A microversion of a computerized tomograph (CT) is described, in which the object is subjected to a successive series of translations with rotation by a small angle in between. The spatial resolution is determined by collimators and translation step lengths and is today, with clinical X-ray tube, of the order of 100 μm. The use of synchrotron radiation instead of X-ray tubes offers the advantages of much higher fluence rates, which can be used to diminish the exposure times from days to minutes or to increase the spatial resolution from 100 μm to about 1 μm. The possibility to receive monoenergetic photons of selectable energy makes it possible to avoid spectral hardening image artifacts, as well as to optimize the information sampling with regard to average absorbed dose or exposure time. Selectable photon energies are valuable also for tomochemistry applications.