Third-order aberration analysis of a Fresnel lens

This paper presents expressions for the third-order aberrations of a Fresnel surface (Seidel coefficients). The formulas are derived in a form that allows analytical aberration analysis to be performed at the stage of layout and preliminary design of a system composed of both classical and Fresnel surfaces. In addition to the five major monochromatic Seidel aberrations of the classical surfaces and the line coma which was described for the Fresnel-type surfaces, another aberration, called quadratic astigmatism, is described in this paper. Although the obtained expressions are an approximation for the third-order aberration domain, i.e. higher-order aberrations are ignored, they provide sufficient accuracy in practice, which is also shown in the paper. The derived expressions can be applied to the analysis of aberrations in schemes using a Fresnel lens, which makes it possible to identify the areas of rational use of elements of this type.