Quantitative corrections for fluctuation electron microscopy.

Anomalously low values of the normalised variance in fluctuation electron microscopy (FEM) have been frequently reported. We present three experimental corrections for quantitative interpretation that significantly modify conventional approaches. FEM relies on measurements of intensity statistics in coherent nanodiffraction patterns. We demonstrate that sampling the nanodiffraction patterns with a pixelated detector removes high-frequency signals and reduces statistical variance. The most significant impact is on the background normalised variance, which arises from random atomic alignments and is distinct from the normalised variance peaks associated with the correlated alignments of medium-range order. Indeed, we show that if the peaks are background-subtracted, their height is much less affected by the detector effect, provided the experimental conditions are optimised. We show that shot noise correction must also be adjusted to account for the camera Modulation Transfer Function (MTF) effects. Additionally, we demonstrate through experiment that the traditional method of thickness correction for a-Si is inadequate and propose an alternative approach to address thickness variations. We speculate on the origin of the anomalous thickness effect in terms of displacement decoherence due to sample 'fluttering' under irradiation.