The end-cap Transition Radiation Tracker (TRT), consisting of 36 modules (wheels), is being constructed as a part of the ATLAS Inner Detector at the CERN LHC. This paper describes a method for determining the wire positions inside the straw proportional tubes (SPT), which are the basic building blocks of the ATLAS TRT, with an accuracy of better than 10 μm . The procedure involves moving a narrow monochromatic X-ray beam across the straw and measuring the counting rate as a function of the position of the X-ray beam in the straw. To achieve this goal, a Beam Directing Device (BDD), providing the possibility to direct the X-ray beam in a chosen direction within some solid angle and supplying an accurate angular measurement system, has been constructed. The results of the wire position measurements performed using this BDD on a full-scale mechanical prototype end-cap wheel of the TRT are presented in this paper.
