Delayed Coincidence Channel Estimation

The most accurate (and currently the most commonly implemented) method for estimating random coinci dences is the delayed channel method. In this scheme, a duplicate data stream containing the timing signals from one channel is delayed for several times the duration of the coincidence window before being sent to the coincidence processing circuitry. This delay removes the correlation between pairs of events arising from actual annihilations, so that any coincidences detected are random. The resulting coincidences are then subtracted from the coincidences in the prompt channel to yield the number of true (and scattered) coincidences. The coincidences in the delayed channel encounter exactly the same dead-time environment as the coincidences in the prompt channel, and the accuracy of the randoms estimate is not affected by the time-dependence of the activity distribution.

While accurate, this method has two principal drawbacks. Firstly, the increased time taken to process the delayed coincidences contributes to the overall system dead time. Secondly, and more importantly, the estimates of the randoms on each line-of-response are individually subject to Poisson counting statistics. The noise in these estimates propagates directly back into the data, resulting in an effective doubling of the statistical noise due to randoms. This compares poorly to the estimation from singles method, since the singles rates are typically two orders of magnitude greater than the randoms rates, so that the fractional noise in the resulting randoms estimate is effectively negligible. To reduce noise, the delayed channel can be implemented with a wider coincidence time window. However, this will further increase the contribution of delayed channel coincidences to system dead time.

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