A new look at anomalous diffraction theory (ADT): Algorithm in cumulative projected-area distribution domain and modified ADT

Abstract

Two recent papers (Opt. Lett. 28 (2003) 179; Appl. Opt. 42 (2003) 6710) show that the conventional anomalous diffraction theory (ADT) can be reformulated by using the probability distribution function of the geometrical paths of rays inside a scattering particle. In this study we further enhance the new ADT formulation by introducing a dimensionless scaled projectile-length (l˜q) defined in the domain of the cumulative projected-area distribution (q) of a particle. The quantity l˜q contains essentially all the information about particle shape and aspect ratio, which, however, is independent of particle dimension (e.g., large and small spheres have the same l˜q). With this feature of l˜q, the present ADT algorithm is computationally efficient if a number of particle sizes and wavelengths are considered, particularly when a random orientation condition is assumed. Furthermore, according to the fundamental ADT assumption regarding the internal field within a scattering particle, we modify ADT on the basis of two rigorous relationships that relate the extinction and absorption cross sections to the internal field. Two tuning factors are introduced in the modified ADT solution, which can be determined for spheres by fitting the modified ADT results to the corresponding Lorenz-Mie solutions. For nonspherical particles, the tuning factors obtained for spheres can be used as surrogates. This approach is tested for the case of circular cylinders whose optical properties can be accurately calculated from the T-matrix method. Numerical computations show that the modified ADT solution is more accurate than its conventional ADT counterpart.