On the Relationship Between the Vogler Algorithm Derivation and the Parabolic Equation for Multiple Knife-Edge Diffraction

We prove the equivalence between the derivation of the Vogler algorithm and the parabolic equation for multiple knife-edge diffraction problems under certain conditions. To illustrate the key ideas, we present two case studies for single and double knife-edge diffraction, where the proposed results generalize the available results in the literature. The insight from our proof can serve two purposes: allowing cross-checking results of the Vogler algorithm and the parabolic equation; and building the foundation on which new methods for solving this essential problem and related ones can be developed.