-600 sector is a separate telescope. For far-spaced antennas, an additional error will be introduced due to different effects of the atmosphere and altitude of objects during synchronous observations.

Systematic calibration error requirements for gravitational-wave detectors via the Cramér–Rao bound

Gravitational-wave (GW) laser interferometers such as Advanced LIGO (The LIGO Scientific Collaboration 2015 Class. Quantum Grav. 32 074001) transduce spacetime strain into optical power fluctuation. Converting this optical power fluctuation back into an estimated spacetime strain requires a calibration process that accounts for both the interferometer’s optomechanical response and the feedback control loop used to control the interferometer test masses. Systematic errors in the calibration parameters lead to systematic errors in the GW strain estimate, and hence to systematic errors in the astrophysical parameter estimates in a particular GW signal. In this work we examine this effect for a GW signal similar to GW150914, both for a low-power detector operation similar to the first and second Advanced LIGO observing runs and for a higher-power operation with detuned signal extraction. We set requirements on the accuracy of the calibration such that the astrophysical parameter estimation is limited by errors introduced by random detector noise, rather than calibration systematics. We also examine the impact of systematic calibration errors on the possible detection of a massive graviton.

The Spectroscopic Signature of Variability in High-redshift Quasars

Abstract Using 16,421 spectra from a sample of 340 quasars (1.62 < z < 3.30) from the Sloan Digital Sky Survey (SDSS) Reverberation Mapping Project, we present an analysis of quasar spectral variability. We confirm the intrinsic Baldwin effect (BE) and brighter-means-bluer trends in which emission line strength and color are associated with changes in luminosity. We then create a composite differential spectrum that captures the wavelength dependence of quasar variability as a function of change in luminosity. When using a bandpass around 1740 Å to describe the luminosity, the differential spectrum follows a power law at longer wavelengths that breaks blueward of 1700 Å. However, the shape of the differential spectrum, the location of the power-law break, and the slope of the intrinsic BE all vary with the choice of bandpass used to define the change in quasar luminosity. We propose that the observed behavior can be explained by inhomogeneous accretion or slim accretion disk models where delays in the reprocessing of incident light on the accretion disk cause local deviations in temperature from the thin-disk model. Finally, we quantify the effects on cosmology studies that are due to the variations in the quasar spectrum in the Lyα forest wavelength range. Using the observed spectroscopic signatures to predict the quasar continuum over the interval 1040 < λ < 1200 Å, we find that the derived spectral templates can reduce the uncertainty of the Lyα forest continuum level in individual epochs from 17.2% to 7.7%, near the level where systematic errors in SDSS flux calibration are expected to dominate.

Dark Energy Survey Year 1 results: Methodology and projections for joint analysis of galaxy clustering, galaxy lensing, and CMB lensing two-point functions

Optical imaging surveys measure both the galaxy density and the gravitational lensing-induced shear fields across the sky. Recently, the Dark Energy Survey (DES) collaboration used a joint fit to two-point correlations between these observables to place tight constraints on cosmology (DES Collaboration et al. 2017). In this work, we develop the methodology to extend the DES year one joint probes analysis to include cross-correlations of the optical survey observables with gravitational lensing of the cosmic microwave background (CMB) as measured by the South Pole Telescope (SPT) and Planck. Using simulated analyses, we show how the resulting set of five two-point functions increases the robustness of the cosmological constraints to systematic errors in galaxy lensing shear calibration. Additionally, we show that contamination of the SPT+Planck CMB lensing map by the thermal Sunyaev-Zel'dovich effect is a potentially large source of systematic error for two-point function analyses, but show that it can be reduced to acceptable levels in our analysis by masking clusters of galaxies and imposing angular scale cuts on the two-point functions. The methodology developed here will be applied to the analysis of data from the DES, the SPT, and Planck in a companion work.

