We demonstrate an active, holographic tomography system, working with limited angle of projections, realized by optical-only, diffraction-based beam steering. The system created for this purpose is a Mach–Zehnder interferometer modified to serve as a digital holographic microscope with a high numerical aperture illumination module and a spatial light modulator (SLM). Such a solution is fast and robust. Apart from providing an elegant solution to viewing angle shifting, it also adds new capabilities of the holographic microscope system. SLM, being an active optical element, allows wavefront correction in order to improve measurement accuracy. Integrated phase data captured with different illumination scenarios within a highly limited angular range are processed by a new tomographic reconstruction algorithm based on the compressed sensing technique: total variation minimization, which is applied here to reconstruct nonpiecewise constant samples. Finally, the accuracy of full measurement and the proposed processing path is tested for a calibrated three-dimensional micro-object as well as a biological object--C2C12 myoblast cell.