A new absorption-based method for studying the internal structure of micro-objects using synchrotron radiation is proposed. The method registers the integral intensity of the beam after passing through the object, and the locality is achieved by focusing the beam with a refractive lens into a nanometer-wide line. In this case, phase contrast is not utilized, the result is obtained immediately, and two-dimensional images of an object are calculated by computed tomography. The method does not require complex mathematical calculations and gives high accuracy results. Model experiments using a silicon carbide substrate and some other parameters were performed for illustrative purposes. Keywords: Synchrotron Radiation, micro-objects, nanofocusing, tomography, micropores.