  We present real-world data processing on measured electron time-of-flight
data via neural networks. Specifically, the use of disentangled variational
autoencoders on data from a diagnostic instrument for online wavelength
monitoring at the free electron laser FLASH in Hamburg. Without a-priori
knowledge the network is able to find representations of single-shot FEL
spectra, which have a low signal-to-noise ratio. This reveals, in a directly
human-interpretable way, crucial information about the photon properties. The
central photon energy and the intensity as well as very detector-specific
features are identified. The network is also capable of data cleaning, i.e.
denoising, as well as the removal of artefacts. In the reconstruction, this
allows for identification of signatures with very low intensity which are
hardly recognisable in the raw data. In this particular case, the network
enhances the quality of the diagnostic analysis at FLASH. However, this
unsupervised method also has the potential to improve the analysis of other
similar types of spectroscopy data.
