Application of matched-filter concepts to unbiased selection of data in pump-probe experiments with free electron lasers

Pump-probe experiments are commonly used at Free Electron Lasers (FEL) to elucidate the femtosecond dynamics of atoms, molecules, clusters, liquids and solids. Maximizing the signal-to-noise ratio of the measurements is often a primary need of the experiment, and the aggregation of repeated, rapid, scans of the pump-probe delay is preferable to a single long-lasting scan. The limited availability of beamtime makes it impractical to repeat measurements indiscriminately, and the large, rapid flow of single-shot data that need to be processed and aggregated into a dataset, makes it difficult to assess the quality of a measurement in real time. In post-analysis it is then necessary to devise unbiased criteria to select or reject datasets, and to assign the weight with which they enter the analysis. One such case was the measurement of the lifetime of Intermolecular Coulombic Decay in the weakly-bound neon dimer. We report on the method we used to accomplish this goal for the pump-probe delay scans that constitute the core of the measurement; namely we report on the use of simple auto- and cross-correlation techniques based on the general concept of "matched filter". We are able to unambiguously assess the signal-to-noise ratio (SNR) of each scan, which then becomes the weight with which a scan enters the average of multiple scans. We also observe a clear gap in the values of SNR, and we discard all the scans below a SNR of 0.45. We are able to generate an average delay scan profile, suitable for further analysis: in our previous work we used it for comparison with theory. Here we argue that the method is sufficiently simple and devoid of human action to be applicable not only in post-analysis, but also for the real-time assessment of the quality of a dataset.