# estimate gain factors by adc spectrum

1. dataset: 6 runs on day080, 6 runs on day095

I combined runs that belong to the same day, and plot adc spectrum for each one of the 18 cells in group 1. Then I compared the slopes of a exponential fit to the region above threshold:

Fit was from ADC channel 600 to 2000. There are two frames for each cells, corresponding to the above two datasets respectively.

2. Following is the math that shows slope1 / slope2 = gain1 / gain2:

Assume the real energy spectrum obeys exponential distribution;

N = N0*exp(-k*E), with the factor k unknown, N is the number of events observed in energy bin E. Using E = ADC*gain as in our convention, then

Plotting N as a function of ADC, then the slope above threshold (shoulder) region is equal to k*gain. Compare the slopes of two datasets, we can show that

slope1 / slope2 = gain1 / gain2. The ratio gain1 / gain2 can be equivalently calculated by the number of triggers above a certain threshold ADCth, as a fraction of the

total number of events, namely

By fixing the same ADCth for each dataset, and compute ln(N/N0) in which N the the number of events above ADCth, we can show that

ln(N1/N10) / ln(N2/N20) = gain1 / gain2

3. Here is a comparion of the gains.  www.star.bnl.gov/protected/spin/yuxip/adcCellslopes_1_095080_6.pdf

For each cell, there are 4 types of gain factors.

gcorrOld:  gain correction factors calibrated for run12080001

gcorrAdc:  calculated by the above method using slopes. ( from adc spectra of 6uns on day080 and 6 runs on day095)

gpredicted: by following the mean ADC variation of LED events. (with 6 run from day095 combined, then compared to the baserun 12080001 )

gpredicted = nomianl gcor for baserun*( 1st pink point / mean of the rest 6 pink points), where the 1st pink point is the mean LED adc of

baserun

gdynamic:  following the mean ADC variation of LED events, but taking into account of the change of pulser intensity, which was described by the blue

dots.  gdynamic = nominal gcor for baserun* (mean of 6 blue points / mean of 6 pink points) , 6 pink points are the ones from day095

My conclusion is that for those cells which have enough number of triggers above threshold, therefore a relatively good exponential fit, the gain factors calculated

from slopes of adc spectra are more close to gdynamic.

ps. Here is the LED channel map: www.star.bnl.gov/protected/spin/yuxip/ledmap/

and the related macros:  www.star.bnl.gov/protected/spin/yuxip/macro/. This can be explained later, if necessary

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