arXiv subjects

Luca Pagano

Publications and source records attributed to Luca Pagano.

At least 19 recordsLinked to original sources

arXiv2026

CosmoForge I: A unified framework for QML power spectrum estimation and pixel-based likelihood analysis

Optimal power spectrum estimation on the largest angular scales of the cosmic microwave background relies on the Quadratic Maximum Likelihood (QML) estimator. Existing public implementations, however, each address only a subset of the problem and none combine power spectrum estimation with a self-consistent pixel-space likelihood within a single framework. We present CosmoForge, a public Python framework that unifies QML power spectrum estimation and pixel-based Gaussian likelihood evaluation for spin-0 and spin-2 fields on the sphere, with general (non-diagonal) noise covariances. The framework is split into three installable packages: CosmoCore (infrastructure), QUBE (Fisher and QML estimation), and PICSLike (pixel-space likelihood). A common interface exposes two interchangeable computation bases $-$ a harmonic basis built on the Sherman-Morrison-Woodbury identity and a direct pixel-space basis $-$ selecting whichever is cheaper for the configuration at hand. Exact algorithmic optimisations reduce the Fisher cost to $\mathcal{O}(\ell_{\rm max}^4)$ for arbitrary noise covariances, with Numba JIT compilation of the hot kernels and MPI parallelisation of the likelihood scan. CosmoForge reproduces the Planck low-$\ell$ Fortran reference implementation across both the QML and pixel-space likelihood pipelines, consistently with double-precision arithmetic. Native multipole binning and three output normalisations (deconvolved, decorrelated, window-convolved) are exposed through a single code path, and the same covariance infrastructure powers both QML estimation and likelihood evaluation. CosmoForge offers a general-purpose, modular, and validated tool for the optimal analysis of large-scale data on the sphere. It is publicly available, pip-installable, and extensible to non-CMB observables.

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arXiv2026

Cross-spectra likelihood for robust $\tau$ constraints from all satellite polarisation data

The Thomson scattering optical depth to reionisation, $\tau$, one of the six parameters of the $\Lambda$CDM model, is primarily constrained by the large-scale E-mode polarisation of the Cosmic Microwave Background (CMB). In this work, we present the E-mode Likelihood for Cross-Analysis (elica), a multi-frequency, harmonic-space likelihood that combines all currently available large-scale satellite polarisation data, namely the Planck LFI 70 GHz channel, the Planck HFI 100 and 143 GHz channels processed with the SRoll2 map-making algorithm, and the WMAP Ka, Q, and V bands. The likelihood is built on an extension of the Hamimeche-Lewis formalism to multi-field partial-sky observations. We validate the pipeline using 500 realistic simulations and find that retaining all cross-spectra and the WMAP-LFI auto-spectrum eliminates the significant bias present when all spectra are retained, while preserving comparable uncertainties in the recovered value of $\tau$. From the low-$\ell$ E-mode power spectrum alone, we obtain $\tau = 0.0575_{-0.0058}^{+0.0048}$ (68% CL). Combining elica with the Planck low-$\ell$ temperature likelihood and the CamSpec high-$\ell$ likelihood, we find $\tau = 0.0581_{-0.0059}^{+0.0048}$ and $\ln(10^{10}A_{\mathrm{s}}) = 3.048_{-0.012}^{+0.011}$. Including ACT{} DR6 + Planck CMB lensing and DESI DR2 BAO measurements, we derive an upper bound on the total neutrino mass of $\sum m_\nu < 0.069$ eV (95% CL). Our results, obtained through careful cross-validation of all available large-scale polarisation datasets, robustly confirm that the optical depth remains relatively low. This severely constrains the possibility of explaining, or even significantly reducing, the tension between DESI-BAO and CMB observations with a high value of $\tau$. The elica likelihood is publicly available.

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arXiv2025

Accurate and efficient likelihood modeling for large-scale CMB data

Accurate parameter estimation from cosmic microwave background data requires reliable likelihood modeling, particularly at large angular scales where angular power spectrum estimators exhibit non-Gaussian statistics. We present a novel approach, based on the Hamimeche-Lewis formalism, that marginalizes over auto-spectra, thus reducing residual biases from noise misestimation and partial sky coverage. We validate our approach by simulating three independent CMB channels, or data splits, in a multi-field setting, comparing to the pixel-based likelihood ground truth estimates for the optical depth $\tau$ and the tensor-to-scalar ratio $r$. We benchmark our method against the main power spectrum based alternatives available in the literature, showing that it outperforms all of them in terms of accuracy, while remaining fast and computationally efficient.

