Scalar integral diffraction methods: unification, accuracy, and comparison with a rigorous boundary element method with application to diffractive cylindrical lenses

Various integral diffraction methods are systematically unified into a single framework, clearly illustrating the interconnections among the numerous scaler and rigorous formulations. This hierarchical depiction of the integral methods makes clear the specific approximations inherent in each integral method. The scaler methods are compared in detail with a rigorous open-region formulation of the boundary element method (BEM). The rigorous BEM provides a reference method for accurately determining the diffracted fields for both TE and TM incidence. The rigorous BEM and the various scalar methods are then applied to the case of focusing of normally incident plane waves by diffractive cylindrical lenses with f-numbers ranging from f/2 to f/0.5. From the diffracted-field calculations, a number of performance metrics are determined including focal spot size, diffraction efficiency, reflected and transmitted powers, and focal-plane sidelobe power. The quantitative evaluation of the performance of the scalar methods with these metrics allows the establishment, for the first time, of the region of validity of the various scaler methods for this application. As expected, the accuracy of the scalar methods decreases as the f-number of the diffractive lenses is reduced. Additionally, some metrics, particularly the focal-plane sidelobe power, appear to be particularly sensitive to the approximations in the scaler methods, and as a result their accuracy is significantly degraded. (C) 1998 Optical Society of America.