Bandpass Correction Research Articles

BEYONDPLANCK

We presentPlanckLow Frequency Instrument (LFI) frequency sky maps derived within the BEYONDPLANCKframework. This framework draws samples from a global posterior distribution that includes instrumental, astrophysical, and cosmological parameters, and the main product is an entire ensemble of frequency sky map samples, each of which corresponds to one possible realization of the various modeled instrumental systematic corrections, including correlated noise, time-variable gain, as well as far sidelobe and bandpass corrections. This ensemble allows for computationally convenient end-to-end propagation of low-level instrumental uncertainties into higher-level science products, including astrophysical component maps, angular power spectra, and cosmological parameters. We show that the two dominant sources of LFI instrumental systematic uncertainties are correlated noise and gain fluctuations, and the products presented here support – for the first time – full Bayesian error propagation for these effects at full angular resolution. We compared our posterior mean maps with traditional frequency maps delivered by the Planck Collaboration, and find generally good agreement. The most important quality improvement is due to significantly lower calibration uncertainties in the new processing, as we find a fractional absolute calibration uncertainty at 70 GHz of Δg0/g0 = 5 × 10−5, which is nominally 40 times smaller than that reported byPlanck2018. However, we also note that the originalPlanck2018 estimate has a nontrivial statistical interpretation, and this further illustrates the advantage of the new framework in terms of producing self-consistent and well-defined error estimates of all involved quantities without the need of ad hoc uncertainty contributions. We describe how low-resolution data products, including dense pixel-pixel covariance matrices, may be produced from the posterior samples directly, without the need for computationally expensive analytic calculations or simulations. We conclude that posterior-based frequency map sampling provides unique capabilities in terms of low-level systematics modeling and error propagation, and may play an important role for future Cosmic Microwave Background (CMB)B-mode experiments aiming at nanokelvin precision.

Field sources near the southern-sky calibrator PKS B1934-638: effect on spectral line observations with SKA-MID and its precursors

ABSTRACT Accurate instrumental bandpass corrections are essential for the reliable interpretation of spectral lines from targeted and survey-mode observations with radio interferometers. Bandpass correction is typically performed by comparing measurements of a strong calibrator source to an assumed model, typically an isolated point source. The wide field-of-view and high sensitivity of modern interferometers means that additional sources are often detected in observations of calibrators. This can introduce errors into bandpass corrections and subsequently the target data if not properly accounted for. Focusing on the standard calibrator PKS B1934-638, we perform simulations to asses this effect by constructing a wide-field sky model. The cases of ASKAP (0.7–1.9 GHz), MeerKAT (UHF: 0.58–1.05 GHz; L-band: 0.87–1.67 GHz) and Band 2 (0.95–1.76 GHz) of SKA-MID are examined. The use of a central point source model during bandpass calibration is found to impart amplitude errors into spectra measured by the precursor instruments at the ∼0.2–0.5 per cent level dropping to ∼0.01 per cent in the case of SKA-MID. This manifests itself as ripples in the source spectrum, the behaviour of which is coupled to the distribution of the array baselines, the solution interval, the primary beam size, the hour-angle of the calibration scan, as well as the weights used when imaging the target. Calibration pipelines should routinely employ complete field models for standard calibrators to remove this potentially destructive contaminant from the data, a recommendation we validate by comparing our simulation results to a MeerKAT scan of PKS B1934-638, calibrated with and without our expanded sky model.

Comparison of MAP method with classical methods for bandpass correction of white LED spectra.

The bandwidth of a spectrometer is an important error-influencing factor in spectral measurement. To obtain accurate results, bandpass correction is an indispensable step in spectral data processing. To deal with such a problem, several methods have been proposed, including the differential operator method using a local polynomial approximation and the Richardson-Lucy method combined with a regularization. Here we employ a method based on the maximum a posteriori estimation. The efficiency of the method is verified through a large number of experiments on the spectra of white light-emitting diodes. By comparing the error of the reference spectrum, it was found that this method can effectively correct spectra, thus providing more accurate information for further analysis.

