represent the [[*Swift*]{}]{} X-ray Cluster Survey (SXCS ), which is based on archival data obtained by the X-ray telescope onboard the [[*Swift*]{}]{} satellite. We achieve more than $90\%$ completeness for extended sources comprising at least $80$ photons in the $0.5$–$2$ keV band, a limit that corresponds to $10^{-14}$ erg cm$^{-2}$ s$^{-1}$ for the deepest SXCS fields. This detection limit is comparable to the one attained by the most sensitive cluster surveys conducted with much larger X-ray telescopes. While evaluating the performance of EXSdetect, we also explored the impact of improved angular resolution and discuss the ideal properties of the next generation of X-ray survey missions. ]{}

Introduction\[introduction\]
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In the past decade, X-ray astronomy reached an unprecedented level in imaging and spectroscopic performances, mostly thanks to the [*Chandra*]{} and [*XMM-Newton*]{} telescopes. Their high imaging quality and large effective area allowed us to discover an increasing complexity in the morphology of X-ray extended sources, which reflects the rich physics involved. Extended X-ray emission may be associated with a variety of Galactic objects: supernova remnants, star-forming regions, or planetary nebulae. In extragalactic fields, it is mostly associated with the hot intra cluster medium (ICM) that permeates the potential well of galaxy clusters 