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Register a new userAn Implementation of Bayesian Lensing Shear Measurement
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Erin S. Sheldon
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The Bayesian gravitational shear estimation algorithm developed by Bernstein and Armstrong (2014) can potentially be used to overcome multiplicative noise bias and recover shear using very low signal-to-noise ratio (S/N) galaxy images. In that work the authors confirmed the method is nearly unbiased in a simplified demonstration, but no test was performed on images with realistic pixel noise. Here I present a full implementation for fitting models to galaxy images, including the effects of a point spread function (PSF) and pixelization. I tested the implementation using simulated galaxy images modeled as Sersic profiles with n=1 (exponential) and n=4 (De Vaucouleurs), convolved with a PSF and a flat pixel response function. I used a round Gaussian model for the PSF to avoid potential PSF-fitting errors. I simulated galaxies with mean observed, post-PSF full-width at half maximum equal to approximately 1.2 times that of the PSF, with log-normal scatter. I also drew fluxes from a log-normal distribution. I produced independent simulations, each with pixel noise tuned to produce different mean S/N ranging from 10-1000. I applied a constant shear to all images. I fit the simulated images to a model with the true Sersic index to avoid modeling biases. I recovered the input shear with fractional error less than 2 x 10^{-3} in all cases. In these controlled conditions, and in the absence of other multiplicative errors, this implementation is sufficiently unbiased for current surveys and approaches the requirements for planned surveys.
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Metacalibration is a recently introduced method to accurately measure weak gravitational lensing shear using only the available imaging data, without need for prior information about galaxy properties or calibration from simulations. The method involves distorting the image with a small known shear, and calculating the response of a shear estimator to that applied shear. The method was shown to be accurate in moderate sized simulations with galaxy images that had relatively high signal-to-noise ratios, and without significant selection effects. In this work we introduce a formalism to correct for both shear response and selection biases. We also observe that, for images with relatively low signal-to-noise ratios, the correlated noise that arises during the metacalibration process results in significant bias, for which we develop a simple empirical correction. To test this formalism, we created large image simulations based on both parametric models and real galaxy images, including tests with realistic point-spread functions. We varied the point-spread function ellipticity at the five percent level. In each simulation we applied a small, few percent shear to the galaxy images. We introduced additional challenges that arise in real data, such as detection thresholds, stellar contamination, and missing data. We applied cuts on the measured galaxy properties to induce significant selection effects. Using our formalism, we recovered the input shear with an accuracy better than a part in a thousand in all cases.
The VST Optical Imaging of the CDFS and ES1 Fields (VOICE) Survey is a Guaranteed Time program carried out with the ESO/VST telescope to provide deep optical imaging over two 4 deg$^2$ patches of the sky centred on the CDFS and ES1 pointings. We present the cosmic shear measurement over the 4 deg$^2$ covering the CDFS region in the $r$-band using LensFit. Each of the four tiles of 1 deg$^2$ has more than one hundred exposures, of which more than 50 exposures passed a series of image quality selection criteria for weak lensing study. The $5sigma$ limiting magnitude in $r$- band is 26.1 for point sources, which is $sim$1 mag deeper than other weak lensing survey in the literature (e.g. the Kilo Degree Survey, KiDS, at VST). The photometric redshifts are estimated using the VOICE $u,g,r,i$ together with near-infrared VIDEO data $Y,J,H,K_s$. The mean redshift of the shear catalogue is 0.87, considering the shear weight. The effective galaxy number density is 16.35 gal/arcmin$^2$, which is nearly twice the one of KiDS. The performance of LensFit on such a deep dataset was calibrated using VOICE-like mock image simulations. Furthermore, we have analyzed the reliability of the shear catalogue by calculating the star-galaxy cross-correlations, the tomographic shear correlations of two redshift bins and the contaminations of the blended galaxies. As a further sanity check, we have constrained cosmological parameters by exploring the parameter space with Population Monte Carlo sampling. For a flat $Lambda$CDM model we have obtained $Sigma_8$ = $sigma_8(Omega_m/0.3)^{0.5}$ = $0.68^{+0.11}_{-0.15}$.