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arXiv2024

A halo model approach to describe clustering and emission of the two main star forming galaxy populations for Cosmic Infrared Background studies

The Cosmic Infrared Background (CIB), traced by the emission from dusty star-forming galaxies, provides a crucial window into the phases of star formation throughout cosmic history. These galaxies, although challenging to detect individually at high redshifts due to their faintness, cumulatively contribute to the CIB which then becomes a powerful probe of galaxy formation, evolution and clustering. Here, we introduce a physically-motivated model for the CIB emission spanning a wide range of frequency and angular resolution, employing a halo model approach and distinguishing, within dark matter halos, between two main populations of star forming galaxies, i.e. normal late-type spiral and irregular galaxies and the progenitors of early-type galaxies. The emission from two galaxy populations maps into different regimes in frequency/resolution space, allowing us to constrain the clustering parameters of the model - $M_{\text{min}}$, the mass of a halo with 50% probability of having a central galaxy and $\alpha$, the power law index regulating the number of satellite galaxies - through a fit to Planck and Herschel-SPIRE CIB anisotropy measurements. We find that, while being able to place constraints on some of the clustering parameters, the Planck frequency and multipole coverage cannot effectively disentangle the contributions from the two galaxy populations. On the other side, the Herschel-SPIRE measurements separate out and constrain the clustering of both populations. Our work, though, highlights an inconsistency of the results between the two datasets, partially already reported in other literature and still not understood.

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arXiv2024

The Simons Observatory: Combining cross-spectral foreground cleaning with multitracer $B$-mode delensing for improved constraints on inflation

The Simons Observatory (SO), due to start full science operations in early 2025, aims to set tight constraints on inflationary physics by inferring the tensor-to-scalar ratio $r$ from measurements of CMB polarization $B$-modes. Its nominal design targets a precision $\sigma(r=0) \leq 0.003$ without delensing. Achieving this goal and further reducing uncertainties requires the mitigation of other sources of large-scale $B$-modes such as Galactic foregrounds and weak gravitational lensing. We present an analysis pipeline aiming to estimate $r$ by including delensing within a cross-spectral likelihood, and demonstrate it on SO-like simulations. Lensing $B$-modes are synthesised using internal CMB lensing reconstructions as well as Planck-like CIB maps and LSST-like galaxy density maps. This $B$-mode template is then introduced into SO's power-spectrum-based foreground-cleaning algorithm by extending the likelihood function to include all auto- and cross-spectra between the lensing template and the SAT $B$-modes. Within this framework, we demonstrate the equivalence of map-based and cross-spectral delensing and use it to motivate an optimized pixel-weighting scheme for power spectrum estimation. We start by validating our pipeline in the simplistic case of uniform foreground spectral energy distributions (SEDs). In the absence of primordial $B$-modes, $\sigma(r)$ decreases by 37% as a result of delensing. Tensor modes at the level of $r=0.01$ are successfully detected by our pipeline. Even with more realistic foreground models including spatial variations in the dust and synchrotron spectral properties, we obtain unbiased estimates of $r$ by employing the moment-expansion method. In this case, delensing-related improvements range between 27% and 31%. These results constitute the first realistic assessment of the delensing performance at SO's nominal sensitivity level. (Abridged)

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arXiv2023

Unraveling the CMB lack-of-correlation anomaly with the cosmological gravitational wave background

