[Hps-ecal] HPS Ecal signals parametrization

[Sho Uemura]

Realized this discussion didn't make it to the ECal list.

Would like more ECal experts to weigh in. I think we need to decide by the 
end of the month for a parametrization to use in the mock data.

On Fri, 4 Apr 2014, Sho Uemura wrote:

> Mean chisq/DOF is 0.56 for 3-pole, 0.68 for double-Gaussian.
>
> http://www.slac.stanford.edu/~meeg/ecalpulsefit/3pole/rchisq.png
>
> http://www.slac.stanford.edu/~meeg/ecalpulsefit/2gaus/rchisq.png
>
> I think that in every fit the 2-Gaussian shape overestimates the rising edge; 
> 3-pole looks better. As Andrea says, the pulse peak is definitely better fit 
> by 3-pole.
>
> On Thu, 3 Apr 2014, Sho Uemura wrote:
>
>> chisq/dof plot attached - I'm using TGraph to fit, which assumes errors of 
>> 1 mV per data point. I use the time range (-200, 60).
>> 
>> On Thu, 3 Apr 2014, Gabriel CHARLES wrote:
>> 
>>> Could you both provide an average value of chi square that the different 
>>> parametrization can be compared easily, please ?
>>> 
>>> Also, from the simulation it appears that the rising edge could be 
>>> present. In attachment you will find a picture with two plots. The top one 
>>> corresponds to the signal after the crystal and the APD, that is the input 
>>> of the preamplifier.
>>> It is obtained by the convolution of the signal of the crystal and the 
>>> APD. The crystal response is composed of the sum of two decreasing 
>>> exponential governed by different time constants. The APD transfert 
>>> function is given by the bottom plot (sorry for the wrong Y axis units).
>>> 
>>> There is no reason for the preamplifier to reduce the tail.
>>> 
>>> I think that if there is no huge difference between the chi square it 
>>> would be better to keep the two gaussian function.
>>> 
>>> ---
>>> Gabriel CHARLES
>>> Institut de Physique Nucléaire d'Orsay
>>> 
>>> On Thu, 3 Apr 2014 13:15:00 -0700 (PDT), Sho Uemura wrote:
>>>> 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
>>>>> 
>>> 
>>> ########################################################################
>>> Use REPLY-ALL to reply to list
>>> 
>>> To unsubscribe from the HPS-SOFTWARE list, click the following link:
>>> https://listserv.slac.stanford.edu/cgi-bin/wa?SUBED1=HPS-SOFTWARE&A=1
>