A measuring and evaluation strategy for the determination of residual stress depth distributions sigma(ij)(z) in real space within different depths beneath the samples surface is introduced. The proposed method allows the analysis of residual stresses within a specific gauge volume using the well-known sin(2) psi-method. Hence it allows a real 'stress scanning' in real space and will be applicable to laboratory X-ray sources as well as middle and high energy synchrotron radiation, consequently holding for different information depths. In contrast to the hitherto applied strain scanning methods the basic idea of the herein proposed procedure considers the use of fixed beam limiting apertures being inserted in the primary and the secondary beam path. In the project, which is a cooperation between the Institute for Materials Engineering (University of Kassel) and the Hahn-Meitner-Institute Berlin, it is distinguished between an angle-dispersive and an energy-dispersive approach. For the angle-dispersive approach (soft X-rays) the gauge element is defined by using beam limiting masks coupled to the samples surface. The geometries of the masks are tailored with respect to the X-ray wavelength and the samples tilt relative to the beam path. For the energy dispersive approach, the gauge volume is defined by a pair of slits, coupled with the sample. Its geometry depends on the psi tilt of the sample and the alignment allows a translation relative to the sample in order to realize the depth scan (see also Part II [I]).