Since the very first observations, the Cosmic Microwave Background (CMB) has revealed on large-scales unexpected features known as anomalies, which challenge the standard $\Lambda$ cold dark matter ($\Lambda$CDM) cosmological model. One such anomaly is the "lack-of-correlation", where the measured two-point angular correlation function of CMB temperature anisotropies is compatible with zero, differently from the predictions of the standard model. This anomaly could indicate a deviation from the standard model, unknown systematics, or simply a rare realization of the model itself. In this study, we explore the possibility that the lack-of-correlation anomaly is a consequence of living in a rare realization of the standard model, by leveraging the potential information provided by the cosmological gravitational wave background (CGWB) detectable by future gravitational wave (GW) interferometers. We analyze both constrained and unconstrained realizations of the CGWB to investigate the extent of information that GWs can offer. To quantify the impact of the CGWB on the lack-of-correlation anomaly, we employ established estimators and introduce a new estimator that addresses the "look-elsewhere" effect. Additionally, we consider three different maximum multipoles, denoted as $\ell_{\rm max}$, to account for the anticipated capabilities of future GW detectors ($\ell_{\rm max} = 4, 6, 10$). Summarizing our findings for the case of $\ell_{\rm max} = 4$, we identify the angular range $[63^\circ - 180^\circ]$ as the region where future observations of the CGWB maximize the probability of rejecting the standard model. Furthermore, we calculate the expected significance of this observation, demonstrating that 98.81% (81.67%) of the GW realizations enhance the current significance of the anomaly when considering the full-sky (masked) Planck SMICA map as our CMB sky.

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arXiv2023

Inference of the optical depth to reionization $\tau$ from $\textit{Planck}$ CMB maps with convolutional neural networks

The optical depth to reionization, $\tau$, is the least constrained parameter of the cosmological $\Lambda$CDM model. To date, its most precise value is inferred from large-scale polarized CMB power spectra from the ${\it Planck}$ High-Frequency Instrument (HFI). These maps are known to contain significant contamination by residual non-Gaussian systematic effects, which are hard to model analytically. Therefore, robust constraints on $\tau$ are currently obtained through an empirical cross-spectrum likelihood built from simulations. In this paper, we present a likelihood-free inference of $\tau$ from polarized ${\it Planck}$ HFI maps which, for the first time, is fully based on neural networks (NNs). NNs have the advantage of not requiring an analytical description of the data and can be trained on state-of-the-art simulations, combining information from multiple channels. By using Gaussian sky simulations and ${\it Planck}$ ${\tt SRoll2}$ simulations, including CMB, noise, and residual instrumental systematic effects, we train, test and validate NN models considering different setups. We infer the value of $\tau$ directly from $Q$ and $U$ maps at $\sim 4^\circ$ pixel resolution, without computing power spectra. On ${\it Planck}$ data, we obtain $\tau_{NN}=0.058 \pm 0.008$, compatible with current EE cross-spectrum results but with a $\sim30\%$ larger uncertainty, which can be assigned to the inherent non-optimality of our estimator and to the retraining procedure applied to avoid biases. While this paper does not improve on current cosmological constraints, our analysis represents a first robust application of NN-based inference on real data and highlights its potential as a promising tool for complementary analysis of near-future CMB experiments, also in view of the ongoing challenge to achieve a detection of primordial gravitational waves.

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arXiv2022

Probing Lorentz-violating electrodynamics with CMB polarization

We perform a comprehensive study of the signatures of Lorentz violation in electrodynamics on the Cosmic Microwave Background (CMB) anisotropies. In the framework of the minimal Standard Model Extension (SME), we consider effects generated by renormalizable operators, both CPT-odd and CPT-even. These operators are responsible for sourcing, respectively, cosmic birefringence and circular polarization. We propagate jointly the effects of all the relevant Lorentz-violating parameters to CMB observables and provide constraints with the most recent CMB datasets. We bound the CPT-even coefficient to $k_{F,E+B} < 2.31 \times 10^{-31}$ at 95\% CL. This improves previous CMB bounds by one order of magnitude. The limits we obtain on the CPT-odd coefficients, i.e. $|k_{(V)00}^{(3)}| < 1.54 \times 10^{-44} \; {\rm GeV}$ and $|\mathbf{k_{AF}}| < 0.74 \times 10^{-44} \; {\rm GeV}$ at 95\% CL, are respectively one and two orders of magnitude stronger than previous CMB-based limits, superseding also bounds from non-CMB searches. This analysis provides the strongest constraints to date on CPT-violating coefficients in the minimal SME from CMB searches.

