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

TL;DR

This paper establishes a theoretical link between the Fresnel transform of an optical field and the Radon transform of its Wigner function, providing a new mathematical framework for analyzing optical field propagation.

Contribution

The paper proves a novel theorem connecting the Fresnel transform of an optical field with the Radon transform of its Wigner function, valid in both spatial and frequency domains.

Findings

Energy density of the output field equals the Radon transform of the input Wigner function.

The theorem applies to fields propagating through [D(-B)(-C)A] optical systems.

The proof is provided in both spatial and frequency domains.

Abstract

We prove a new theorem about the relationship between optical field Wigner function'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 the Wigner function of the input field, where the Radon transform parameters are D,B. We prove this theorem in both spatial-domain and frequency-domain.