Shape Reconstruction and Weak Lensing Measurement with Interferometers: A Shapelet Approach

We present a new approach for image reconstruction and weak lensingmeasurements with interferometers. Based on the shapelet formalism presented inRefregier (2001), object images are decomposed into orthonormal Hermite basisfunctions. The shapelet coefficients of a collection of sources aresimultaneously fit on the uv plane, the Fourier transform of the sky brightnessdistribution observed by interferometers. The resulting chi-square fit islinear in its parameters and can thus be performed efficiently by simple matrixmultiplications. We show how the complex effects of bandwidth smearing, timeaveraging and non-coplanarity of the array can be easily and fully correctedfor in our method. Optimal image reconstruction, co-addition, astrometry, andphotometry can all be achieved using weighted sums of the derived coefficients.As an example we consider the observing conditions of the FIRST radio survey(Becker et al. 1995; White et al. 1997). We find that our method accuratelyrecovers the shapes of simulated images even for the sparse uv sampling of thissnapshot survey. Using one of the FIRST pointings, we find our method compareswell with CLEAN, the commonly used method for interferometric imaging. Ourmethod has the advantage of being linear in the fit parameters, of fitting allsources simultaneously, and of providing the full covariance matrix of thecoefficients, which allows us to quantify the errors and cross-talk in imageshapes. It is therefore well-suited for quantitative shape measurements whichrequire high-precision. In particular, we show how our method can be combinedwith the results of Refregier & Bacon (2001) to provide an accurate measurementof weak lensing from interferometric data.Comment: 9 pages, 5 figures. To appear in ApJ; minor changes to match accepted versio