Hard X-ray imaging of solar flares using interpolated visibilities

RHESSI produces solar flare images with the finest angular and spectral resolutions ever achieved at hard X-ray energies. Because this instrument uses indirect, collimator-based imaging techniques, the "native" output of which is in the form of "visibilities" (two-dimensional spatial Fourier components of the image), the development and application of robust, accurate, visibility-based image reconstruction techniques is required. Recognizing that the density of spatial-frequency (u, v) coverage by RHESSI is much sparser than that normally encountered in radio astronomy, we therefore introduce a method for image reconstruction from a relatively sparse distribution of sampled visibilities. The method involves spline interpolation at spatial frequencies less than the largest sampled frequency and the imposition of a positivity constraint on the image to reduce the ringing effects resulting from an unconstrained Fourier transform inversion procedure. Using simulated images consisting both of assumed mathematical forms and of the type of structure typically associated with solar flares, we validate the fidelity, accuracy, and robustness with which the new procedure recovers input images. The method faithfully recovers both single and multiple sources, both compact and extended, over a dynamic range of ~ 10 : 1. The performance of the method, which we term as uv_smooth, is compared with other RHESSI image reconstruction algorithms currently in use and its advantages summarized. We also illustrate the application of the method using RHESSI observations of four solar flares.