Shapelets: A New Method to Measure Galaxy Shapes

Parametrising galaxy morphologies is a challenging task, e.g., in shear measurements of weak lensing or investigations of galaxy evolution. The huge variety of morphologies requires an approach that is highly flexible, e.g., accounting for azimuthal structure. We revisit the method of sersiclets, where galaxy morphologies are decomposed into basis functions based on the Sersic profile. This approach is justified by the fact that the Sersic profile is the first-order Taylor ex...

The precision study of dark matter using weak lensing by large scale structure is strongly constrained by the accuracy with which one can measure galaxy shapes. Several methods have been devised but none have demonstrated the ability to reach the level of precision required by future weak lensing surveys. In this Letter we explore new avenues to the existing Shapelets approach, combining a priori knowledge of the galaxy profile with the power of orthogonal basis function deco...

We introduce a new approach to the modelling of the light distribution of galaxies, an orthonormal polar base formed by a combination of Chebyshev rational functions and Fourier polynomials that we call CHEF functions, or CHEFs. We have developed an orthonormalization process to apply this basis to pixelized images, and implemented the method as a Python pipeline. The new basis displays remarkable flexibility, being able to accurately fit all kinds of galaxy shapes, including...

We seek to understand the impact on shape estimators obtained from circular and elliptical shapelet models under two realistic conditions: (a) only a limited number of shapelet modes is available for the model, and (b) the intrinsic galactic shapes are not restricted to shapelet models. We create a set of simplistic simulations, in which the galactic shapes follow a Sersic profile. By varying the Sersic index and applied shear, we quantify the amount of bias on shear estima...

We present a method to simulate deep sky images, including realistic galaxy morphologies and telescope characteristics. To achieve a wide diversity of simulated galaxy morphologies, we first use the shapelets formalism to parametrize the shapes of all objects in the Hubble Deep Fields. We measure this distribution of real galaxy morphologies in shapelet parameter space, then resample it to generate a new population of objects. These simulated galaxies can contain spiral arms,...

We reinterpret the shear estimator developed by Zhang & Komatsu (2011) within the framework of Shapelets and propose the Fourier Power Function Shapelets (FPFS) shear estimator. Four shapelet modes are calculated from the power function of every galaxy's Fourier transform after deconvolving the Point Spread Function (PSF) in Fourier space. We propose a novel normalization scheme to construct dimensionless ellipticity and its corresponding shear responsivity using these shapel...

Aims: We discuss the applicability and reliability of the shapelet technique for scientific image analysis. Methods: We quantify the effects of non-orthogonality of sampled shapelet basis functions and misestimation of shapelet parameters. We perform the shapelet decomposition on artificial galaxy images with underlying shapelet models and galaxy images from the GOODS survey, comparing the publicly available IDL implementation with our new C++ implementation. Results: Non-ort...

Images acquired with a telescope are blurred and corrupted by noise. The blurring is usually modeled by a convolution with the Point Spread Function and the noise by Additive Gaussian Noise. Recovering the observed image is an ill-posed inverse problem. Sparse deconvolution is well known to be an efficient deconvolution technique, leading to optimized pixel Mean Square Errors, but without any guarantee that the shapes of objects (e.g. galaxy images) contained in the data will...

Lens modeling of resolved image data has advanced rapidly over the past two decades. More recently pixel-based approaches, wherein the source is reconstructed on an irregular or adaptive grid, have become popular. Generally, the source reconstruction takes place in a Bayesian framework and is guided by a set of sensible priors. We discuss the integration of a shapelets-based method into a Bayesian framework and quantify the required regularization. In such approaches, the sou...

Current and upcoming wide-field, ground-based, broad-band imaging surveys promise to address a wide range of outstanding problems in galaxy formation and cosmology. Several such uses of ground-based data, especially weak gravitational lensing, require highly precise measurements of galaxy image statistics with careful correction for the effects of the point-spread function (PSF). In this paper, we introduce the SHERA (SHEar Reconvolution Analysis) software to simulate ground-...