Artifacts in digital coincidence timing

Digital methods are becoming increasingly popular for measuring time differences, and are the de facto standard in PET cameras. These methods usually include a master system clock and a (digital) arrival time estimate for each detector that is obtained by comparing the detector output signal to some reference portion of this clock (such as the rising edge). Time differences between detector signals are then obtained by subtracting the digitized estimates from a detector pair. A number of different methods can be used to generate the digitized arrival time of the detector output, such as sending a discriminator output into a time to digital converter (TDC) or digitizing the waveform and applying a more sophisticated algorithm to extract a timing estimator.All measurement methods are subject to error, and one generally wants to minimize these errors and so optimize the timing resolution. A common method for optimizing timing methods is to measure the coincidence timing resolution between two timing signals whose time difference should be constant (such as detecting gammas from positron annihilation) and selecting the method that minimizes the width of the distribution (i.e. the timing resolution). Unfortunately, a common form of error (a nonlinear transfer function) leads to artifacts that artificially narrow this resolution, which can lead to erroneous selection of the 'optimal' method. The purpose of this note is to demonstrate the origin of this artifact and suggest that caution should be used when optimizing time digitization systems solely on timing resolution minimization.