LEMONY – a library of empirical medium-resolution spectra by observations with the NAOC Xinglong 2.16-m and YNAO Gaomeigu 2.4-m telescopes

This study expands the coverage and improves the homogeneity of the distribution of MILES template stars in the parameter space, as well as extends the wavelength coverage of the template spectra to the far red beyond the Ca\,{\sc{ii}} triplet. To achieve this we have carried out a major observational campaign using the OMR long-slit spectrograph mounted on the NAOC 2.16\,m telescope and the YFOSC long-slit spectrograph mounted on the YNAO 2.4\,m telescope. The original sample is based on the MILES library, supplemented by 918 stars selected from PASTEL database. In total, 822 OMR and 1,324 YFOSC spectra, covering respectively the wavelength ranges $\lambda\lambda$3800--5180 and $\lambda\lambda$5150--9000, have been collected and reduced. The spectra have a mean resolution FWHM (full-width at half-maximum) of $\sim 3.3$\,{\AA} and are wavelength- and flux-calibrated to an accuracy of $\sim 20$\,km\,s$^{-1}$ and $\sim 5$\,per\,cent, respectively. The spectra are further corrected for systematic errors in the wavelength calibration to an accuracy of $\sim 4$\,km\,s$^{-1}$ by cross-correlating with the theoretical spectra. Almost all the spectra have an average signal to noise ratio (SNR) better than 100 per pixel. Combined with the MILES spectra, there are now 1,731, 1,542, 1,324 and 1,273 stars with spectra covering respectively $\lambda\lambda$3800--5180, $\lambda\lambda$3800--7500, $\lambda\lambda$5150--9000 and $\lambda\lambda$3800--9000. This paper describes our template star selection, the observation and data reduction, and presents the reduced spectra collected hitherto.

Field Permeability Tests: Importance of Calibration and Synchronous Monitoring for Barometric Pressure Sensors

Pressure transducers (PTs) and an atmospheric pressure transducer (APT) were used to register test data during two types of permeability tests, which were performed in 14 wells monitoring a confined aquifer installed in the lab, and a field rising-head test in clay. The constant-head tests were performed using a peristaltic pump and thus functioned as constant flow rate tests until stabilization of the water level in the well riser pipe. The rising-head tests were started by the sudden removal of a slug of water. This article presents, first, the method used to calibrate the transducers to assess their systematic calibration error (offset) values. Then, it quantifies the influence of synchronized monitoring for the (PT-APT) pair on short- and long-term test data, which had never been done before. The results indicate that the pair calibration cannot be neglected and that the synchronized monitoring is important for all tests, except maybe for a short-duration variable-head test. For most tests, however, the barometric fluctuation with time plays a significant role.

On the accuracy of aerosol photoacoustic spectrometer calibrations using absorption by ozone

Abstract. In recent years, photoacoustic spectroscopy has emerged as an invaluable tool for the accurate measurement of light absorption by atmospheric aerosol. Photoacoustic instruments require calibration, which can be achieved by measuring the photoacoustic signal generated by known quantities of gaseous ozone. Recent work has questioned the validity of this approach at short visible wavelengths (404 nm), indicating systematic calibration errors of the order of a factor of 2. We revisit this result and test the validity of the ozone calibration method using a suite of multipass photoacoustic cells operating at wavelengths 405, 514 and 658 nm. Using aerosolised nigrosin with mobility-selected diameters in the range 250–425 nm, we demonstrate excellent agreement between measured and modelled ensemble absorption cross sections at all wavelengths, thus demonstrating the validity of the ozone-based calibration method for aerosol photoacoustic spectroscopy at visible wavelengths.

Calibration error of laser calorimeter due to the unequal distribution of heat in its receiving element

Background: It is well known that the problem of improving the accuracy of measurements is fundamental in metrology and does not lose its relevance, regardless of the successes achieved in its solution. The task of increasing the accuracy of state standards of measurement units is constantly at the center of this problem. The scientific and applied value of the search for ways to solve this problem is increasing significantly in the light of modern requirements for ensuring environmental friendliness and reducing the resource consumption of promising industrial production. Objectives of the work is to study of ways to improve the methodology for taking into account the nonequivalence of replacing an optical signal with an electric one when calibrating calorimetric measuring transducers that are part of state standards for laser energy units. Materials and methods:. Theoretical and experimental thermophysical and mathematical models of the receiving element of the calorimetric measuring transducer are proposed and studied, which, unlike the known models based on the thermally thin plate, allow one to evaluate the effect of the uneven distribution of heat in the receiving element on the calibration error of the calorimetric measuring transducer. The substitution coefficient, according to the model, depends only on the geometry of the receiving element and the time constants of its heating and cooling, which are determined experimentally. Results: Theoretical analysis and experimental verification of the proposed models have confirmed their effectiveness in reducing the systematic calibration error of the measuring transducers. Conclusion: The proposed thermophysical and mathematical models of the receiving element of the calorimetric measuring transducer should be used in the certification practice of the State standards of Ukraine of laser energy units.