A non-dimensional approach to diffraction phenomena in the Fresnel approximation

The paper presents a theoretical and numerical study of the diffraction problem approached in the Fresnel approximation. The problem was formulated by a non-dimensional approach, which implies the definition of two non-dimensional quantities: F and ζ. In particular the parameter F is the well-known Fresnel number, whose value was usually used to classify diffraction regime. In analyzing the numerical approach some limitations imposed by the discretization arise; in particular these limitations constrain the level of sampling to be used for the diffracting field by requiring more and more elements when the diffraction conditions become more severe — i.e. increasing the dimension of the diffracting aperture and/or decreasing the distance of the plane where the diffracted field is observed.

Research Highlights
► Diffraction formula in the Fresnel approximation based on non dimensional model.
► Governing parameters of the theoretical problem: F (Fresnel number) and ζ (=z/λ).
► For numerical problem two additional discretization parameters must be considered.
► Discretization parameters in the numerical simulation are constrained by F.