We present and describe im3shape, a new publicly available galaxy shape measurement code for weak gravitational lensing shear. im3shape performs a maximum likelihood fit of a bulge-plus-disc galaxy model to noisy images, incorporating an applied point spread function. We detail challenges faced and choices made in its design and implementation, and then discuss various limitations that affect this and other maximum likelihood methods. We assess the bias arising from fitting an incorrect galaxy model using simple noise-free images and find that it should not be a concern for current cosmic shear surveys. We test im3shape on the GREAT08 Challenge image simulations, and meet the requirements for upcoming cosmic shear surveys in the case that the simulations are encompassed by the fitted model, using a simple correction for image noise bias. For the fiducial branch of GREAT08 we obtain a negligible additive shear bias and sub-two percent level multiplicative bias, which is suitable for analysis of current surveys. We fall short of the sub-percent level requirement for upcoming surveys, which we attribute to a combination of noise bias and the mis-match between our galaxy model and the model used in the GREAT08 simulations. We meet the requirements for current surveys across all branches of GREAT08, except those with small or high noise galaxies, which we would cut from our analysis. Using the GREAT08 metric we we obtain a score of Q=717 for the usable branches, relative to the goal of Q=1000 for future experiments. The code is freely available from https://bitbucket.org/joezuntz/im3shape
Cosmic shear is a primary cosmological probe for several present and upcoming surveys investigating dark matter and dark energy, such as Euclid or WFIRST. The probe requires an extremely accurate measurement of the shapes of millions of galaxies based on imaging data. Crucially, the shear measurement must address and compensate for a range of interwoven nuisance effects related to the instrument optics and detector, noise, unknown galaxy morphologies, colors, blending of sources, and selection effects. This paper explores the use of supervised machine learning (ML) as a tool to solve this inverse problem. We present a simple architecture that learns to regress shear point estimates and weights via shallow artificial neural networks. The networks are trained on simulations of the forward observing process, and take combinations of moments of the galaxy images as inputs. A challenging peculiarity of this ML application is the combination of the noisiness of the input features and the requirements on the accuracy of the inverse regression. To address this issue, the proposed training algorithm minimizes bias over multiple realizations of individual source galaxies, reducing the sensitivity to properties of the overall sample of source galaxies. Importantly, an observational selection function of these source galaxies can be straightforwardly taken into account via the weights. We first introduce key aspects of our approach using toy-model simulations, and then demonstrate its potential on images mimicking Euclid data. Finally, we analyze images from the GREAT3 challenge, obtaining competitively low shear biases despite the use of a simple training set. We conclude that the further development of ML approaches is of high interest to meet the stringent requirements on the shear measurement in current and future surveys. A demonstration implementation of our technique is publicly available.
A likelihood-based method for measuring weak gravitational lensing shear in deep galaxy surveys is described and applied to the Canada-France-Hawaii Telescope (CFHT) Lensing Survey (CFHTLenS). CFHTLenS comprises 154 sq deg of multicolour optical data from the CFHT Legacy Survey, with lensing measurements being made in the i band to a depth i(AB)<24.7, for galaxies with signal-to-noise ratio greater than about 10. The method is based on the lensfit algorithm described in earlier papers, but here we describe a full analysis pipeline that takes into account the properties of real surveys. The method creates pixel-based models of the varying point spread function (PSF) in individual image exposures. It fits PSF-convolved two-component (disk plus bulge) models, to measure the ellipticity of each galaxy, with bayesian marginalisation over model nuisance parameters of galaxy position, size, brightness and bulge fraction. The method allows optimal joint measurement of multiple, dithered image exposures, taking into account imaging distortion and the alignment of the multiple measurements. We discuss the effects of noise bias on the likelihood distribution of galaxy ellipticity. Two sets of image simulations that mirror the observed properties of CFHTLenS have been created, to establish the methods accuracy and to derive an empirical correction for the effects of noise bias.
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