Harmonic analysis of cosmic microwave background data -- II. From ring-sets to the sky

Challinor, A.; Mortlock, D.; Leeuwen, F. van; Lasenby, A.; Hobson, M.; Ashdown, M.; Efstathiou, G.

doi:10.1046/j.1365-8711.2002.05255.x

Cited by 23 publications

(31 citation statements)

References 44 publications

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“…We note that, although not considered in this work, most of the complications associated with low resolution mapmaking can be directly addressed by constructing the map in harmonic domain instead of pixel domain (Challinor et al 2002;Armitage & Wandelt 2004;Armitage-Caplan & Wandelt 2009). A study of residual noise covariance with such methods would make an interesting extension to that presented here.…”

Section: Resultsmentioning

confidence: 99%

Residual noise covariance forPlancklow-resolution data analysis

Keskitalo

Ashdown

Cabella

et al. 2010

A&A

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Aims. We develop and validate tools for estimating residual noise covariance in Planck frequency maps, we also quantify signal error effects and compare different techniques to produce low-resolution maps. Methods. We derived analytical estimates of covariance of the residual noise contained in low-resolution maps produced using a number of mapmaking approaches. We tested these analytical predictions using both Monte Carlo simulations and by applying them to angular power spectrum estimation. We used simulations to quantify the level of signal errors incurred in the different resolution downgrading schemes considered in this work. Results. We find excellent agreement between the optimal residual noise covariance matrices and Monte Carlo noise maps. For destriping mapmakers, the extent of agreement is dictated by the knee frequency of the correlated noise component and the chosen baseline offset length. Signal striping is shown to be insignificant when properly dealt with. In map resolution downgrading, we find that a carefully selected window function is required to reduce aliasing to the subpercent level at multipoles, > 2N side , where N side is the HEALPix resolution parameter. We show that, for a polarization measurement, reliable characterization of the residual noise is required to draw reliable constraints on large-scale anisotropy.Conclusions. Methods presented and tested in this paper allow for production of low-resolution maps with both controlled sky signal error level and a reliable estimate of covariance of the residual noise. We have also presented a method for smoothing the residual noise covariance matrices to describe the noise correlations in smoothed, bandwidth-limited maps.

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Section: Resultsmentioning

confidence: 99%

Residual noise covariance forPlancklow-resolution data analysis

Keskitalo

Ashdown

Cabella

et al. 2010

A&A

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“…Various strategies for speeding up ML estimation have been proposed, such as exploiting the symmetries of the scan strategy (Oh, Spergel & Hinshaw 1999), using hierarchical decomposition (Dore, Knox & Peel 2001), iterative multigrid method (Pen 2003), etc. Variants employing linear combinations of , such as a lm on a set of rings in the sky, can alleviate the computational demands in special cases (Challinor et al 2002; van Leeuwen et al 2002; Wandelt & Hansen 2003). Other promising ‘exact’ power estimation methods have been recently proposed (Knox, Christensen & Skordis 2001; Jewell, Levin & Anderson 2004; Wandelt 2003).…”

Section: Introductionmentioning

confidence: 99%

Cosmic microwave background power spectrum estimation with non-circular beam and incomplete sky coverage

Mitra¹,

Sengupta²,

Ray³

et al. 2009

Monthly Notices of the Royal Astronomical Society

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Over the last decade, measurements of the cosmic microwave background (CMB) anisotropy have spearheaded the remarkable transition of cosmology into a precision science. However, addressing the systematic effects in the increasingly sensitive, high‐resolution, ‘full’ sky measurements from different CMB experiments poses a stiff challenge. The analysis techniques must not only be computationally fast to contend with the huge size of the data, but the higher sensitivity also limits the simplifying assumptions which can then be invoked to achieve the desired speed without compromising the final precision goals. While maximum likelihood is desirable, the enormous computational cost makes the suboptimal method of power spectrum estimation using pseudo‐Cl unavoidable for high‐resolution data. The debiasing of the pseudo‐Cl needs account for non‐circular beams, together with non‐uniform sky coverage. We provide a (semi)analytic framework to estimate bias in the power spectrum due to the effect of beam non‐circularity and non‐uniform sky coverage, including incomplete/masked sky maps and scan strategy. The approach is perturbative in the distortion of the beam from non‐circularity, allowing for rapid computations when the beam is mildly non‐circular. We advocate that it is computationally advantageous to employ ‘soft’ azimuthally apodized masks whose spherical harmonic transform die down fast with m. We numerically implement our method for non‐rotating beams. We present preliminary estimates of the computational cost to evaluate the bias for the upcoming CMB anisotropy probes (lmax∼ 3000), with angular resolution comparable to the Planck surveyor mission. We further show that this implementation and estimate are applicable for rotating beams on equal declination scans, and can possibly be extended to simple approximations to other scan strategies.

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“…As shown by Challinor et al (2002) the correlations in the noise between different Fourier modes on the rings are expected to be negligible. This expectation was verified and we therefore treat the noise covariance matrix, N, for those data as diagonal.…”

Section: Sky Reconstructionmentioning

confidence: 96%

A deconvolution map-making method for experiments with circular scanning strategies

Harrison

Leeuwen

Ashdown³

2011

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Aims. We investigate the performance of a deconvolution map-making algorithm for an experiment with a circular scanning strategy, specifically in this case for the analysis of Planck data, and we quantify the effects of making maps using simplified approximations to the true beams. Methods. We present an implementation of a map-making algorithm which allows the combined treatment of temperature and polarisation data, and removal of instrumental effects, such as detector time constants and finite sampling intervals, as well as the deconvolution of arbitrarily complex beams from the maps. This method may be applied to any experiment with a circular scanningstrategy.Results. Low-resolution experiments were used to demonstrate the ability of this method to remove the effects of arbitrary beams from the maps and to demonstrate the effects on the maps of ignoring beam asymmetries. Additionally, results are presented of an analysis of a realistic full-scale simulated data-set for the Planck LFI 30 GHz channel. Conclusions. Our method successfully removes the effects of the beams from the maps, and although it is computationally expensive, the analysis of the Planck LFI data should be feasible with this approach.

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Harmonic analysis of cosmic microwave background data -- II. From ring-sets to the sky

Cited by 23 publications

References 44 publications

Residual noise covariance forPlancklow-resolution data analysis

Residual noise covariance forPlancklow-resolution data analysis

Cosmic microwave background power spectrum estimation with non-circular beam and incomplete sky coverage

A deconvolution map-making method for experiments with circular scanning strategies

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