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arXiv2022

Planck constraints on cross-correlations between anisotropic cosmic birefringence and CMB polarization

Cosmic Birefringence (CB) is the in-vacuo rotation of the linear polarization direction of photons during propagation, caused by parity-violating extensions of Maxwell electromagnetism. We build low resolution CB angle maps using Planck Legacy and NPIPE products and provide for the first time estimates of the cross-correlation spectra $C_L^{αE}$ and $C_L^{αB}$ between the CB and the CMB polarization fields. We also provide updated CB auto-correlation spectra $C_L^{αα}$ as well as the cross-correlation $C_L^{αT}$ with the CMB temperature field. We report constraints by defining the scale-invariant amplitudes $A^{αX} \equiv L(L + 1)C_L^{αX}/2π$, where $X = α, T, E, B$, finding no evidence of CB. In particular, we find $A^{αE} = (-7.8 \pm 5.6)$ nK deg and $A^{αB} = (0.3 \pm 4.0)$ nK deg at 68% C.L..

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arXiv2022

No evidence for EDE from Planck data in extended scenarios

The latest data release from the ACT CMB experiment (in combination with previous WMAP data) shows evidence for an Early Dark Energy component at more than $3$ standard deviations. The same conclusion has been recently shown to hold when temperature data from the Planck experiment limited to intermediate angular scales ($l \le 650$) are included while it vanishes when the full Planck dataset is considered. However, it has been shown that the full Planck dataset exhibits an anomalous lensing component and a preference for a closed universe at the level of three standard deviation. It is therefore of utmost importance to investigate if these anomalies could anti-correlate with an early dark energy component and hide its presence during the process of parameter extraction. Here we demonstrate that extended parameters choices as curvature, equation of state of dark energy and lensing amplitude $A_L$ have no impact on the Planck constraints on EDE. In practice, EDE does not solve Planck angular spectra anomalies. This indicates that current CMB evidence for an EDE component comes essentially from the ACT-DR4 dataset.

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arXiv2022

In-flight polarization angle calibration for LiteBIRD: blind challenge and cosmological implications

We present a demonstration of the in-flight polarization angle calibration for the JAXA/ISAS second strategic large class mission, LiteBIRD, and estimate its impact on the measurement of the tensor-to-scalar ratio parameter, r, using simulated data. We generate a set of simulated sky maps with CMB and polarized foreground emission, and inject instrumental noise and polarization angle offsets to the 22 (partially overlapping) LiteBIRD frequency channels. Our in-flight angle calibration relies on nulling the EB cross correlation of the polarized signal in each channel. This calibration step has been carried out by two independent groups with a blind analysis, allowing an accuracy of the order of a few arc-minutes to be reached on the estimate of the angle offsets. Both the corrected and uncorrected multi-frequency maps are propagated through the foreground cleaning step, with the goal of computing clean CMB maps. We employ two component separation algorithms, the Bayesian-Separation of Components and Residuals Estimate Tool (B-SeCRET), and the Needlet Internal Linear Combination (NILC). We find that the recovered CMB maps obtained with algorithms that do not make any assumptions about the foreground properties, such as NILC, are only mildly affected by the angle miscalibration. However, polarization angle offsets strongly bias results obtained with the parametric fitting method. Once the miscalibration angles are corrected by EB nulling prior to the component separation, both component separation algorithms result in an unbiased estimation of the r parameter. While this work is motivated by the conceptual design study for LiteBIRD, its framework can be broadly applied to any CMB polarization experiment. In particular, the combination of simulation plus blind analysis provides a robust forecast by taking into account not only detector sensitivity but also systematic effects.

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arXiv2021

CMB polarization as a tool to constrain the optical properties of the Universe

We present a novel formalism to describe the $in$ $vacuo$ conversion between polarization states of propagating radiation, also known as generalized Faraday effect (GFE), in a cosmological context. Thinking of GFE as a potential tracer of new, isotropy- and/or parity-violating physics, we apply our formalism to the cosmic microwave background (CMB) polarized anisotropy power spectra, providing a simple framework to easily compute their observed modifications. In so doing, we re-interpret previously known results, namely the $in$ $vacuo$ rotation of the linear polarization plane of CMB photons (or cosmic birefringence) but also point out that GFE could lead to the partial conversion of linear into circular polarization. We notice that GFE can be seen as an effect of light propagating in an anisotropic and/or chiral medium (a "dark crystal") and recast its parameters as the components of an effective "cosmic susceptibility tensor". For a wave number-independent susceptibility tensor, this allows us to set an observational bound on a GFE-induced CMB circularly polarized power spectrum, or $VV$, at $C_{\ell}^{VV} < 2 \times 10^{-5} μK^2$ (95 \% C.L.), at its peak $\ell\simeq 370$, which is some 3 orders of magnitude better than presently available direct $VV$ measurements. We argue that, unless dramatic technological improvements will arise in direct $V$-modes measurements, cosmic variance-limited linear polarization surveys expected within this decade should provide, as a byproduct, superior bounds on GFE-induced circular polarization of the CMB.

