The reconstruction of an object from its image is studied from the point of view of the coherence theory including detection in the process of imaging. Finite-size objects permit the use of the theory of entire functions to prove that if the transformation from object to image is linear (detection is not included in imaging) the object can be reconstructed uniquely. Non-linear transformations from object to image (detection is included in imaging) for weak visibility objects and for a particular choice of the diffraction function are also studied. In the first case a finite-size object is determined uniquely, in the second case the reconstructed object is determined apart from the phase, which can sometimes be determined from the dispersion relations. Further, the similarity between an object and its image is investigated. It is shown that partial coherence creates typical non-linearity in imaging which results in an interval of eigenvalues (similarity coefficients) and that there may arise the branching of a structure imaged similarly into several structures imaged similarly.