March 30, 2004

Note-- The following will be expanded and reorganized in the near future.

Figure 1 shows the ratio of the relative gains determined from the procedure which follows below to the gains Steve determined from the ANL QA/C measurements (elog 697). The X axis is binned such that strips which map onto the same MAPMT are adjacent to each other.

Figure 1 -- Ratio of relative gains to QA gains

Figure 2 shows the the same ratio, zoomed in on the first four MAPMT tubes in box 05S1. Each tube is fit to a 0th-order polynomial (aka "pol0" or "p0" for root and paw devotees). While all 36 fit parameters are shown on the graph... it will be near impossible to read them. Sorry. Figure 2a shows the distribution of fits to each tube.

Figure 2 -- Ratio of relative gains to QA gains, 05S1-01 through 05S1-04

Figure 2a -- Distribution of fit parameters

Since the QA gains get corrected by a factor of [(HV/750)**8.3], the uncertatinty in the realative tube-to-tube gains can be fairly large. To try to remove this uncertainty, I divide out the fit to each tube. This is shown for 05S1-01 through 05S1-04 in figure 3.

Figure 3 -- Ratio of relative gains to QA gains, 05S1-01 through 05S1-04, divided by fit

Figure 4 shows the distribution of the ratio between the measured relative gains and the QA gains. The fit is to a gaussian, over the range 0.5 to 1.5.

Figure 4 -- Distribution of relative gains to QA gains (renormalized to tube fits)

It should be noted that there are a few strips for which my relative gain algorithm fails. I have not yet applied any sanity checks on the results. This may account for some of the larger differences shown in figure 4.

The above figures, assuming a fixed QA gain of 1.0, can be found in this directory. The RMS on the figure 4 above is smaller than the corresponding figure, assuming unit QA gains. Thus it is likely that there is a weak correlation between the QA gains and the final measured gains.

Relative SMD Gains, Take 1


Relative strip-to-strip SMD gains are extracted by matching energetic towers to SMD strips, fitting the shower-distribution to a simple shower-shape, and minimizing the residual distributions.

Data Sample
  1. Used eemcCalibration data...
  2. Runs R5056046 R5056047 R5056061 R5057072 R5058069 R5059023 R5059029 R5059033 R5062005 (600k events)
  3. Initial gains for strip i are the mean #p.e/mip for strip i * 8 ADC channels/1p.e.
  4. Cluster finder parameters:
  5. Selected clusters/seed towers with > 4 nonzero strips
  6. Selected clusters/seed towers with > 1 degree of freedom in fits
The Algorithm

Relative strip-to-strip gain matching using fits to the SMD distributions were extracted in the following way. Energetic clusters which satisfied the above criteria were analysed The SMD distributions beneath the seed tower of each cluster which passed the above cuts were fit to the following shower shape:

Equation 1

A residual distribution (the data minus the fit) was calculated. Figure 1 shows an example histogram (1a), its residual (1b) and its fractional residual (1c), defined as the residual divided by the actual yield.

Figure 1a -- Fit to SMD profile using shower shape defined above ....... Figure 1b -- Residual histogram (Data-Fit)

Figure 1c -- Fractional residual histogam (Data-Fit)/Data

If the SMD strips had uniform gains, then the fractional-residual for each strip would, on average, be zero. Strip-to-strip gain variations produce a shift in the fractional-residual of each strip, averaged over many events. We can use this to test and improve the gain-matching of the SMD strips in each plane. In other words, the fractional-residual is really just the fractional- difference between the true gain and the gain we have assumed.

The fractional-residual for each strip within 3 sigma of the mean of the shower shape was binned in a profile histogram (TProfile). In other words, for each strip we average the fractional-residual over all events in the run list. The resulting histogram for plane 05V is shown in figure 2.

Figure 2 -- Mean fractional-residual vs. strip index, 05V

Links to plots for all 8 extant planes 05V 05U 06V 06U 07V 07U 08V 08U

To better quantify how well the SMD planes are gain matched, we project figure 2 onto the y axis... this gives us the distribution of gain-shifts for each plane.

Figure 3 -- Mean fractional-residual distribution for 05V

Links to plots for all 8 extant planes 05V 05U 06V 06U 07V 07U 08V 08U

A better estimate for the gain for each strip is g_i prime = g_i / ( 1 + f_i ), where f_i is the mean fractional-residual for strip i, read off from figure 2. Applying this formula to all ~288 x 8 strips, we have a new set of gains which we can use to process the data. We can calculate the mean fractional-residuals for each strip (figure 4) based on these new gains...

Figure 4 -- Mean fractional-residuals vs strip index, 05V, new gains

Links to plots for all 8 extant planes 05V 05U 06V 06U 07V 07U 08V 08U

Projected onto the y axis, we have

Figure 5 -- Mean fractional-residual distribution for 05V, new gains

Links to plots for all 8 extant planes 05V 05U 06V 06U 07V 07U 08V 08U


There is a clear improvement in the residuals for each strip in each plane. The improvement is better for the lower-numbered strips where, presumably, we have more statistics. I expect that further iterations will produce improvements for larger strip numbers as well.

Table 1 shows the RMS deviations of the fractional residuals for each plane using the original gains and the gains calculated from the fractional-residual histograms. It shows tha the intial gain-matching of the SMD strips was pretty good, to typically around 10 percent. After the first iteration, the RMS deviation shows that we have a (software) improvement in the gains... to about 8%. Further iterations are in production.

Table 1 -- RMS of fractional-residuals for each plane, initial gains and first iteration
plane RMS initial RMS 1st iter RMS 2nd iter RMS 3rd iter RMS 4th iter
05U 0.1079 0.0856 0.0903 0.0802 0.0693
05V 0.1297 0.0952 0.0681 0.0615 0.0615
06U 0.1125 0.0994 0.0737 0.0656 0.0658
06V 0.1080 0.0797 0.0718 0.0792 0.0699
07U 0.0930 0.0650 0.0683 0.0708 0.0796
07V 0.1022 0.0870 0.0672 0.0799 0.0695
08U 0.1472 0.1120 0.0705 0.0760 0.0647
08V 0.0943 0.0725 0.0968 0.0842 0.0882

03/23/04 Added entries in the above table for second, third and fourth iteration.

Take 2

Table 1 shows the RMS of the mean fractional residuals (MFR) for each plane for four iteratations of the SMD gain-matching algorithm, which were run last night without any guidance from me. The following pages compare the results from each plane in each successive iteration.

Plane 05V
Plane 05U
Plane 06V
Plane 06U
Plane 07V
Plane 07U
Plane 08V
Plane 08U

Jason C. Webb
Last modified: Mon Mar 22 16:23:03 EST 2004