Afterpulsing Probability

Photon-counting detectors have an increased probability of producing background pulses within the microseconds following the detection of a photon. These afterpulses are detectable in almost any conventional PMT. It is believed that they are caused by ion feedback, or by luminescence of the dynode material and the glass of the tube. 

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The afterpulsing probability can be measured by illuminating the detector by a source of continuous classic light, such as an incandescent lamp or an LED, and recording the detector pulses in the FIFO (time-tag) mode of a TCSPC module. 

The results given below are believed to be representative of the particular detectors or groups of detectors described. However, detector parameters may vary for different specimens of the same type, and will depend on possible changes in the manufacturing process. This is especially the case with parameters that depend on the gain, such as maximum count rate and afterpulsing probability. 

A typical correlation function of the afterpulses is shown in Fig. 6.38. The afterpulsing probability is relatively high, especially for the NIR-sensitive versions. The afterpulsing ceases after one microsecond and can, as usual, be reduced by operating the tube at reduced gain. 

The afterpulse probability for an R931 is shown in Fig. 6.52. As usual, the afterpulse probability depends on the operating voltage. The afterpulses appear within a time interval of about 3.5 ps. 

It is important to point out that even at 77 = 0 the observed value V = 0.942 0.006 is far from its ideal value of V = 0. One important source of error is the finite retrieval efficiency, which is limited by two factors. Due to the atomic memory decoherence rate 7C, the finite retrieval time Tr always results in a finite loss probability p 7c Tr. For the correlation measurements we use a relatively weak retrieve laser ( 2 mW) to reduce the number of background photons and to avoid APD dead-time effects. The resulting anti-Stokes pulse width is on the order of the measured decoherence time, so the atomic excitation decays before it is fully retrieved. Moreover, even as 7C —> 0 the retrieval efficiency is limited by the finite optical depth q of the ensemble, which yields an error scaling as p 1/ y/rj. The measured maximum retrieval efficiency at 77 = 0 corresponds to about 0.3. In addition to finite retrieval efficiency, many other factors reduce correlations, including losses in the detection system, background photons, APD afterpulsing effects, and imperfect spatial mode-matching. 

The height of the afterpulsing peak depends on the count rate. The reason is that the probability of detecting the afterpulse of a previously detected photon is constant, whereas the probability of detecting another photon increases with the count rate. To make the results directly comparable different detectors must be tested at the same count rate. 

Like afterpulsing, instability is probably eaused by ion feedback and possibly luminescence of dynodes. Therefore some manufaeturers specify not only a maximum operating voltage for their PMTs but also a maximum safe gain. 

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