Comparison of fringe-tracking algorithms for single-mode near-infrared long-baseline interferometers

To enable optical long baseline interferometry toward faint objects, long integrations are necessary despite atmospheric turbulence. Fringe trackers are needed to stabilize the fringes and thus increase the fringe visibility and phase signal-to-noise ratio (SNR), with efficient controllers robust to instrumental vibrations, and to subsequent path fluctuations and flux drop-outs. We report on simulations, analysis and comparison of the performances of a classical integrator controller and of a Kalman controller, both optimized to track fringes under realistic observing conditions for different source magnitudes, disturbance conditions, and sampling frequencies. The key parameters of our simulations (instrument photometric performance, detection noise, turbulence and vibrations statistics) are based on typical observing conditions at the Very Large Telescope observatory and on the design of the GRAVITY instrument, a 4-telescope single-mode long baseline interferometer in the near-infrared, next in line to be installed at VLT Interferometer. We find that both controller performances follow a two-regime law with the star magnitude, a constant disturbance limited regime, and a diverging detector and photon noise limited regime. Moreover, we find that the Kalman controller is optimal in the high and medium SNR regime due to its predictive commands based on an accurate disturbance model. In the low SNR regime, the model is not accurate enough to be more robust than an integrator controller. Identifying the disturbances from high SNR measurements improves the Kalman performances in case of strong optical path difference disturbances.Comment: Accepted for publication in A&A. 17 pages 15 figure

Filling in CMB map missing data using constrained Gaussian realizations

For analyzing maps of the cosmic microwave background sky, it is necessary to mask out the region around the galactic equator where the parasitic foreground emission is strongest as well as the brightest compact sources. Since many of the analyses of the data, particularly those searching for non-Gaussianity of a primordial origin, are most straightforwardly carried out on full-sky maps, it is of great interest to develop efficient algorithms for filling in the missing information in a plausible way. We explore practical algorithms for filling in based on constrained Gaussian realizations. Although carrying out such realizations is in principle straightforward, for finely pixelized maps as will be required for the Planck analysis a direct brute force method is not numerically tractable. We present some concrete solutions to this problem, both on a spatially flat sky with periodic boundary conditions and on the pixelized sphere. One approach is to solve the linear system with an appropriately preconditioned conjugate gradient method. While this approach was successfully implemented on a rectangular domain with periodic boundary conditions and worked even for very wide masked regions, we found that the method failed on the pixelized sphere for reasons that we explain here. We present an approach that works for full-sky pixelized maps on the sphere involving a kernel-based multi-resolution Laplace solver followed by a series of conjugate gradient corrections near the boundary of the mask.Comment: 22 pages, 14 figures, minor changes, a few missing references adde

Instrumental and Analytic Methods for Bolometric Polarimetry

We discuss instrumental and analytic methods that have been developed for the first generation of bolometric cosmic microwave background (CMB) polarimeters. The design, characterization, and analysis of data obtained using Polarization Sensitive Bolometers (PSBs) are described in detail. This is followed by a brief study of the effect of various polarization modulation techniques on the recovery of sky polarization from scanning polarimeter data. Having been successfully implemented on the sub-orbital Boomerang experiment, PSBs are currently operational in two terrestrial CMB polarization experiments (QUaD and the Robinson Telescope). We investigate two approaches to the analysis of data from these experiments, using realistic simulations of time ordered data to illustrate the impact of instrumental effects on the fidelity of the recovered polarization signal. We find that the analysis of difference time streams takes full advantage of the high degree of common mode rejection afforded by the PSB design. In addition to the observational efforts currently underway, this discussion is directly applicable to the PSBs that constitute the polarized capability of the Planck HFI instrument.Comment: 23 pages, 11 figures. for submission to A&

Multi-Detector Multi-Component spectral matching and applications for CMB data analysis

We present a new method for analyzing multi--detector maps containing contributions from several components. Our method, based on matching the data to a model in the spectral domain, permits to estimate jointly the spatial power spectra of the components and of the noise, as well as the mixing coefficients. It is of particular relevance for the analysis of millimeter--wave maps containing a contribution from CMB anisotropies.Comment: 15 pages, 7 Postscript figures, submitted to MNRA

