Linear canonical Wigner distribution and its application

Linear canonical transform (LCT) form a three-parameter family of intergral transforms with wide application in optics. In this paper, we investigate the linear canonical Wigner distribution (LCWD) which is based on the LCT and the classical Wigner distribution (WD). Firstly, the definition of LCWD is discussed. Moreover, the transformation law for the LCWD through a first-order optical system is derived. This new phase-space distribution provides analysis of signals in both space and LCT domains simultaneously. Then, the main properties of LCWD are investigated in detail. Finally, the application of the LCWD is presented. The LCWD is found to be the appropriate phase-space distribution function for light-beam characterization in first-order optical system. Moreover, the moment matrix formalism for beam characterization is studied.