The electromagnetic wavefront diffracted by an object carries information about the shape of the object from which the wave was emitted. Being able to record the phase and intensity of such a wave thus allows to reconstruct the object from the information carried by the wave, even if the object is no longer present. Among the reconstruction techniques, holography plays a big part. However the waves may experience a great variety of distortions on their way from the object to the measurement apparatus. Thus being able to shape the wavefront at will is key in holography. Micromirror light modulators are powerful tools for that matter and are well known for holographic applications. This paper explores the fundamental principles for digitally reconstructing a precise image of an object, but also for digitally correcting an imperfectly shaped wavefront, by exploiting the diffraction properties of light on a reflective surface. The methods presented here have been implemented as part of practical work for 2nd year students at the Ecole Polytechnique (last year of undergraduate program).