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arXiv2021

Detailed study of HWP non-idealities and their impact on future measurements of CMB polarization anisotropies from space

We study the propagation of a specific class of instrumental systematics to the reconstruction of the B-mode power spectrum of the cosmic microwave background (CMB). We focus on the non-idealities of the half-wave plate (HWP), a polarization modulator that is to be deployed by future CMB experiments, such as the phase-A satellite mission LiteBIRD. We study the effects of non-ideal HWP properties, such as transmittance, phase shift, and cross-polarization. To this end, we developed a simple, yet stand-alone end-to-end simulation pipeline adapted to LiteBIRD. We analyzed the effects of a possible mismatch between the measured frequency profiles of HWP properties (used in the mapmaking stage of the pipeline) and the actual profiles (used in the sky-scanning step). We simulated single-frequency, CMB-only observations to emphasize the effects of non-idealities on the BB power spectrum. We also considered multi-frequency observations to account for the frequency dependence of HWP properties and the contribution of foreground emission. We quantified the systematic effects in terms of a bias $\Delta r$ on the tensor-to-scalar ratio, $r$, with respect to the ideal case without systematic effects. We derived the accuracy requirements on the measurements of HWP properties by requiring $\Delta r < 10^{-5}$ (1% of the expected LiteBIRD sensitivity on $r$). Our analysis is introduced by a detailed presentation of the mathematical formalism employed in this work, including the use of the Jones and Mueller matrix representations.

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arXiv2020

Lack-of-correlation anomaly in CMB large scale polarisation maps

We present an assessment of the CMB large scale anomalies in polarisation using the two-point correlation function as a test case. We employ the state of the art of large scale polarisation datasets: the first based on a Planck 2018 HFI 100 and 143 GHz cross-spectrum analysis, based on SRoll2 processing, and the second from a map-based approach derived through a joint treatment of Planck 2018 LFI and WMAP-9yr. We consider the well-known $S_{1/2}$ estimator, which measures the distance of the two-point correlation function from zero at angular scales larger than $60^{\circ}$, and rely on realistic simulations for both datasets to assess confidence intervals. By focusing on the pure polarisation field described by either the $Q$ and $U$ Stokes parameters or by the local $E-$modes, we show that the first description is heavily influenced by the quadrupole (which is poorly constrained in both datasets) while the second one is more suited for an analysis containing higher multipoles up to $\ell \sim 10$, limit above which both datasets become markedly noise dominated. We find that both datasets exhibit a lack-of-correlation anomaly in pure polarisation, similar to the one observed in temperature, which is better constrained by the less noisy Planck HFI 100$\times$143 data, where its significance lies at about $99.5\%$. We perform our analysis using realizations that are either constrained or non-constrained by the observed temperature field, and find similar results in the two cases.

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arXiv2020

Planck 2018 constraints on anisotropic birefringence and its cross-correlation with CMB anisotropy

Parity-violating extensions of standard electromagnetism produce cosmic birefringence, the in vacuo rotation of the linear polarisation direction of a photon during propagation. We employ {\it Planck} 2018 CMB polarised data to constrain anisotropic birefringence, modeled by its angular power spectrum $C_{\ell}^{αα}$, and the cross-correlation with CMB temperature maps, $C_{\ell}^{αT}$, at scales larger than $\sim$15 degrees. We present joint limits on the scale invariant quantity, $A^{αα} \equiv \ell (\ell +1) \, C_{\ell}^{αα} / 2 π$, and on the analogous amplitude for the cross-correlation, $A^{αT} \equiv \ell (\ell +1) \, C_{\ell}^{αT} / 2 π$. We find no evidence of birefringence within the error budget and obtain $A^{αα} < 0.104 \, \mbox{[deg$^2$]}$ and $A^{αT}=1.50^{+2.41}_{-4.10} \, \mbox{[$μ$K$\cdot$deg] both at } 95 \% \mbox{ C.L.}$. The latter bound appears competitive in constraining a few early dark energy models recently proposed to alleviate the $H_{0}$ tension. Slicing the joint likelihood at $A^{αT}=0$, the bound on $A^{αα}$ becomes tighter at $A^{αα} < 0.085 \, \mbox{[deg$^2$]}$ at 95$\% \mbox{ C.L.}$. In addition we recast the constraints on $A^{αα}$ as a bound on the amplitude of primordial magnetic fields responsible for Faraday rotation, finding $B_{1 {\tiny \mbox{Mpc}}} < 26.9$ nG and $B_{1 {\tiny \mbox{Mpc}}} < 24.3$ nG at 95$\%$ C.L. for the marginalised and sliced case respectively.

