This thesis discusses various large multi-dimensional dataset analysis methods and their applications. Particular attention is paid to non-linear optimization analyses and general processing algorithms and frameworks when the datasets are significantly larger than the available computer memory. All new presented algorithms and frameworks were implemented in the HyperSpy analysis toolbox.

A novel Smart Adaptive Multi-dimensional Fitting (SAMFire) algorithm is presented and applied across a range of scanning transmission electron microscope (STEM) experiments. As a result, the Stark effect in quantum disks was mapped in a cathodoluminescence STEM experiment, and fully quantifiable 3D atomic distributions of a complex boron nitride core-shell nanoparticle were reconstructed from an electron energy loss spectrum (EELS) tilt-series. The EELS analysis also led to the development of two new algorithms to extract EELS near-edge structure fingerprints from the original dataset. Both approaches do not rely on standards, are not limited to thin or constant thickness particles and do not require atomic resolution. A combination of the aforementioned fingerprinting techniques and SAMFire allows robust quantifiable EELS analysis of very large regions of interest.

A very large dataset loading and processing framework, “LazySignal”, was developed and tested on scanning precession electron diffraction (SPED) data. A combination of SAMFire and LazySignal allowed efficient analysis of large diffraction datasets, successfully mapping strain across an extended (ca. 1 μm × 1 μm) region and classifying the strain fields around precipitate needles in an aluminium alloy.