There is a quest for new knowledge and methods to study various materials and processes on surfaces and interfaces at the nanoscale. It concerns ablation, phase transitions, physical and chemical transformations, dissolution, selforganization etc. Obviously, to achieve an appropriate resolution it is necessary to use a corresponding wavelength . Higher resolution can be obtained with shorter wavelengths. On the other hand, in surface modification, ablation, study of buried interfaces etc. the penetration length of radiation into the materials, which depends on the wavelength and angle of incidence, plays important role... Considering these factors the experimental studies in nano-physics and nanotechnology are usually carried out using X-ray radiation with a photon energy of 0.1-10 keV. As far as surfaces and films are investigated, it is reasonable to use an X-ray microscope operating in the reflection mode. However, in this spectral range a substantial portion of the radiation is reflected only at small grazing angles (e.g. ≤ 10°). Thus, the idea of grazing incidence reflection-mode X-ray microscope has been developed. In this paper, we consider one of possible schemes of such an X-ray microscope. Our analysis and simulation is based on the extension of the Fresnel propagation theory to tilted object problems.