Non-spherical particles are ubiquitous in nature as well as process engineering applications. Especially the reliable detection of ice crystals in flight by commercial airliners has received a considerable amount of attention from physicists and engineers alike during the recent years. While the problem of the scattering of a plane electromagnetic wave by a homogeneous and isotropic spherical particle such as a raindrop can be considered completely solved, the same is not true for non-spherical particles. Here is still an intense focus of research and development. This includes, but is not limited to the theoretical, numerical, and experimental side of the problem, due to a manifold number of difficulties. This work describes several different numerical and semi-analytic methods, which may be applied to the solution of the scattering problem. These methods have been developed in order to cover the entire range of the characteristic Mie size parameter. Most importantly, a direct application of the methods is the calibration and interpretation of the measurement results of the PHIPS probe, which was used to conduct a HALO campaign for the characterisation of atmospheric ice crystals. Specifically, the calculation methods of the finite integration of Maxwell’s equations, as well as the transition operator method, which is widely used in the fields of classical as well as quantum mechanical scattering theory. Unique among existing codes, the geometrical optics derivative methods are applicable to any geometry and to any sort of continuous or discontinuous refractive index distribution. Furthermore, the predictive methods have been applied to a number of representative example geometries, and the influence of wave polarisation and particle orientation has been investigated through statistical sampling. Additionally, a computational class has been implemented in order to consider the influence of shaped beam incidence on the scattered light intensity distribution. Such a shaped beam plays a central role in measurement devices based on the Time-Shift principle, where the particle illumination is provided by a laser beam with a Gaussian profile. The limits of applicability of the different computational approaches are also indicated in the thesis. Furthermore, several modern measurement approaches have been evaluated with regards to their applicability to nonspherical particles. This includes the aforementioned Time-Shift principle, and Interferometric Imaging. The analysis of the different measurement techniques is documented in the experimental section of the thesis. Tentative measurements of the phase functions of ice crystals in a laboratory environment have also been conducted and the specific requirements for handling and conducting optical experiments with ice crystals are also explained in the document. As a common problem of all the measurement principle, the limited dynamic range of the optical detectors used in practice could be identified. A final important aspect addressed in the thesis is the production and storage of ice crystals with optical properties as natural as possible. For this purpose, a compact cloud chamber was developed, that provided the necessary properties, both in terms of quantity, as well as quality of the ice crystals produced by the device. Construction and operational details of the cloud chamber are reported in the last chapter of the thesis.