Abstract
Measurements in general are limited in accuracy by the presence of noise. This also holds true for highly sophisticated scintillation-based CCD cameras, as they are used in medical applications, astronomy or transmission electron microscopy. Further, signals measured with pixelated detectors are convolved with the inherent detector point spread function. The Poisson noise, arising from the quantized nature of the beam electrons, gets correlated by this convolution, which allows to reconstruct the detector PSF based on the Wiener-Khinchin theorem and the Pearson correlation coefficients under homogeneous illumination conditions. However, correlation also has a strong impact on the noise statistics of basic operations like the binning of signals, as it is usually done in electron energy-loss spectroscopy. Thus, this paper aims to give an insight into the different noise contributions occurring on such detectors, into their underlying statistics and their correlation. Detectors usually suffer from gain non-linearities and quantum efficiency deviations, which must be corrected for optimal results. All these operations influence the noise and are influenced by it, vice versa. In this work, we mathematically describe all these changes and show them experimentally. Methods on how to measure individual noise and correlation parameters are described allowing readers to implement routines for finding them. Sufficient knowledge on the noise of a measurement is not only crucial for classifying its quality and meaningfulness, but also allows for better post-processing operations like deconvolution, which is a common practice in spectroscopy to enhance signals.