Extinction cross sections of nonspherical particles in the anomalous diffraction approximation

We have applied an anomalous diffraction approximation in order to obtain extinction cross sections of a variety of nonspherical particles in a simple analytical form. Specifically, we have derived extinction cross sections of partial spheres, cones, and prismatic columns with triangular, rectangular, trapezium, and hexagonal bases. We have also derived an addition theorem showing how the extinction cross section of an arbitrary column with a polygonal base can be obtained. The extinction cross section of a long cylinder is obtained as the limiting case of a polygonal-based prismatic column with the number of sides approaching infinity.