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

In this paper we describe a self-contained method for performing the spectral-imaging deconvolution of X-ray data on clusters of galaxies observed by the ASCA satellite. Spatially resolved spectral studies of data from this satellite 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 but also of energy. To perform a correction for these effects we employ maximum-likelihood deconvolution of the image (within energy bands of 1 keV) to determine the spatial redistribution, followed by a Monte Carlo energy reassignment of photon energies with position to determine the spectral redistribution. We present tests on simulated cluster data, convolved with the various instrumental characteristics and the X-ray background, which show that our methodology can successfully recover a variety of intrinsic temperature profiles in typical observational circumstances. In Paper II (this issue) we shall apply our spectral-imaging deconvolution procedure to a large sample of galaxy clusters to determine temperature profiles.