Efficient calculation of broadband light scattering spectra from spherical, homogeneous particles

The scattering of light from spherical particles is important to many fields of science. Analysis of scattered light can provide powerful insight into the properties of the particle from which it is scattered. One technique that is finding increasing use in the field of aerosol science is broadband light scattering, i.e. measurement and fitting of elastic light scattering spectra over a wide range of wavelengths. However, calculation of the broadband scattering spectra can be computationally expensive, slowing down the analysis of data that require the evaluation of many spectra across a range of trial particle sizes and wavelength-dependent refractive indices. We outline an efficient algorithm for calculating broadband spectra. A key stage of this calculation is integrating over the collection aperture. Particular attention is paid to evaluating the necessary numerical integrals efficiently by taking advantage of new results involving the parity or modular values of the number of angular grid points used. These considerations are also useful in deriving empirical limits that can be used to evaluate integrals in a single step. The algorithm developed is capable of generating spectra with typical experimental parameters in a few seconds or less on a desktop computer, paving the way for extensive data analysis. The resulting Python code is made freely available.