A gigantic detector, the ATLAS project, is under construction at CERN for particle physics research at the Large Hadron Collider which is to be ready by 2006. An X-ray tomograph has been developed, designed and constructed at CERN in order to control the mechanical quality of the ATLAS muon chambers. We reached a measurement accuracy of 2μm systematic and 2μm statistical uncertainties in the horizontal and vertical directions in the working area 220cm (horizontal)×60cm (vertical). Here we describe in detail the fundamental approach of the basic principle chosen to achieve such good accuracy. In order to crosscheck our precision, key results of measurements are presented.