Data Fitting

Pulse shape analysis can be regarded as an inverse problem. Knowing the response of the detector we would like to infer the interaction position, deposited energy, time and number of interactions. In this context data fitting has various applications:

• To determine the interaction position of the psd of the GSI scanner, we fit the measured light distribution with the expected distribution to derive the x and y position (seperately). In this case we are using a minimization ala Brent where the parameter is the shift of a reference distribution along the x (or y) axis to obtain the best match between the measured and the reference distribution. This procedure is rather slow, while deducing the position from the peak position of the light distribution alone is not accurate enough. Considering that the light distribution has a rather well defined shape, it might be possible to speed up the minimization by using this information for the fitting procedure.
• To correct the time walk caused by leading edge triggering one can use measured data to obtain a fit for the walk effect in dependence of the deposited energy and then use this for the correction.
• In a similar manner, the time walk effect that is present with large volume germanium detectors when using constant fraction discrimination can be corrected. In this case one has to find the relation between the shape of the signal and the time walk effect. As there are typically in the order of 50 relevant amplitudes recorded per signal, this is not a trivial task (e.g. 100Mhz sampling and a rise time of up to ~300ns). We are following two different approaches to deal with this situation: One can either try to reduce the amount of parameters and then try to fit the walk effect based on this reduced data. The second approach is to train an artificial neural network to obtain the necessary correction.
• Actually, the situation is very similar when trying to infer the interaction position (and not only the timing) from the signal shape. However, having 3 target variables (x,y and z) complicates the task.

Artificial Neural Networks for least squares fitting

A feedforward backpropagation neural network has been implemented. As a first trial we used it to correct the time walk that is present with leading edge discrimination.

• ArtificialNeuralNetworks.pdf: Artificial Neural Networks for least squares fitting

-- TobiasHabermann - 11 Feb 2015