Shapelets Web Pages


Shapelets are a complete, orthonormal set of 2D basis functions constructed from Laguerre or Hermite polynomials weighted by a Gaussian. A linear combination of these functions can be used to model any image, in a similar way to Fourier or wavelet synthesis. The shapelet decomposition is particularly efficient for images localised in space, and provide a high level of compression for individual galaxies in astronomical data. The basis has many elegant mathematical properties that make it convenient for image analysis and processing. The formalism was first introduced to astronomy by Alexandre Refregier & David Bacon, and a related method has also been independently suggested by Gary Bernstein & Mike Jarvis.

This shapelets web site is maintained by Richard Massey.

IDL shapelets software:

The IDL shapelets software requires IDL v5.4 or above. A stand-alone set of core routines is available, including everything you need to decompose images into shapelets and to manipulate them. Routines to generate multicolour simulated astronomical images are also now documented and publicly available. New! We would be interested to collaborate with anyone requiring more advanced applications.

Published shapelets papers:

These papers describe the core shapelets method, and define the notation and conventions used by the publicly available IDL code. The following papers describe various applications of shapelets. Note that some of these papers use slightly different notation and conventions. Also try searching for more shapelets-related papers on astro-ph, NASA ADS or google scholar. The following papers specifically discuss the use of shapelets to measure weak gravitational lensing.

Online resources:



Valid HTML 4.01!

Valid CSS!