Example event. Isolated cluster (tower) found in 05TB01. No other isolated clusters found in sectors 5-8 which satisfied the above cuts.
Figure 1
The number of MIPs crossing the SMD plane were determined from the ADC response of each strip, using Jan's fast-food-quality gains. (The gains for plane 05U were hardwired into the code to provide gains for all strips and planes, until initial gains are loaded into the database.) These were summed over all strips within the seed tower of an identified cluster, averaged over 10k events, and plotted versus cluster energy. Only clusters isolated within a given sector were considered.
Figure 2
The energy response of the strips shows the right behavior -- linear with respect to associated tower response. The slope should tell us something about the absolute gains of the strips... specifically, see the PDB section on electromagnetic showers. In principle, we can calculate the expected energy-deposit w/in the SMD for various incident particle energies. The difference between electron- and photon-induced showers can be ignored for the moment.
We can improve on the method outlined above by fitting the SMD response to a shower-shape. The shape used in the following plots is a double gaussian with a constrained mean and width. (note-- different event from above histograms).
Figure 3
Steve suggested that the residual histograms could then be used to better gain match strips. The next two plots show the difference between the SMD profile histogram and the fit to the shower shape. The plan would be to histogram the fractional difference between the fit and the data, and adjust relative gains to minimize this difference. One probably wants to limit consideration to a range of 2-3 sigma around the fit mean, and apply cuts on chi-squared so as not to bias ourselves with bad fits.
Figure 4
The shower-shape used is the sum of two gaussians with a common mean and widths with a fixed ratio. This prodoces a four-parameter fit:
Equation 1
The current fitting algorithm is as follows:
(NOTE: sigma and Y are taken to be 10% larger than this to start)
The algorithm is somewhat robust, although I only fit about 1-dozen events by hand with it. One can miss the maximum bin by a strip or two, and it will snap onto the maximum pretty quickly.
The restriction on the fit-range was put in place to improve the overall chi^2 of the fits. However, typical widths (as shown below) will be ~0.8 strips. A fit +/- 3 sigma around the mean will be over ~5 strips. With a four parameter fit... we quickly run out of degrees of freedom. This might make desirable a simultaneous fit to both views, with common yields and widths.
Other problems....
Now some plots... (best viewed with your web browser maximized...)
When the mean N_mip vs E_cluster is plotted, we see the same behavior from the fits as when we simply sum the strips under the seed tower... namely a linear increase with an offset. The offsets may differ because the SMD distributions are not being polluted as much by stray hits along the strips, since we restrict the range of the fits. The slopes have changed significantly, though. One possible reason for this is that we're always performing a single shower fit... and missing pi0's.
Relative strip-to-strip gain matching using fits to the SMD distributions were extracted in the following way. Energetic clusters were identified, and the number of MIPS in the SMD U and V were histogramed versus strip index (indexed from 0). The resulting distributions were fit to the shower-shape described above. Events were selected where the fit had at least one degree of freedom, so that the four-parameter fit would not (by definition) go through the center of each of the data points.
The difference between the data yield for each strip within 3 sigma of the fit mean (sigma of the larger gaussian) was calculated, and divided by the data yield. This is the fractional-difference between the yield and the fit. The fractional difference for each strip was averaged over all events in the runs specified below. This average fractional difference should be due primarily to strip-to-strip gain variations.
And now the resulting plots...
