Shapelets — II. A method for weak lensing measurements

By Alexandre Refregier, D. Bacon. 2001

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Weak gravitational lensing provides a unique method to directly measure the distribution of mass in the Universe. Because the distortions induced by lensing in the shape of background galaxies are small, the measurement of weak lensing requires high precision. Here, we present a new method for obtaining reliable weak shear measurements. It is based on the shapelet function formalism presented in an earlier paper in which galaxy images are decomposed into several shape components, each providing independent estimates of the local shear. The formalism affords an efficient modelling and deconvolution of the point spread function. Using the unique properties of shapelets under distortions, we construct a simple, minimum variance estimator for the shear. We describe how we implement the method in practice, and test the method using realistic simulated images. We find our method to be stable and reliable for conditions analogous to ground-based surveys. Compared to earlier methods, our method has the advantages of being accurate, linear, mathematically well-defined, and optimally sensitive, as it uses the full shape information available for each galaxy.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/407a358a1bfd6459a1e92cc811c023ee9c61330d

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Citations in the corpus

CFHTLenS: Improving the quality of photometric redshifts with precision photometry (2011, methodology): “Shapelets have the useful property that a convolution of any two of them can be written as a new (generally infinite) shapelet series: Sab ⊗ Scd = ∑ ef CaceCbdfSef (A3) and expressions for the matrix elements Clmn are given in Refregier & Bacon (2003).”
The Shear TEsting Programme 2: Factors affecting high precision weak lensing analyses (2006, methodology): “They are modelled using shapelets (Bernstein & Jarvis 2002; Refregier 2003; Refregier & Bacon 2003; Massey & Refregier 2005), a (complete) set of orthogonal basis functions that can be used to describe the shape of any isolated object.”
COSMOS: Three-dimensional Weak Lensing and the Growth of Structure (2007, methodology): “This program has also sped the development of a next generation of even more accurate shear measurement methods (Bridle et al. 2002; Refregier & Bacon 2003; Bernstein & Jarvis 2002; Massey & Refregier 2005; Mandelbaum et al. 2005; Kuijken 2006; Nakajima & Bernstein 2007;Massey et al. 2006).”
Evidence of the accelerated expansion of the Universe from weak lensing tomography with COSMOS (2009, methodology): “The images were created with the Massey et al. (2004) image simulation pipeline, which uses shapelets (Refregier & Bacon 2003; Massey & Refregier 2005) to model galaxy and PSF shapes, as already employed for the STEP2 simulations (Massey et al. 2007a).”
Gravitational lensing analysis of the Kilo-Degree Survey (2015, background): “…used to characterize the galaxy populations (e.g. Kelly & McKay 2004; Melchior, Meneghetti & Bartelmann 2007), to measure weak lensing shear (e.g. Refregier & Bacon 2003; Kuijken 2006) and flexion (e.g. Bacon et al. 2006; Massey et al. 2007; Velander, Kuijken & Schrabback 2011) and for…”
Observational probes of cosmic acceleration (2012, methodology): “The “shapelet” basis (Refregier, 2003; Refregier and Bacon, 2003), derived from energy eigenstates of a 2D quantum harmonic oscillator, is useful in both types of methods.”
The shear power spectrum from the COMBO-17 survey (2002, background): “…the ellipticities, eij = ( e1 e2 e2 −e1 ) (1) of each galaxy from its quadrupole moments at a given isophotal threshold (Kaiser, Squires and Broadhurst, 1995) or by examining the distortion to a set of orthogonal modes describing the galaxy shape (Refregier & Bacon 2003; Bernstein & Jarvis, 2002).”
Shear calibration biases in weak-lensing surveys (2003, methodology): “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).”
The Shear Testing Programme – I. Weak lensing analysis of simulated ground-based observations (2005, methodology): “Thorough testing of these newer techniques is however somewhat lacking in the literature, although see Refregier & Bacon (2003) and Massey, Refregier & Bacon (2004a) for tests of the shapelets method.”
Weak Gravitational Lensing by Large-Scale Structure (2003, methodology): “Refregier & Bacon (2003) and, independently, Bernstein & Jarvis (2001) developed a new method based on the decomposition of the galaxies into shape components or “shapelets”.”
Galaxy–galaxy weak lensing in the Sloan Digital Sky Survey: intrinsic alignments and shear calibration errors (2004, methodology): “…currently the largest item in the calibration error budget; this error will be reduced in future studies by using more accurate but computationally expensive PSF correction methods such as re-Gaussianization (Hirata & Seljak 2003) or shapelet decomposition (Refreiger 2003b; Refregier & Bacon 2003).”
Systematic errors in weak lensing: application to SDSS galaxy-galaxy weak lensing (2005, methodology): “…1287–1322 Downloaded from https://academic.oup.com/mnras/article-abstract/361/4/1287/1117325 by guest on 27 July 2018 direct fitting of the convolved galaxy to the data (Bernstein & Jarvis 2002) or deconvolution regularized by a cutoff in the orthogonal function expansion (Refregier & Bacon 2003).”