97 research outputs found
Sparse image reconstruction on the sphere: analysis and synthesis
We develop techniques to solve ill-posed inverse problems on the sphere by
sparse regularisation, exploiting sparsity in both axisymmetric and directional
scale-discretised wavelet space. Denoising, inpainting, and deconvolution
problems, and combinations thereof, are considered as examples. Inverse
problems are solved in both the analysis and synthesis settings, with a number
of different sampling schemes. The most effective approach is that with the
most restricted solution-space, which depends on the interplay between the
adopted sampling scheme, the selection of the analysis/synthesis problem, and
any weighting of the l1 norm appearing in the regularisation problem. More
efficient sampling schemes on the sphere improve reconstruction fidelity by
restricting the solution-space and also by improving sparsity in wavelet space.
We apply the technique to denoise Planck 353 GHz observations, improving the
ability to extract the structure of Galactic dust emission, which is important
for studying Galactic magnetism.Comment: 11 pages, 6 Figure
A new map-making algorithm for CMB polarisation experiments
With the temperature power spectrum of the cosmic microwave background (CMB)
at least four orders of magnitude larger than the B-mode polarisation power
spectrum, any instrumental imperfections that couple temperature to
polarisation must be carefully controlled and/or removed. Here we present two
new map-making algorithms that can create polarisation maps that are clean of
temperature-to-polarisation leakage systematics due to differential gain and
pointing between a detector pair. Where a half wave plate is used, we show that
the spin-2 systematic due to differential ellipticity can also by removed using
our algorithms. The algorithms require no prior knowledge of the imperfections
or temperature sky to remove the temperature leakage. Instead, they calculate
the systematic and polarisation maps in one step directly from the time ordered
data (TOD). The first algorithm is designed to work with scan strategies that
have a good range of crossing angles for each map pixel and the second for scan
strategies that have a limited range of crossing angles. The first algorithm
can also be used to identify if systematic errors that have a particular spin
are present in a TOD. We demonstrate the use of both algorithms and the ability
to identify systematics with simulations of TOD with realistic scan strategies
and instrumental noise.Comment: 11 pages, 6 figure
Optimal scan strategies for future CMB satellite experiments
The B-mode polarisation power spectrum in the Cosmic Microwave Background
(CMB) is about four orders of magnitude fainter than the CMB temperature power
spectrum. Any instrumental imperfections that couple temperature fluctuations
to B-mode polarisation must therefore be carefully controlled and/or removed.
We investigate the role that a scan strategy can have in mitigating certain
common systematics by averaging systematic errors down with many crossing
angles. We present approximate analytic forms for the error on the recovered
B-mode power spectrum that would result from differential gain, differential
pointing and differential ellipticity for the case where two detector pairs are
used in a polarisation experiment. We use these analytic predictions to search
the parameter space of common satellite scan strategies in order to identify
those features of a scan strategy that have most impact in mitigating
systematic effects. As an example we go on to identify a scan strategy suitable
for the CMB satellite proposed for the ESA M5 call. considering the practical
considerations of fuel requirement, data rate and the relative orientation of
the telescope to the earth. Having chosen a scan strategy we then go on to
investigate the suitability of the scan strategy.Comment: 21 pages, 11 figures, Comments welcom
Removing beam asymmetry bias in precision CMB temperature and polarisation experiments
Asymmetric beams can create significant bias in estimates of the power
spectra from CMB experiments. With the temperature power spectrum many orders
of magnitude stronger than the B-mode power spectrum any systematic error that
couples the two must be carefully controlled and/or removed. Here, we derive
unbiased estimators for the CMB temperature and polarisation power spectra
taking into account general beams and general scan strategies. A simple
consequence of asymmetric beams is that, even with an ideal scan strategy where
every sky pixel is seen at every orientation, there will be residual coupling
from temperature power to B-mode power if the orientation of the beam asymmetry
is not aligned with the orientation of the co-polarisation. We test our
correction algorithm on simulations of two temperature-only experiments and
demonstrate that it is unbiased. The simulated experiments use realistic scan
strategies, noise levels and highly asymmetric beams. We also develop a
map-making algorithm that is capable of removing beam asymmetry bias at the map
level. We demonstrate its implementation using simulations and show that it is
capable of accurately correcting both temperature and polarisation maps for all
of the effects of beam asymmetry including the effects of temperature to
polarisation leakage.Comment: 18 pages, 9 figure
Removing beam asymmetry bias in precision CMB temperature and polarisation experiments
Asymmetric beams can create significant bias in estimates of the power
spectra from CMB experiments. With the temperature power spectrum many orders
of magnitude stronger than the B-mode power spectrum any systematic error that
couples the two must be carefully controlled and/or removed. Here, we derive
unbiased estimators for the CMB temperature and polarisation power spectra
taking into account general beams and general scan strategies. A simple
consequence of asymmetric beams is that, even with an ideal scan strategy where
every sky pixel is seen at every orientation, there will be residual coupling
from temperature power to B-mode power if the orientation of the beam asymmetry
is not aligned with the orientation of the co-polarisation. We test our
correction algorithm on simulations of two temperature-only experiments and
demonstrate that it is unbiased. The simulated experiments use realistic scan
strategies, noise levels and highly asymmetric beams. We also develop a
map-making algorithm that is capable of removing beam asymmetry bias at the map
level. We demonstrate its implementation using simulations and show that it is
capable of accurately correcting both temperature and polarisation maps for all
of the effects of beam asymmetry including the effects of temperature to
polarisation leakage.Comment: 18 pages, 9 figure
Sparse Bayesian mass-mapping with uncertainties: hypothesis testing of structure
A crucial aspect of mass-mapping, via weak lensing, is quantification of the
uncertainty introduced during the reconstruction process. Properly accounting
for these errors has been largely ignored to date. We present results from a
new method that reconstructs maximum a posteriori (MAP) convergence maps by
formulating an unconstrained Bayesian inference problem with Laplace-type
-norm sparsity-promoting priors, which we solve via convex
optimization. Approaching mass-mapping in this manner allows us to exploit
recent developments in probability concentration theory to infer theoretically
conservative uncertainties for our MAP reconstructions, without relying on
assumptions of Gaussianity. For the first time these methods allow us to
perform hypothesis testing of structure, from which it is possible to
distinguish between physical objects and artifacts of the reconstruction. Here
we present this new formalism, demonstrate the method on illustrative examples,
before applying the developed formalism to two observational datasets of the
Abel-520 cluster. In our Bayesian framework it is found that neither Abel-520
dataset can conclusively determine the physicality of individual local massive
substructure at significant confidence. However, in both cases the recovered
MAP estimators are consistent with both sets of data
Effect of vessel wettability on the foamability of "ideal" surfactants and "real-world" beer heads
The ability to tailor the foaming properties of a solution by controlling its chemical composition is highly desirable and has been the subject of extensive research driven by a range of applications. However, the control of foams by varying the wettability of the foaming vessel has been less widely reported. This work investigates the effect of the wettability of the side walls of vessels used for the in situ generation of foam by shaking aqueous solutions of three different types of model surfactant systems (non-ionic, anionic and cationic surfactants) along with four different beers (Guinness Original, Banks’s Bitter, Bass No 1 and Harvest Pale). We found that hydrophilic vials increased the foamability only for the three model systems but increased foam stability for all foams except the model cationic system. We then compared stability of beer foams produced by shaking and pouring and demonstrated weak qualitative agreement between both foam methods. We also showed how wettability of the glass controls bubble nucleation for beers and champagne and used this effect to control exactly where bubbles form using simple wettability patterns
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