Compressive and Noncompressive Power Spectral Density Estimation from Periodic Nonuniform Samples

This paper presents a novel power spectral density estimation technique for band-limited, wide-sense stationary signals from sub-Nyquist sampled data. The technique employs multi-coset sampling and incorporates the advantages of compressed sensing (CS) when the power spectrum is sparse, but applies to sparse and nonsparse power spectra alike. The estimates are consistent piecewise constant approximations whose resolutions (width of the piecewise constant segments) are controlled by the periodicity of the multi-coset sampling. We show that compressive estimates exhibit better tradeoffs among the estimator's resolution, system complexity, and average sampling rate compared to their noncompressive counterparts. For suitable sampling patterns, noncompressive estimates are obtained as least squares solutions. Because of the non-negativity of power spectra, compressive estimates can be computed by seeking non-negative least squares solutions (provided appropriate sampling patterns exist) instead of using standard CS recovery algorithms. This flexibility suggests a reduction in computational overhead for systems estimating both sparse and nonsparse power spectra because one algorithm can be used to compute both compressive and noncompressive estimates.Comment: 26 pages, single spaced, 9 figure

Measuring galaxy cluster masses with CMB lensing using a Maximum Likelihood estimator: Statistical and systematic error budgets for future experiments

We develop a Maximum Likelihood estimator (MLE) to measure the masses of galaxy clusters through the impact of gravitational lensing on the temperature and polarization anisotropies of the cosmic microwave background (CMB). We show that, at low noise levels in temperature, this optimal estimator outperforms the standard quadratic estimator by a factor of two. For polarization, we show that the Stokes Q/U maps can be used instead of the traditional E- and B-mode maps without losing information. We test and quantify the bias in the recovered lensing mass for a comprehensive list of potential systematic errors. Using realistic simulations, we examine the cluster mass uncertainties from CMB-cluster lensing as a function of an experiment's beam size and noise level. We predict the cluster mass uncertainties will be 3 - 6% for SPT-3G, AdvACT, and Simons Array experiments with 10,000 clusters and less than 1% for the CMB-S4 experiment with a sample containing 100,000 clusters. The mass constraints from CMB polarization are very sensitive to the experimental beam size and map noise level: for a factor of three reduction in either the beam size or noise level, the lensing signal-to-noise improves by roughly a factor of two.Comment: 28 pages, 5 figures: figs 2, 3 updated, references added: accepted for publication in JCA

CMB Aberration and Doppler Effects as a Source of Hemispherical Asymmetries

Our peculiar motion with respect to the CMB rest frame represents a preferred direction in the observed CMB sky since it induces an apparent deflection of the observed CMB photons (aberration) and a shift in their frequency (Doppler). Both effects distort the multipoles $a_{\ell m}$'s at all $\ell$'s. Such effects are real as it has been recently measured for the first time by Planck according to what was forecast in some recent papers. However, the common lore when estimating a power spectrum from CMB is to consider that Doppler affects only the $\ell=1$ multipole, neglecting any other corrections. In this work we use simulations of the CMB sky in a boosted frame with a peculiar velocity $\beta = v/c = 1.23 \times 10^{-3}$ in order to assess the impact of such effect on power spectrum estimations in different regions of the sky. We show that the boost induces a north-south asymmetry in the power spectrum which is highly significant and non-negligible, of about (0.58 $\pm$ 0.10)% for half-sky cuts when going up to $\ell$ = 2500. We suggest that these effects are relevant and may account for some of the north-south asymmetries seen in the Planck data, being especially important at small scales. Finally we analyze the particular case of the ACT experiment, which observed only a small fraction of the sky and show that it suffers a bias of about 1% on the power spectrum and of similar size on some cosmological parameters: for example the position of the peaks shifts by 0.5% and the overall amplitude of the spectrum is about 0.4% lower than a full-sky case.Comment: 13 pages, 5 figure