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arXiv2020

Likelihood methods for CMB experiments

A great deal of experimental effort is currently being devoted to the precise measurements of the cosmic microwave background (CMB) sky in temperature and polarisation. Satellites, balloon-borne, and ground-based experiments scrutinize the CMB sky at multiple scales, and therefore enable to investigate not only the evolution of the early Universe, but also its late-time physics with unprecedented accuracy. The pipeline leading from time ordered data as collected by the instrument to the final product is highly structured. Moreover, it has also to provide accurate estimates of statistical and systematic uncertainties connected to the specific experiment. In this paper, we review likelihood approaches targeted to the analysis of the CMB signal at different scales, and to the estimation of key cosmological parameters. We consider methods that analyze the data in the spatial (i.e., pixel-based) or harmonic domain. We highlight the most relevant aspects of each approach and compare their performance.

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arXiv2018

The Impact of Primordial Magnetic Fields on Future CMB Bounds on Inflationary Gravitational Waves

We discuss whether an unaccounted contribution to the Cosmic Microwave Background polarization $B$-mode by primordial magnetic fields (PMFs) can bias future constraints on inflationary gravitational waves. As a case-study, we consider a scale-invariant PMF spectrum with amplitude of $\approx{1}\,{\mathrm{nG}}$ on $1\,\mathrm{Mpc}$ scales, compatible with current cosmological bounds. We find a degeneracy in the $B$-mode spectra between PMFs and inflationary gravitational waves. If PMFs of this amplitude are not accounted for, future CMB experiments could claim a false detection of a tensor-to-scalar ratio $r\approx 0.007$, close to the predictions of Starobinsky and $α$-attractor models. The degeneracy can be broken if $B$-modes are measured also at multipoles $\ell\gtrsim 900$: more precisely experiments like CMB-S4 or CORE-M5 would be able to discriminate PMFs from primordial GWs at high statistical significance. Experiments like LiteBIRD or PIXIE will not be able to break the degeneracy and will need complementary bounds coming, for example, from measurements of anisotropies in the Faraday rotation angle of CMB polarization. This reinforces the importance of future experimental constraints on PMFs.

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arXiv2017

POLOCALC: a Novel Method to Measure the Absolute Polarization Orientation of the Cosmic Microwave Background

We describe a novel method to measure the absolute orientation of the polarization plane of the CMB with arcsecond accuracy, enabling unprecedented measurements for cosmology and fundamental physics. Existing and planned CMB polarization instruments looking for primordial B-mode signals need an independent, experimental method for systematics control on the absolute polarization orientation. The lack of such a method limits the accuracy of the detection of inflationary gravitational waves, the constraining power on the neutrino sector through measurements of gravitational lensing of the CMB, the possibility of detecting Cosmic Birefringence, and the ability to measure primordial magnetic fields. Sky signals used for calibration and direct measurements of the detector orientation cannot provide an accuracy better than 1 deg. Self-calibration methods provide better accuracy, but may be affected by foreground signals and rely heavily on model assumptions. The POLarization Orientation CALibrator for Cosmology, POLOCALC, will dramatically improve instrumental accuracy by means of an artificial calibration source flying on balloons and aerial drones. A balloon-borne calibrator will provide far-field source for larger telescopes, while a drone will be used for tests and smaller polarimeters. POLOCALC will also allow a unique method to measure the telescopes' polarized beam. It will use microwave emitters between 40 and 150 GHz coupled to precise polarizing filters. The orientation of the source polarization plane will be registered to sky coordinates by star cameras and gyroscopes with arcsecond accuracy. This project can become a rung in the calibration ladder for the field: any existing or future CMB polarization experiment observing our polarization calibrator will enable measurements of the polarization angle for each detector with respect to absolute sky coordinates.

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