Extracting the Calibration Constant for Droop Compensation from the DFL/FAT Data
August 15, 2005N. Kitamura
Summary
It has been demonstrated that the droop in the long-pulse response can be compensated for by a simple DSP algorithm containing a single calibratable parameter equal to the time constant of the uncompensated droop response. In the following it is shown that the data being collected in the DFL/FAT is sufficient to determine the time constant for individual DOMs, although the method of extracting the time constant needs optimization. The calibration parameter can be computed and databased offline after the FAT, and no software or hadware changes are required for the FAT.
Source Data
During the cold-soak (-20C and -45), the DOM response to approximately 1000 (970) shots of highly attenuated 50-usec-wide pulses are recorded. Because of the low light-level, the individual channel trace contains short pulses spread over the capture window, plus noise pulses.
Here are some examples (DOM name: “Volcanology”):
Fig 1Sample FADC records. Horizontal units: usec.
Fig 2FADC records superimposed. Horizontal units: usec. Saturated traces, containing 0 or 1023, have been excluded. There are noise pulses everywhere, but there are overwhelmingly more pulses in the 0 – 50 usec region, where the optical response is expected.
Fig 3Red: sum of all curves in Fig 2, divided by the number of curves; Blue: fit to a simple exponential. The Red is a combined response of the PMT Base Board Toroid FADC. The simple exponential model used for the Blue contains two parameters: the time constant and the baseline. It is only the time constant that is needed for the droop compensation computation. As shown below, the quality of this fit matters!
Droop Compensation
Droop is caused by the low-frequency cut-off of the ac-coupling transformer, characterizable as a single pole high-pass filter. Droop compensation applies the inverse of this filter to the FADC data in the form of a single-pole low-pass filter.
/ Fig 4 Blue: Original response. Red: Compensated response using the time constant shown in Fig 3, which appears to have been over-compensated. (Note: we don’t know the actual pulse shape of the input optical pulse.)/ Fig 5 The time constant used in the compensating filter has been increased by a fudge factor of 20%. Now the compensated curve looks more like a square pulse, but the fitted curve (Red dots) is visibly off the data (blue).
As shown above, the method of determining the time constnat, tau, still needs work.
Fig 6 The filter used for Fig 5 has been applied to the individual FADC records.
Conclusion
Correcting the FADC data using the characterized response requires no DOM hardware design change.
For the DOMs that are going to be deployed in the 05/06 season, using the extension (i.e., optimized version) of the above method is probably the only way to correct the FADC data.
/nk