Methods for improving the accuracy of Commission Internationale de L’Eclairage tristimulus values of object color by calculation – Part I: Improvement on measurement bandpass and intervals

Color is one of the most important appearance properties of objects. To digitize color, measuring and calculating tristimulus values are the most basic work besides obtaining reflectance spectrum. However, the accuracy of tristimulus values varies with instruments, measuring, and calculation methods. Textiles and some other application of color demand high color quality due to their special utilization. The series of our studies aim to analyze and evaluate some mathematical solutions in order to improve the accuracy of tristimulus values. The studies include two parts: (1) Part I concentrates on measurement bandpass and intervals and their corresponding improvement algorithms, (2) Part II focuses on the influence of measurement ranges and their truncation errors and some algorithms to overcome the truncation errors. In Part I (current article), measurement errors caused by bandpass and test intervals in the spectrophotometer are analyzed. Then, algorithms including two bandpass corrections (3-point correction and 5-point correction), three interpolations (third-order polynomial interpolation Lagrange and Spline, a fifth-order polynomial interpolation Sprague), two Oleari deconvolution methods (zero- and second-order), and three optimization weighting table methods (ASTM Table 6, Table LLR, and Table LWL) are studied systemically by programming MATLAB software and basing on measuring the spectral reflectance of 1301 chips in Munsell Color Book with Commission Internationale de L’Eclairage (CIE) 1964 color-matching functions and D65 standard illuminant. The results show that all algorithms mentioned above yield very positive effects, and among them, Table LWL performs best with reducing the bandpass error and intervals error to 7‰ of its original error and is recommended.

The beamformer and correlator for the Large European Array for Pulsars

The Large European Array for Pulsars combines Europe's largest radio telescopes to form a tied-array telescope that provides high signal-to-noise observations of millisecond pulsars (MSPs) with the objective to increase the sensitivity of detecting low-frequency gravitational waves. As part of this endeavor we have developed a software correlator and beamformer which enables the formation of a tied-array beam from the raw voltages from each of telescopes. We explain the concepts and techniques involved in the process of adding the raw voltages coherently. We further present the software processing pipeline that is specifically designed to deal with data from widely spaced, inhomogeneous radio telescopes and describe the steps involved in preparing, correlating and creating the tied-array beam. This includes polarization calibration, bandpass correction, frequency dependent phase correction, interference mitigation and pulsar gating. A link is provided where the software can be obtained.

SED-dependent galactic extinction prescription forEuclidand future cosmological surveys

The outcome of upcoming cosmological surveys will depend on the accurate estimates of photometric redshifts. In the framework of the implementation of the photo-z algorithm for Euclid, we are exploring new avenues to improve template-fitting methods. The paper focusses on the prescription of the extinction of source light by dust in the Milky Way. Since Galactic extinction strongly correlates with wavelength and photometry is commonly obtained in broad-band filters, the amount of absorption depends on the source SED, a point often neglected as the SED is not known a-priori. A consequence of this is that the observed E(B-V) (=A_B-A_V) will be different from the E(B-V) used to normalise the absorption law k_lambda (=A_lambda/E(B-V)). Band-pass corrections are required to renormalise the law for a given SED. We assess the band-pass corrections of a range of SEDs and find they vary by up to 20%. We investigate how dust-to-reddening scaling factors depend of the sources used for their calibration. We derive scaling factors from the color excesses of z<0.4 SDSS red galaxies and show that band-pass corrections predict the observed differences. Extinction is then estimated for a range of SEDs and filters relevant to Euclid and other cosmological ground-based surveys. For high extinction line-of-sights (E(B-V)>0.1, ~8% of the Euclid survey), the variations in corrections can be ~0.1mag in the `bluer' optical filters and ~0.04mag in the NIR filters. An inaccurate correction of extinction critically affects photo-z. In particular, for high extinctions and z<0.5, the bias (mean D_z=z_phot-z_real) exceeds 0.2%(1+z), the precision required by weak-lensing analyses. Additional uncertainty on the MW extinction law further reduces the photo-z precision. We propose a new prescription of Galactic absorption for template-fitting algorithms that takes into consideration the dependence of extinction with SED.

The Study of Spectral Correction Algorithm of Charge-Coupled Device Array Spectrometer

The charge-coupled device (CCD) array spectrometer is used for quick and simultaneous measurement of light spectrum. In scientific research and industrial application, the spectral correction algorithm is important to obtain the accurate values of photometry and chromaticity. The accuracy of spectrum depends on the correction of wavelength position, the linearity correction of CCD, the elimination of noise and dark current, the bandpass correction, the stray light correction, and the correction of frequency response. Many correction algorithms are studied to improve the CCD array spectrometer measurement. In this paper, we review and compare the correction algorithms from the past literature. Furthermore, we integrate them and find out an optimal algorithm to process the correction of spectrum measurement. The best results of luminous flux correction (ΔY) and chromatic correction (Δu'v') provide decreasing the difference of reference standard about 90%. The optimal correction algorithm provides a convenient method to enhance the measurement quality of CCD array spectrometer without changing the design of physical hardware.

