Reconstruction of Coherence Matrix in X-Representation Using Nonclassical Hartmann Sensor

We show the coherence properties of a signal can be measured by a Hartmann wavefront sensor in a nonclassical regime. Recasting the detection theory of the classical Hartmann sensor in the sense of quantum tomography enables to measure the coherence function, which is an analogy to the density matrix of mixed quantum states. Two methods were tested for the reconstruction of the coherence matrix from the intensity scan in the nonclassical mode of the Hartmann sensor. The reconstruction was performed in a classic way using the POVM matrix and using data pattern tomography.