Phase reconstruction from intensity measurements in one-parameter canonical-transform systems

In this paper, we consider the one-parameter canonical transform of an optical signal and derive the relationship between its local spatial frequency (signal phase derivative) and the derivative of the squared modulus of the one-parameter canonical transform with respect to the parameter. From this relationship we conclude that the phase of the signal can be reconstructed by letting the signal propagate in an appropriate one-parameter canonical-transform system and then measure two intensity profiles for two close values of the parameter.