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Modern cosmic microwave background (CMB) analysis pipelines regularly employ complex time-domain filters, beam models, masking, and other techniques during the production of sky maps and their corresponding angular power spectra. However, these processes can generate couplings between multipoles from the same spectrum and from different spectra, in addition to the typical power attenuation. Within the context of pseudo-C_ℓbased,MASTER-style analyses, the net effect of the time-domain filtering is commonly approximated by a multiplicative transfer function,F_ℓ, that can fail to capture mode mixing and is dependent on the spectrum of the signal. To address these shortcomings, we have developed a simulation-based spectral correction approach that constructs a two-dimensional transfer matrix,$J_{\mathit{\ell }\mathit{\ell }\prime }$, which contains information about mode mixing in addition to mode attenuation. We demonstrate the application of this approach on data from the first flight of theSpiderballoon-borne CMB experiment.

We present the first linear polarization measurements from the 2015 long-duration balloon flight ofSpider, which is an experiment that is designed to map the polarization of the cosmic microwave background (CMB) on degree angular scales. The results from these measurements include maps and angular power spectra from observations of 4.8% of the sky at 95 and 150 GHz, along with the results of internal consistency tests on these data. While the polarized CMB anisotropy from primordial density perturbations is the dominant signal in this region of sky, Galactic dust emission is also detected with high significance. Galactic synchrotron emission is found to be negligible in theSpiderbands. We employ two independent foreground-removal techniques to explore the sensitivity of the cosmological result to the assumptions made by each. The primary method uses a dust template derived fromPlanckdata to subtract the Galactic dust signal. A second approach, which constitutes a joint analysis ofSpiderandPlanckdata in the harmonic domain, assumes a modified-blackbody model for the spectral energy distribution of the dust with no constraint on its spatial morphology. Using a likelihood that jointly samples the template amplitude andrparameter space, we derive 95% upper limits on the primordial tensor-to-scalar ratio from Feldman–Cousins and Bayesian constructions, findingr< 0.11 andr< 0.19, respectively. Roughly half the uncertainty inrderives from noise associated with the template subtraction. New data at 280 GHz fromSpider’s second flight will complement thePlanckpolarization maps, providing powerful measurements of the polarized Galactic dust emission.