Proton radiotherapy has recently become a popular form of cancer treatment. For maximum effectiveness, accurate models are needed to calculate proton angular scattering and energy loss. Scattering events are statistically independent and may be calculated from the effective number of events per reciprocal multiple scattering angle or energy loss. It is shown that multiple scattering distributions from Molière’s scattering law can be convolved by depth for accurate numerical calculation of angular distributions in several example materials. This obviates the need for correction factors to the analytic solution and its approximations. It is also shown that numerically solving Molière’s scattering law in terms of the complete (non-small angle) differential cross section and large angle approximations extends the validity of Molière theory to large angles. To calculate probability energy loss distributions, Landau-Vavilov theory is adapted to Fourier transforms and extended to very thick targets through convolution over the probability energy loss distributions in each depth interval. When the depth is expressed in terms of the continuous slowing down approximation (CSDA) the resulting probability energy loss distributions rely on the mean excitation energy as the sole material dependent parameter. Through numerical calculation of the CSDA over the desired energy loss, this allows the energy loss cross section to vary across the distribution and accurately accounts for broadening and skewness for thick targets in a compact manner. An analytic, Fourier transform solution to Vavilov’s integral is shown. A single scattering nuclear model that calculates large angle dose distributions that have a similar functional form to FLUKA (FLUktuierende KAskade) Monte Carlo, is also introduced. For incorporation into Monte Carlo or a treatment planning system, lookup tables of the number of scattering events or cross sections for different clinical energies may be used to determine angular or energy loss distributions.

Fluctuation Electron Microscopy (FEM) has become an effective materials' structure characterization technique, capable of probing medium-range order (MRO) that may be present in amorphous materials. Although its sensitivity to MRO has been exercised in numerous studies, FEM is not yet a quantitative technique. The holdup has been the discrepancy between the computed kinematical variance and the experimental variance, which previously was attributed to source incoherence. Although high-brightness, high coherence, electron guns are now routinely available in modern electron microscopes, they have not eliminated this discrepancy between theory and experiment. The main objective of this thesis was to explore, and to reveal, the reasons behind this conundrum.

The study was started with an analysis of the speckle statistics of tilted dark-field TEM images obtained from an amorphous carbon sample, which confirmed that the structural ordering is sensitively detected by FEM. This analysis also revealed the inconsistency between predictions of the source incoherence model and the experimentally observed variance.

FEM of amorphous carbon, amorphous silicon and ultra nanocrystalline diamond samples was carried out in an attempt to explore the conundrum. Electron probe and sample parameters were varied to observe the scattering intensity variance behavior. Results were compared to models of probe incoherence, diffuse scattering, atom displacement damage, energy loss events and multiple scattering. Models of displacement decoherence matched the experimental results best.

Decoherence was also explored by an interferometric diffraction method using bilayer amorphous samples, and results are consistent with strong displacement decoherence in addition to temporal decoherence arising from the electron source energy spread and energy loss events in thick samples.

It is clear that decoherence plays an important role in the long-standing discrepancy between experimental FEM and its theoretical predictions.