Comparison of the Richardson–Lucy method and a classical approach for spectrometer bandpass correction

Bandpass correction in spectrometer measurements using monochromators is often necessary in order to obtain accurate measurement results. The classical approach of spectrometer bandpass correction is based on local polynomial approximations and the use of finite differences. Here we compare this approach with an extension of the Richardson–Lucy method, which is well known in image processing, but has not been applied to spectrum bandpass correction yet. Using an extensive simulation study and a practical example, we demonstrate the potential of the Richardson–Lucy method. In contrast to the classical approach, it is robust with respect to wavelength step size and measurement noise. In almost all cases the Richardson–Lucy method turns out to be superior to the classical approach both in terms of spectrum estimate and its associated uncertainties.

Optimization by Smoothed Bandpass Calibration in Radio Spectroscopy

Abstract We have developed the Smoothed Bandpass Calibration (SBC) method and the best suitable scan pattern to optimize radio spectroscopic observations. Adequate spectral smoothing is applied to the spectrum toward OFF-source blank sky adjacent to a target source for the purpose of bandpass correction. Because the smoothing process reduces noise, we can reduce the integration time for OFF-source scans while keeping the signal-to-noise ratio. Since smoothing is not applied to ON-source scans, the spectral resolution for line features is maintained. An optimal smoothing window is determined by the bandpass flatness evaluated by the spectral Allan variance (SAV). An efficient scan pattern is designed for OFF-source scans within the bandpass-stability time scale estimated by the time-based Allan variance (TAV). We tested the SBC using a digital spectrometer, VESPA, at the VERA Iriki station. For a targeted noise level of 5 $ \times$10$ ^{-4}$ as its ratio to the system noise, the optimal smoothing window was 32–60 channels (ch) over the whole bandwidth of 1024 ch, and the optimal scan pattern was designed as a sequence of 70 s ON $ +$ 10 s OFF scan pairs. The noise level by the SBC has been improved by a factor of 1.74, compared with that by the conventional method. The total telescope-time to reach our target with the SBC was 400 s, which is 1$ /$ 3 of 1200 s required in the conventional way. Improvements in the telescope-time efficiency with the SBC were calculated to be 3$ \times$ (for single-beam scans), 2$ \times$ (dual-beam), and 1.3$ \times$ (on-the-fly). The SBC is useful for optimizing scan patterns for observations from now on, and also for improving the signal-to-noise ratios of archival data if ON- and OFF-source spectra are separately recorded, though the efficiency depends on the spectral stability of the receiving system.

Bandwidth correction for LED chromaticity

AbstractThe spectral bandwidth formulae of Stearns and Stearns (Color Res Appl 1988; 13: 257–259) are generalized for an arbitrary slit function. Correction coefficients are derived in terms of moments of the slit function. Application to model LED spectra measured with a compact, fiber‐coupled spectrometer having bandwidth of order 12 nm, and a nonlinear wavelength scale shows that accurate LED color measurements may be obtained with such an instrument. Fitting of the relatively broad slit function to line spectra for accurate wavelength calibration is also described. Such fitting, coupled consistently with the bandpass correction, improves the accuracy color measurements with a broad‐response spectrometer. © 2006 Wiley Periodicals, Inc. Col Res Appl, 31, 374–380, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20242

Effects of spectral bandpass on SeaWiFS-retrieved near-surface optical properties of the ocean

A simple correction method to remove the spectral bandpass effects of the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) on the derived normalized water-leaving radiances and ocean-near-surface chlorophyll concentration is developed and implemented in the SeaWiFS data-processing system. SeaWiFS has not only in-band response structures but also significant sensor out-of-band contributions. The effects of the SeaWiFS out-of-band contribution at the green bands is particularly significant for the derived normalized water-leaving radiances and therefore for the retrieved ocean-near-surface chlorophyll concentration. With the sensor spectral bandpass corrections, the low chlorophyll concentration is even lower in the clear ocean regions, whereas there are almost no changes for the oceans with a chlorophyll concentration of >0.2 mg/m(3).