Deconvolution of ASCA X-ray data - I. Spectral-imaging method

In this paper we describe a self-contained method for performing the spectr al-imaging deconvolution of X-ray data on clusters of galaxies observed by the ASCA satellite. Spatially resolved spectral studies of data from this s atellite require such a correction, because its optics redistribute photons over regions that are of comparable size to the angular scales of interest in clusters. This scattering is a function not only of spatial position bu t also of energy. To perform a correction for these effects we employ maxim um-likelihood deconvolution of the image (within energy bands of 1 keV) to determine the spatial redistribution, followed by a Monte Carlo energy reas signment of photon energies with position to determine the spectral redistr ibution. We present tests on simulated cluster data, convolved with the var ious instrumental characteristics and the X-ray background, which show that our methodology can successfully recover a variety of intrinsic temperatur e profiles in typical observational circumstances. In Paper II (this issue) we shall apply our spectral-imaging deconvolution procedure to a large sam ple of galaxy clusters to determine temperature profiles.