ArtDeco: A beam deconvolution code for absolute CMB measurements

We present a method for beam deconvolution for cosmic microwave background (CMB) anisotropy measurements. The code takes as input the time-ordered data, along with the corresponding detector pointings and known beam shapes, and produces as output the harmonic a_Tlm, a_Elm, and a_Blm coefficients of the observed sky. From these one can further construct temperature and Q and U polarisation maps. The method is applicable to absolute CMB measurements with wide sky coverage, and is independent of the scanning strategy. We test the code with extensive simulations, mimicking the resolution and data volume of Planck 30GHz and 70GHz channels, but with exaggerated beam asymmetry. We apply it to multipoles up to l=1700 and examine the results in both pixel space and harmonic space. We also test the method also in presence of white noise.Comment: 15 page

Iterative destriping and photometric calibration for Planck-HFI, polarized, multi-detector map-making

We present an iterative scheme designed to recover calibrated I, Q, and U maps from Planck-HFI data using the orbital dipole due to the satellite motion with respect to the Solar System frame. It combines a map reconstruction, based on a destriping technique, juxtaposed with an absolute calibration algorithm. We evaluate systematic and statistical uncertainties incurred during both these steps with the help of realistic, Planck-like simulations containing CMB, foreground components and instrumental noise, and assess the accuracy of the sky map reconstruction by considering the maps of the residuals and their spectra. In particular, we discuss destriping residuals for polarization sensitive detectors similar to those of Planck-HFI under different noise hypotheses and show that these residuals are negligible (for intensity maps) or smaller than the white noise level (for Q and U Stokes maps), for l > 50. We also demonstrate that the combined level of residuals of this scheme remains comparable to those of the destriping-only case except at very low l where residuals from the calibration appear. For all the considered noise hypotheses, the relative calibration precision is on the order of a few 10e-4, with a systematic bias of the same order of magnitude.Comment: 18 pages, 21 figures. Match published versio

The impact of beam deconvolution on noise properties in CMB measurements: Application to Planck LFI

We present an analysis of the effects of beam deconvolution on noise properties in CMB measurements. The analysis is built around the artDeco beam deconvolver code. We derive a low-resolution noise covariance matrix that describes the residual noise in deconvolution products, both in harmonic and pixel space. The matrix models the residual correlated noise that remains in time-ordered data after destriping, and the effect of deconvolution on it. To validate the results, we generate noise simulations that mimic the data from the Planck LFI instrument. A $\chi^2$ test for the full 70 GHz covariance in multipole range $\ell=0-50$ yields a mean reduced $\chi^2$ of 1.0037. We compare two destriping options, full and independent destriping, when deconvolving subsets of available data. Full destriping leaves substantially less residual noise, but leaves data sets intercorrelated. We derive also a white noise covariance matrix that provides an approximation of the full noise at high multipoles, and study the properties on high-resolution noise in pixel space through simulations.Comment: 22 pages, 25 figure

MADAM - a map-making method for CMB experiments

We present a new map-making method for cosmic microwave background (CMB) measurements. The method is based on the destriping technique, but it also utilizes information about the noise spectrum. The low-frequency component of the instrument noise stream is modelled as a superposition of a set of simple base functions, whose amplitudes are determined by means of maximum-likelihood analysis, involving the covariance matrix of the amplitudes. We present simulation results with 1/f noise and show a reduction in the residual noise with respect to ordinary destriping. This study is related to Planck Low Frequency Instrument (LFI) activities.We present a new map-making method for cosmic microwave background (CMB) measurements. The method is based on the destriping technique, but it also utilizes information about the noise spectrum. The low-frequency component of the instrument noise stream is modelled as a superposition of a set of simple base functions, whose amplitudes are determined by means of maximum-likelihood analysis, involving the covariance matrix of the amplitudes. We present simulation results with 1/f noise and show a reduction in the residual noise with respect to ordinary destriping. This study is related to Planck Low Frequency Instrument (LFI) activities.We present a new map-making method for cosmic microwave background (CMB) measurements. The method is based on the destriping technique, but it also utilizes information about the noise spectrum. The low-frequency component of the instrument noise stream is modelled as a superposition of a set of simple base functions, whose amplitudes are determined by means of maximum-likelihood analysis, involving the covariance matrix of the amplitudes. We present simulation results with 1/f noise and show a reduction in the residual noise with respect to ordinary destriping. This study is related to Planck Low Frequency Instrument (LFI) activities.Peer reviewe

Effects of Destriping Errors on CMB Polarisation Power Spectra and and Pixel Noise Covariances

Low frequency detector noise in CMB experiments must be corrected to produce faithful maps of the temperature and polarization anisotropies. For a Planck-type experiment the low frequency noise corrections lead to residual stripes in the maps. Here I show that for a ring torus and idealised detector geometry it is possible to calculate analytically the effects of destriping errors on the temperature and polarization power spectra. It is also possible to compute the pixel-pixel noise covariances for maps of arbitrary resolution. The analytic model is compared to numerical simulations using a realistic detector and scanning geometries. We show that Planck polarization maps at 143 GHz should be signal dominated on large scales. Destriping errors are the dominant source of noise for the temperature and polarization power spectra at multipoles ell < 10. A fast Monte-Carlo method for characterising noise, including destriping errors, is described that can be applied to Planck. This Monte-Carlo method can be used to quantify pixel-pixel noise covariances and to remove noise biases in power spectrum estimates.Comment: 19 pages submitted to MNRA

