Changes

=== Modeling of realistic signals ===

=== Modeling of realistic signals ===

[[Scint_Amp_resp.png|thumb|395px|Figure 3: Comparison of the naive superposition of simultaneous single-pixel events with the expected pulse shape taking into account scintillators response. The decay time of an excitation in the scintillator is 2.7 ns]]

[[Image:Scint_Amp_resp.png|thumb|395px|Figure 3: Comparison of the naive superposition of simultaneous single-pixel events with the expected pulse shape taking into account scintillators response. The decay time of an excitation in the scintillator is 2.7 ns]]

Figure 3 presents multi-pixel signals expected on the output of the amplifier. Simple superposition of 500 simultaneous pixel discharges is compared with a realistic signal shape. The single-pixel pulse shaped by the amplifier as described above has been convolved with the exponential distribution of photons from the scintillator. This is due to the cascade of optical excitations and decays initiated by the high-energy tagging electron passing through the scintillator bulk. The overall light flash decay time in BCF-20 is 2.7 ns. Thus we may expect the arrival of the photons to be distributed as an exponential distribution with this characteristic time. (The differences in optical path are thought to be negligible on this scale.) Of course, the smooth distribution assumes sampling of infinitely many photons. The expected signal in the hundreds of activated pixels is sufficient or, at the very least this convolution with the ideal distribution presents the mean shape of the resulting signals.  

Figure 3 presents multi-pixel signals expected on the output of the amplifier. Simple superposition of 500 simultaneous pixel discharges is compared with a realistic signal shape. The single-pixel pulse shaped by the amplifier as described above has been convolved with the exponential distribution of photons from the scintillator. This is due to the cascade of optical excitations and decays initiated by the high-energy tagging electron passing through the scintillator bulk. The overall light flash decay time in BCF-20 is 2.7 ns. Thus we may expect the arrival of the photons to be distributed as an exponential distribution with this characteristic time. (The differences in optical path are thought to be negligible on this scale.) Of course, the smooth distribution assumes sampling of infinitely many photons. The expected signal in the hundreds of activated pixels is sufficient or, at the very least this convolution with the ideal distribution presents the mean shape of the resulting signals.  

Note the significant attenuation when the scintillator decay time is taken into account. The dynamic range of the readout is a concern for the expected signals: about 300 pixels, exceeding 500 with proposed reflection coating on the upstream end of scintillating fibers. Since the integral of the pulse is preserved (being proportionate to the charge deposited in the SiPM), the effort to shorten the pulses lead to amplification, threatening that the full intensity signals will exceed the full range (currently 1.5 V in the amplifier design). This upper-range estimate of 500 pixels for the signal is safely within range.

Note the significant attenuation when the scintillator decay time is taken into account. The dynamic range of the readout is a concern for the expected signals: about 300 pixels, exceeding 500 with proposed reflection coating on the upstream end of scintillating fibers. Since the integral of the pulse is preserved (being proportionate to the charge deposited in the SiPM), the effort to shorten the pulses lead to amplification, threatening that the full intensity signals will exceed the full range (currently 1.5 V in the amplifier design). This upper-range estimate of 500 pixels for the signal is safely within range.