The Wigner distribution function and Hamilton's characteristics of a geometric-optical system

Four system functions have been defined for an optical system; each of these functions describes the system completely in terms of Fourier optics. From the system functions the Wigner distribution function of an optical system has been defined; although derived from Fourier optics, this Wigner distribution function can directly be interpreted in terms of geometrical optics. In the special case of a geometric-optical system, the Wigner distribution function clearly demonstrates the relations that exist between the four system functions and the four Hamilton's characteristics of the system.