BSMD Calibration - A few plots (test)

Updated on Tue, 2009-06-30 08:38. Originally created by martinc on 2009-06-30 08:34.

BSMD Calibration - Additional Plots
Monday June 29th 2009

M.J.M. Codrington

Texas A&M University

For previous updates, please click here, and here.

Calibration Method 2 - Additional Plots

Fitting the ADC histograms with a higher order exponential, for example, one of the form;

e(P0+P1x+P2x2)

should yield a better fit, than a simple exponential. However, the two parameters P₁ and P₂ do not directly translate to a relative gain per strip, and therefore, do not separately carry useful information about SMD gain variation. These two parameters must somehow be combined, to give one parameter that can be interpreted as a gain.

We found two possible solutions, for this problem. ;

Function 1

e[P0+P1x+αx2]

Where α = average value of P2P1

Function 2

e[P0+P1x+β(P1x)2]

Where β = average value of P2P12

In the following results, the two functions, Function 1 and Function 2 will be referred to as F1 and F2 respectively.

Calibration Results

Live Strips
Live Strips are defined as those strips that;
1.    Had greater than 100 entries before calibration
2.       Did not yield a negative slope with fit from 1 – 130 ADC channels (the slope was multiplied by -1, so this flagged those strips, with a positive initial slope)
3.       Strips that had > 0% calibration

Function & SMD Plane	Live Strips
F1 – SMD-η	14,873
F1 – SMD-φ	15,674
F2 – SMD-η	14,876
F2 – SMD-φ	15,674

Table 1 – Live Strips

Calibrated and Non-Calibrated Strips

Function & SMD Plane	Calibrated Strips	Negative Divergence	Positive Divergence	Negative Overshoot	Positive Overshoot
F1 – SMD-η	12,747	786	300	748	292
F1 – SMD-φ	12,266	1,098	1,549	333	428
F2 – SMD-η	12,494	644	188	1,058	492
F2 – SMD-φ	12,668	794	1,227	438	547

Table 2 – Numbers of Calibrated and Non-Calibrated SMD-η & SMD-φ Strips for Calibration with F1 & F2

Function & SMD Plane	% Calibrated Strips	% Negative Divergence	% Positive Divergence	% Negative Overshoot	% Positive Overshoot
F1 – SMD-η	85.71	5.28	2.02	5.03	1.96
F1 – SMD-φ	78.26	7.01	9.88	2.12	2.73
F2 – SMD-η	83.99	4.33	1.26	7.11	3.31
F2 – SMD-φ	80.82	5.07	7.83	2.79	3.49