[Hps-ecal] HPS Ecal signals parametrization

[Sho Uemura]

I tried two more parametrizations. These are parametrizations commonly 
used for the APV25 preamp that we use in the SVT.

CR-RC: t*exp(-t/tp)
3-pole, or CR-RC-RC: t^2*exp(-t/tp)

3-pole seems to fit well, I think better than the asymmetric Gaussian. 
CR-RC seems no better than the Gaussian. Other parametrizations I tried 
(variations on CR-RC or 3-pole using more than one time constant) were 
degenerate with CR-RC or 3-pole, so I didn't include those plots.

Plots attached are for 3-pole function. All plots for 3-pole and CR-RC, 
and the pyroot scripts I used, are online:

http://www.slac.stanford.edu/~meeg/ecalpulsefit/

I also see what you see, where there are 2 clusters in the distribution of 
shape parameters. I chose the center of the larger cluster (with the 
faster time constant) and refit all the events with this time constant 
fixed; those plots are named "fit2" and as expected they fit the faster 
pulses well and the slower pulses poorly.

More data will help.

I plotted the three parametrizations we have, see plot4.pdf attached. If 
we agree that the Gaussian has an unphysical rising edge, I think we 
should use 3-pole.

On Tue, 1 Apr 2014, Andrea Celentano wrote:

> Dear all,
> here are some results about HPS Ecal signals parametrization.
> I took data with the crystal placed vertically, APD gain 150, room 
> temperature. I put a threshold ~ 20 mV to keep only big enough signals, out 
> of the noise.
> I acquired data with a 2.5Gs/s oscilloscope, 1 GHz bandwidth, 50 Ohm input 
> impedance.
>
> I used the same* configuration employed at JLab for cabling: 8m 3M cable ---> 
> passive splitter ---> 3m lemo cable.
>
> *actually I employed an 8 meters 3M cable instead of 7m because the latter is 
> not available here in Genova.
>
> Attached you find a postcript file with the results. (outGood.ps shows the 
> fit results covering some parts of the signal, outGood1.ps no)
>
> - Neglect first blank page
> - Pages from 2 to 32 are the 31 signals I got, with superimposed the fit 
> performed with the two-gaussians parametrization. Each chi2 fit is performed 
> independently.
> Signals are in mV and ns.
> Note that near ~ 100 ns there is probably a reflection due to some impedance 
> mismatch in the cables chain.
> However,  I am not using those points to fit. I am fitting the data in 
> between -200 ns and +80 ns. The function is then plotted in the full time 
> range.
>
> - Last page is a summary of the fits performed. Two 1d-histograms are the 
> distributions of the two time constants used in the parametrization. Then I 
> am plotting also their correlation, as well as the correlation of the 
> rise-time (par[1]) with the signal amplitude (from the fit).
>
> I noted that the fit parameters Trise, Tfall are not distributed as two 
> gaussians. In particular, for Trise there is an accumulation of events at ~ 5 
> ns and ~ 7 ns, correlated with corresponding Tfall at ~ 15 and ~20 ns. 
> Actually, I see that, other than the amplitude, signals do not have always 
> the same shape: look, for example, at signals n.5 and n.6 (ps pages n.5 and 
> n.6).
>
> Attached you find also the C implementation of the signal parametrization, in 
> form of a "double fun(double *x,double  *par)" used by ROOT when fitting 
> trough TF1.
> Finally, I am attaching also the raw data for the 31 signals I got, so if 
> you're interested you can play with different signal parametrizations.
>
> I am planning to take more data these days.
>
>
> Bests,
>
> Andrea
>
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