Local wave fronts at diffractive elements

Equations for calculating the principal curvatures and principal directions of local wave fronts in an optical system that consists of diffractive curved or plane surfaces between isotropic and homogeneous media are presented. The equations for refractive and reflecting surfaces are obtained as special cases of the equations for diffractive surfaces. This method is a kind of generalized ray tracing and permits an easy determination of the position of the local focus or the position and direction of the local focal lines in the case of local astigmatism; it must be emphasized that elements and systems with spherical aberration or coma also have local astigmatism.