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Register a new userPolarization measurements analysis I. Impact of the full covariance matrix on polarization fraction and angle measurements
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With the forthcoming release of high precision polarization measurements, such as from the Planck satellite, the metrology of polarization needs to improve. In particular, it is crucial to take into account full knowledge of the noise properties when estimating polarization fraction and angle, which suffer from well-known biases. While strong simplifying assumptions have usually been made in polarization analysis, we present a method for including the full covariance matrix of the Stokes parameters in estimates for the distributions of the polarization fraction and angle. We thereby quantify the impact of the noise properties on the biases in the observational quantities. We derive analytical expressions for the pdf of these quantities, taking into account the full complexity of the covariance matrix, including the Stokes I intensity components. We perform simulations to explore the impact of the noise properties on the statistical variance and bias of the polarization fraction and angle. We show that for low variations of the effective ellipticity between the Q and U components around the symmetrical case the covariance matrix may be simplified as is usually done, with negligible impact on the bias. For S/N on intensity lower than 10 the uncertainty on the total intensity is shown to drastically increase the uncertainty of the polarization fraction but not the relative bias, while a 10% correlation between the intensity and the polarized components does not significantly affect the bias of the polarization fraction. We compare estimates of the uncertainties affecting polarization measurements, addressing limitations of estimates of the S/N, and we show how to build conservative confidence intervals for polarization fraction and angle simultaneously. This study is the first of a set of papers dedicated to the analysis of polarization measurements.
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With the forthcoming release of high precision polarization measurements, such as from the Planck satellite, it becomes critical to evaluate the performance of estimators for the polarization fraction and angle. These two physical quantities suffer from a well-known bias in the presence of measurement noise, as has been described in part I of this series. In this paper, part II of the series, we explore the extent to which various estimators may correct the bias. Traditional frequentist estimators of the polarization fraction are compared with two recent estimators: one inspired by a Bayesian analysis and a second following an asymptotic method. We investigate the sensitivity of these estimators to the asymmetry of the covariance matrix which may vary over large datasets. We present for the first time a comparison among polarization angle estimators, and evaluate the statistical bias on the angle that appears when the covariance matrix exhibits effective ellipticity. We also address the question of the accuracy of the polarization fraction and angle uncertainty estimators. The methods linked to the credible intervals and to the variance estimates are tested against the robust confidence interval method. From this pool of estimators, we build recipes adapted to different use-cases: build a mask, compute large maps, and deal with low S/N data. More generally, we show that the traditional estimators suffer from discontinuous distributions at low S/N, while the asymptotic and Bayesian methods do not. Attention is given to the shape of the output distribution of the estimators, and is compared with a Gaussian. In this regard, the new asymptotic method presents the best performance, while the Bayesian output distribution is shown to be strongly asymmetric with a sharp cut at low S/N.Finally, we present an optimization of the estimator derived from the Bayesian analysis using adapted priors.
POLARBEAR-2 (PB-2) is a cosmic microwave background (CMB) polarization experiment that will be located in the Atacama highland in Chile at an altitude of 5200 m. Its science goals are to measure the CMB polarization signals originating from both primordial gravitational waves and weak lensing. PB-2 is designed to measure the tensor to scalar ratio, r, with precision {sigma}(r) < 0.01, and the sum of neutrino masses, {Sigma}m{ u}, with {sigma}({Sigma}m{ u}) < 90 meV. To achieve these goals, PB-2 will employ 7588 transition-edge sensor bolometers at 95 GHz and 150 GHz, which will be operated at the base temperature of 250 mK. Science observations will begin in 2017.
[Abridged] The measurement of the polarization of the Cosmic Microwave Background radiation is one of the current frontiers in cosmology. In particular, the detection of the primordial B-modes, could reveal the presence of gravitational waves in the early Universe. The detection of such component is at the moment the most promising technique to probe the inflationary theory describing the very early evolution of the Universe. We present the updated performance forecast of the Large Scale Polarization Explorer (LSPE), a program dedicated to the measurement of the CMB polarization. LSPE is composed of two instruments: Strip, a radiometer-based telescope on the ground in Tenerife, and SWIPE (Short-Wavelength Instrument for the Polarization Explorer) a bolometer-based instrument designed to fly on a winter arctic stratospheric long-duration balloon. The program is among the few dedicated to observation of the Northern Hemisphere, while most of the international effort is focused into ground-based observation in the Southern Hemisphere. Measurements are currently scheduled in Winter 2021/22 for SWIPE, with a flight duration up to 15 days, and in Summer 2021 with two years observations for Strip. We describe the main features of the two instruments, identifying the most critical aspects of the design, in terms of impact into performance forecast. We estimate the expected sensitivity of each instrument and propagate their combined observing power to the sensitivity to cosmological parameters, including the effect of scanning strategy, component separation, residual foregrounds and partial sky coverage. We also set requirements on the control of the most critical systematic effects and describe techniques to mitigate their impact. LSPE can reach a sensitivity in tensor-to-scalar ratio of $sigma_r<0.01$, and improve constrains on other cosmological parameters.
A fraction of the light observed from edge-on disk galaxies is polarized due to two physical effects: selective extinction by dust grains aligned with the magnetic field, and scattering of the anisotropic starlight field. Since the reflection and transmission coefficients of the reflecting and refracting surfaces in an optical system depend on the polarization of incoming rays, this optical polarization produces both (a) a selection bias in favor of galaxies with specific orientations and (b) a polarization-dependent PSF. In this work we build toy models to obtain for the first time an estimate for the impact of polarization on PSF shapes and the impact of the selection bias due to the polarization effect on the measurement of the ellipticity used in shear measurements. In particular, we are interested in determining if this effect will be significant for WFIRST. We show that the systematic uncertainties in the ellipticity components are $8times 10^{-5}$ and $1.1 times 10^{-4}$ due to the selection bias and PSF errors respectively. Compared to the overall requirements on knowledge of the WFIRST PSF ellipticity ($4.7times 10^{-4}$ per component), both of these systematic uncertainties are sufficiently close to the WFIRST tolerance level that more detailed studies of the polarization effects or more stringent requirements on polarization-sensitive instrumentation for WFIRST are required.
SPTpol is a dual-frequency polarization-sensitive camera that was deployed on the 10-meter South Pole Telescope in January 2012. SPTpol will measure the polarization anisotropy of the cosmic microwave background (CMB) on angular scales spanning an arcminute to several degrees. The polarization sensitivity of SPTpol will enable a detection of the CMB B-mode polarization from the detection of the gravitational lensing of the CMB by large scale structure, and a detection or improved upper limit on a primordial signal due to inflationary gravity waves. The two measurements can be used to constrain the sum of the neutrino masses and the energy scale of inflation. These science goals can be achieved through the polarization sensitivity of the SPTpol camera and careful control of systematics. The SPTpol camera consists of 768 pixels, each containing two transition-edge sensor (TES) bolometers coupled to orthogonal polarizations, and a total of 1536 bolometers. The pixels are sensitive to light in one of two frequency bands centered at 90 and 150 GHz, with 180 pixels at 90 GHz and 588 pixels at 150 GHz. The SPTpol design has several features designed to control polarization systematics, including: single-moded feedhorns with low cross-polarization, bolometer pairs well-matched to difference atmospheric signals, an improved ground shield design based on far-sidelobe measurements of the SPT, and a small beam to reduce temperature to polarization leakage. We present an overview of the SPTpol instrument design, project status, and science projections.
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