Relation between Fresnel transform of input light field and the two-parameter Radon transform of Wigner function of the field

This paper proves a new theorem on the relationship between optical field Wigner function's two-parameter Radon transform and optical Fresnel transform of the field, i.e., when an input field ψ( x') propagates through an optical D( -B) ( -C) A] system, the energy density of the output field is equal to the Radon transform of the Wigner function of the input field, where the Radon transform parameters are D,B. It prove this theorem in both spatial-domain and frequency-domain, in the latter case the Radon transform parameters are A,C.