Development of educational content for machine structures

Tässä diplomityössä tarkastellaan teräksisten konerakenteiden suunnitteluun liittyviä näkökohtia. Lisäksi pohditaan, mitä aihealueita konerakenteiden opetussisältöön tulisi kuulua. Apuna suunnittelunäkökohtien muodostamisessa olivat haastattelut koneenrakennusalan yrityksissä työskentelevien henkilöiden kanssa. Haastatellut henkilöt olivat opiskelleet Tampereen teknillisessä yliopistossa konetekniikkaa ja hiljattain siirtyneet työelämään konerakenteiden suunnittelun pariin. Työn ohessa oli tavoitteena kehittää TTY:n opintojaksoa Konerakenteiden suunnittelu. Diplomityön alussa esitetään konerakenteiden suunnitteluun liittyviä näkökohtia kirjallisuuden pohjalta. Erityisesti pyritään tarkastelemaan niitä asioita, joita tutkimukseen osallistuneet henkilöt nostivat esille. Alussa esitetyt näkökohdat ovat siis osittain muodostettu myös haastattelujen aineistoa hyödyntäen, kirjallisuuteen liittäen. Tämän jälkeen esitellään tutkimuksessa käytetty haastattelumenetelmä sekä annetaan perusteet haastateltavien valinnalle. Lisäksi tuodaan esille, kuinka haastattelut lopulta toteutuivat. Haastatteluaineistoon perustuen, konerakenteiden suunnittelijan on otettava huomioon seuraavia näkökohtia: toimivuus, turvallisuus, kustannukset ja valmistettavuus sekä rakenteen ulkonäkö. Suunnittelu tapahtuu näkökohtiin liittyvien reunaehtojen puitteissa. Esimerkiksi turvallisuusnäkökohtaan liittyy konedirektiivin edellyttämät turvallisuusvaatimukset. Haastattelun aineistosta nousivat esille varsinkin levyrakenteiden yleisyys konerakenteissa, kustannusnäkökulman rajoittavuus suunnittelussa sekä hitsausliitosten käsittelyn tarpeellisuus opetussisällössä. Tutkimuksen tuloksissa tuodaan esille myös yleisiä suunnitteluvinkkejä sekä suunnittelun ohessa hyödynnettyä lähdeaineistoa. Lisäksi haastattelun aineistosta on pyritty poimimaan suunnitteluhuomioita liittyen esimerkiksi liitosten suunnitteluun sekä korroosionestoon. Haastatteluiden perusteella muodostetaan arvio, kuinka merkittäviä eri aihealueet ovat konerakenteiden opetussisällössä. Lopuksi pohditaan muun muassa tutkimuksen onnistumista sekä muodostetaan ehdotus Konerakenteiden suunnittelu -kurssin luentoaiheiksi

Application of beam deconvolution technique to power spectrum estimation for CMB measurements

We present two novel methods for the estimation of the angular power spectrum of cosmic microwave background (CMB) anisotropies. We assume an absolute CMB experiment with arbitrary asymmetric beams and arbitrary sky coverage. The methods differ from the earlier ones in that the power spectrum is estimated directly from the time-ordered data, without first compressing the data into a sky map, and they take into account the effect of asymmetric beams. In particular, they correct the beam-induced leakage from temperature to polarization. The methods are applicable to a case where part of the sky has been masked out to remove foreground contamination, leaving a pure CMB signal, but incomplete sky coverage. The first method (deconvolution quadratic maximum likelihood) is derived as the optimal quadratic estimator, which simultaneously yields an unbiased spectrum estimate and minimizes its variance. We successfully apply it to multipoles up to l = 200. The second method is derived as a weak-signal approximation from the first one. It yields an unbiased estimate for the full multipole range, but relaxes the requirement of minimal variance. We validate the methods with simulations for the 70 GHz channel of Planck surveyor, and demonstrate that we are able to correct the beam effects in the TT, EE, BB and TE spectra up to multipole l = 1500. Together, the two methods cover the complete multipole range with no gap in between.Peer reviewe

Making cosmic microwave background temperature and polarization maps with MADAM

Peer reviewe

Effects of Destriping Errors on Estimates of the CMB Power Spectrum

Destriping methods for constructing maps of the Cosmic Microwave Background (CMB) anisotropies have been investigated extensively in the literature. However, their error properties have been studied in less detail. Here we present an analysis of the effects of destriping errors on CMB power spectrum estimates for Planck-like scanning strategies. Analytic formulae are derived for certain simple scanning geometries that can be rescaled to account for different detector noise. Assuming {Planck-like low-frequency noise, the noise power spectrum is accurately white at high multipoles (l<50). D estriping errors, though dominant at lower multipoles, are small in comparison to the cosmic variance. These results show that simple destriping map-making methods should be perfectly adequate for the analysis of Planck data and support the arguments given in an earlier paper in favour of applying a fast hybrid power spectrum estimator to CMB data with realistic `1/f' noise.Comment: 13 pages, 6 figures, submitted to MNRA

Planck intermediate results III : The relation between galaxy cluster mass and Sunyaev-Zeldovich signal

Peer reviewe