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We prove a new theorem about the relationship between optical field Wignerfunction's Radon transform and optical Fresnel transform of the field, i.e.,when an input field Phi(x') propagates through an optical [D(-B)(-C)A] system,the energy density of the output field is equal to the Radon transform of theWigner function of the input field, where the Radon transform parameters areD,B. We prove this theorem in both spatial-domain and frequency-domain.

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