Shapes and Shears, Stars and Smears: Optimal Measurements for Weak Lensing

By G. Bernstein, Michael J. Jarvis. 2001

436 citations recorded by the source corpus.

We present the theoretical and analytical bases of optimal techniques to measure weak gravitational shear from images of galaxies. We first characterize the geometric space of shears and ellipticity and then use this geometric interpretation to analyze images. The steps of this analysis include measurement of object shapes on images, combining measurements of a given galaxy on different images, estimating the underlying shear from an ensemble of galaxy shapes, and compensating for the systematic effects of image distortion, bias from point-spread function (PSF) asymmetries, and "dilution" of the signal by the seeing. These methods minimize the ellipticity measurement noise, provide calculable shear uncertainty estimates, and allow removal of systematic contamination by PSF effects to arbitrary precision. Galaxy images and PSFs are expressed as "Laguerre expansions," a two-dimensional generalization of the Edgeworth expansion, making the PSF correction and shape measurement relatively straightforward and computationally efficient. We also discuss sources of noise-induced bias in weak-lensing measurements—selection biases, and "centroid" biases arising from noise rectification—and provide a solution for these and previously identified biases.

Subfields: Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/efb4f3016ec7deb79b747162854791edcaa10f88

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Citations in the corpus

Cosmology from cosmic shear power spectra with Subaru Hyper Suprime-Cam first-year data (2018, background): “…galaxy, γ(obs), is estimated from the measured ellipticity e as follows: γ(obs) = 1 1 + 〈m〉 ( e 2R − c ) , (2) whereR represents the responsivity that describes the response of our ellipticity definition to a small shear (Kaiser et al. 1995; Bernstein & Jarvis 2002) and is given by R= 1−〈e2rms〉 .”
The Disk Substructures at High Angular Resolution Project (DSHARP). II. Characteristics of Annular Substructures (2018, background): “Even when an intensity profile deviates from a Gaussian, a Gaussian fit should still provide a good estimate of the source inclination and P.A. provided that the emission is axisymmetric and much larger than the PSF (e.g., Bernstein & Jarvis 2002).”
The first-year shear catalog of the Subaru Hyper Suprime-Cam Subaru Strategic Program Survey (2017, background): “One of these is “noise bias” (e.g., Bernstein & Jarvis 2002; Hirata et al. 2004; Kacprzak et al. 2012; Melchior & Viola 2012; Refregier et al. 2012), wherein the pixel noise modifies the shape of the likelihood surface and causes the maximumlikelihood estimator of per-galaxy shapes to be biased.”
Systematic errors in future weak-lensing surveys: requirements and prospects for self-calibration (2005, background): “Realistic assessments of systematic errors is likely to impact strategies for measuring the weak lensing shear (Bernstein 2002, Bernstein & Jarvis 2002, Rhodes et al. 2004, Mandelbaum et al. 2005).”
Weak Lensing Measurement of the Mass--Richness Relation of SDSS redMaPPer Clusters (2016, background): “We are interested in lensing shears, not distortions2, so we must correct for the difference, and also for the fact that shears do not add linearly (Bernstein & Jarvis 2002).”
Cosmological parameter constraints from galaxy-galaxy lensing and galaxy clustering with the SDSS DR7 (2012, background): “29) to a small shear (Kaiser et al. 1995; Bernstein & Jarvis 2002); R = 1− e2rms.”
The Shear TEsting Programme 2: Factors affecting high precision weak lensing analyses (2006, methodology): “Nor does matching has a significant effect on the overall mean polarization of galaxies, which is always consistent with zero both before and after matching – as might not have been the case in the presence of selection effects (Bernstein & Jarvis 2002; Hirata & Seljak 2003).”
Effects of Photometric Redshift Uncertainties on Weak-Lensing Tomography (2005, background): “Such studies have stimulated work on how to improve the PSF reconstruction (Jarvis & Jain 2004), estimate shear from noisy maps (Bernstein & Jarvis 2002; Hirata & Seljak 2003; Hoekstra 2004), and protect against the small-scale biases in the power spectrum (Huterer & White 2005).”
THE DARK ENERGY CAMERA (2004, background): “The DES science goals require a large-area survey with accurate photometry of faint sources in g, r, i, and zbands, as well as accurate shape measurements (Bernstein & Jarvis 2002), particularly in rband and iband.”
Shear calibration biases in weak-lensing surveys (2003, background): “Recently, there have been several new approaches proposed dealing with various aspects of this problem developed by Kaiser (2000), Bernstein & Jarvis (2002) (BJ02) and Refregier & Bacon (2003).”
Results of the GREAT08 Challenge?: an image analysis competition for cosmological lensing: Results o (2009, background): “For more information, see Bernstein & Jarvis (2002), Nakajima & Bernstein (2007) and appendix D of the GREAT08 Handbook.”
CFHTLenS: the Canada–France–Hawaii Telescope Lensing Survey – imaging data and catalogue products (2012, background): “One notable exception is Bernstein & Jarvis (2002) who advocate the weak lensing analysis of individual exposure data rather than stacks, by averaging the shear measurements from multiple exposures on a catalogue level.”
Cosmological constraints from cosmic shear two-point correlation functions with HSC survey first-year data (2019, background): “…galaxy as γ̂i = 1 1+ m̄ [ ei 2R − ci ] , (1) with the weighted-average multiplicative bias factor, m̄= ∑ i wimi ∑ i wi , (2) and the shear responsivity R representing the response of the distortion to a small shear (Kaiser et al. 1995; Bernstein & Jarvis 2002) given by R= 1− ∑ i wie 2 rms ∑ i wi .”
Bayesian galaxy shape measurement for weak lensing surveys – III. Application to the Canada–France–Hawaii Telescope Lensing Survey (2012, methodology): “However, although the weight is designed to be isotropic, it is possible for there to exist a form of ‘orientation bias’ similar to the selection bias discussed by Kaiser (2000) and Bernstein & Jarvis (2002).”
Potential sources of contamination to weak lensing measurements: constraints from N-body simulations (2006, methodology): “…galaxy shapeson weak lensing measurements we then define and use the alternative ellipticity parametersei given by ei = εi 2R , (4) where the responsivityR is a correction to account for the response of an ensemble of galaxies to weak lensing shear (Rhodes et al. 2000; Bernstein & Jarvis 2002).”