Improving PSF modelling for weak gravitational lensing using new methods in model selection

A simple theoretical framework for the description and interpretation of spatially correlated modelling residuals is presented, and the resulting tools are found to provide a useful aid to model selection in the context of weak gravitational lensing. The description is focused upon the specific problem of modelling the spatial variation of a telescope point spread function (PSF) across the instrument field of view, a crucial stage in lensing data analysis, but the technique may be used to rank competing models wherever data are described empirically. As such it may, with further development, provide useful extra information when used in combination with existing model selection techniques such as the Akaike and Bayesian Information Criteria, or the Bayesian evidence. Two independent diagnostic correlation functions are described and the interpretation of these functions demonstrated using a simulated PSF anisotropy field. The efficacy of these diagnostic functions as an aid to the correct choice of empirical model is then demonstrated by analyzing results for a suite of Monte Carlo simulations of random PSF fields with varying degrees of spatial structure, and it is shown how the diagnostic functions can be related to requirements for precision cosmic shear measurement. The limitations of the technique, and opportunities for improvements and applications to fields other than weak gravitational lensing, are discussed.Comment: 18 pages, 12 figures. Modified to match version accepted for publication in MNRA

S\'{e}rsic galaxy models in weak lensing shape measurement: model bias, noise bias and their interaction

Cosmic shear is a powerful probe of cosmological parameters, but its potential can be fully utilised only if galaxy shapes are measured with great accuracy. Two major effects have been identified which are likely to account for most of the bias for maximum likelihood methods in recent shear measurement challenges. Model bias occurs when the true galaxy shape is not well represented by the fitted model. Noise bias occurs due to the non-linear relationship between image pixels and galaxy shape. In this paper we investigate the potential interplay between these two effects when an imperfect model is used in the presence of high noise. We present analytical expressions for this bias, which depends on the residual difference between the model and real data. They can lead to biases not accounted for in previous calibration schemes. By measuring the model bias, noise bias and their interaction, we provide a complete statistical framework for measuring galaxy shapes with model fitting methods from GRavitational lEnsing Accuracy Testing (GREAT) like images. We demonstrate the noise and model interaction bias using a simple toy model, which indicates that this effect can potentially be significant. Using real galaxy images from the Cosmological Evolution Survey (COSMOS) we quantify the strength of the model bias, noise bias and their interaction. We find that the interaction term is often a similar size to the model bias term, and is smaller than the requirements of the current and shortly upcoming galaxy surveys.Comment: 11 pages, 3 figure

Characterization and correction of charge-induced pixel shifts in DECam

Interaction of charges in CCDs with the already accumulated charge distribution causes both a flux dependence of the point-spread function (an increase of observed size with flux, also known as the brighter/fatter effect) and pixel-to-pixel correlations of the Poissonian noise in flat fields. We describe these effects in the Dark Energy Camera (DECam) with charge dependent shifts of effective pixel borders, i.e. the Antilogus et al. (2014) model, which we fit to measurements of flat-field Poissonian noise correlations. The latter fall off approximately as a power-law r^-2.5 with pixel separation r, are isotropic except for an asymmetry in the direct neighbors along rows and columns, are stable in time, and are weakly dependent on wavelength. They show variations from chip to chip at the 20% level that correlate with the silicon resistivity. The charge shifts predicted by the model cause biased shape measurements, primarily due to their effect on bright stars, at levels exceeding weak lensing science requirements. We measure the flux dependence of star images and show that the effect can be mitigated by applying the reverse charge shifts at the pixel level during image processing. Differences in stellar size, however, remain significant due to residuals at larger distance from the centroid.Comment: typo and formatting fixes, matches version published in JINS

Measurement and Calibration of Noise Bias in Weak Lensing Galaxy Shape Estimation

Weak gravitational lensing has the potential to constrain cosmological parameters to high precision. However, as shown by the Shear TEsting Programmes (STEP) and GRavitational lEnsing Accuracy Testing (GREAT) Challenges, measuring galaxy shears is a nontrivial task: various methods introduce different systematic biases which have to be accounted for. We investigate how pixel noise on the image affects the bias on shear estimates from a Maximum-Likelihood forward model-fitting approach using a sum of co-elliptical S\'{e}rsic profiles, in complement to the theoretical approach of an an associated paper. We evaluate the bias using a simple but realistic galaxy model and find that the effects of noise alone can cause biases of order 1-10% on measured shears, which is significant for current and future lensing surveys. We evaluate a simulation-based calibration method to create a bias model as a function of galaxy properties and observing conditions. This model is then used to correct the simulated measurements. We demonstrate that this method can effectively reduce noise bias so that shear measurement reaches the level of accuracy required for estimating cosmic shear in upcoming lensing surveys.Comment: 12 pages, 4 figures, submitted to MNRA

Cosmological applications of weak gravitational flexion

Modern cosmology has reached an important juncture, at which the ability to make measurements of unprecedented accuracy has led to conclusions that are a fundamental challenge to natural science. The discovery that, in our current best model, the dynamics of the Universe are completely dominated by unseen dark matter and dark energy can do little but completely alter the shape of physics research in the 21st Century. Unfortunately,much of our insight into these phenomenamust come from observations of visible matter alone; this raises serious problems, as the tracing of dark matter by visible matter is as yet poorly understood. Gravitational lensing offers strong prospects for probing the interwoven history of dark and visible matter, as mass in any form may be detected where it exists untraced by baryons. In this Thesis I describe advances made in the field of weak gravitational lensing, which constrains the properties of the matter distribution on cosmological scales using a statistical analysis of the coherent gravitational distortions of distant galaxy images. I summarize the development of gravitational flexion, a higher order extension to traditional weak lensing, and describe my work done to bring the study of flexion to a stage where it may be employed to make accurate cosmological measurements. I show how flexion is sensitive to matter structure on smaller physical scales than existing lensing techniques and, therefore, promises to shed new light upon key untested predictions of cosmological models if it can be measured to sufficient accuracy. I discuss the success of my efforts in this direction, and describe the issues to be encountered in the careful analysis of this subtle gravitational signal. This research has involved advances in many areas: the calculation of theoretical flexion predictions, the refinement of image analysis methods for accurate galaxy shape estimation, and the practical application of these new flexion techniques to extragalactic imaging data. The culmination of these efforts is a new maximum likelihood analysis of the galaxy-galaxy lensing signal in the Hubble Space Telescope Galaxy Evolution from Morphology and SEDs (GEMS) Survey, incorporating improvements and modifications necessary for the combination of flexion with traditional weak lensing measurements. The results of this work, and particularly the extent to which measurements of flexion provide extra cosmological insight, are discussed in detail. The conclusion is a summary of all that has been learned about the use of flexion as an accurate probe of cosmology, and a discussion of its prospects for answering some of the many questions that remain about dark matter. Within the next few year wide-area survey telescopes will begin imaging huge volumes of deep space, with the measurement of the gravitational lensing signal being given high priority in the analysis of these data. Within this context, the primary inquiry of this Thesis is the extent to which the application of flexion measurement techniques will help shed new light upon the unseen, and currently poorly understood, components of the Universe

Noise bias in weak lensing shape measurements

Weak lensing experiments are a powerful probe of cosmology through their measurement of the mass distribution of the universe. A challenge for this technique is to control systematic errors that occur when measuring the shapes of distant galaxies. In this paper we investigate noise bias, a systematic error that arises from second order noise terms in the shape measurement process. We first derive analytical expressions for the bias of general Maximum Likelihood Estimators (MLEs) in the presence of additive noise. We then find analytical expressions for a simplified toy model in which galaxies are modeled and fitted with a Gaussian with its size as a single free parameter. Even for this very simple case we find a significant effect. We also extend our analysis to a more realistic 6-parameter elliptical Gaussian model. We find that the noise bias is generically of the order of the inverse-squared signal-to-noise ratio (SNR) of the galaxies and is thus of the order of a percent for galaxies of SNR of 10, i.e. comparable to the weak lensing shear signal. This is nearly two orders of magnitude greater than the systematics requirements for future all-sky weak lensing surveys. We discuss possible ways to circumvent this effect, including a calibration method using simulations discussed in an associated paper.Comment: 8 pages, 3 figures, submitted to MNRA