New Algorithms for Improved Digital Pulse Arrival Timing With Sub-GSps ADCs

The ability to measure pulse times of arrival with resolutions at or below 100 ps is becoming increasingly desirable in various fields, typically for signals originating from photon detectors such as photomultiplier tubes (PMTs) or silicon photo-multipliers. Achieving the best results has typically required digitizing signals at rates between 4 and 20 giga-samples/second (GSps), followed by off-line processing, since such in-line processing technologies as digital signal processors and field-programmable gate arrays (FPGAs) cannot handle the data rates. For multichannel applications, the cost of GSps digitizers also becomes an issue. In this paper, we present two new methods for achieving similar time resolutions that are designed for FPGA in-line implementations operating with digitizers running at 250-500 mega-samples/second (MSps), approximately a factor of ten times slower. The first method uses a modified sinc function to interpolate the arriving pulse twice, once to precisely estimate its maximum M and once on its leading edge to locate the constant fraction point $f \cdot M$ as the pulse's arrival time. The second method takes the ratio of two points captured from a rapidly changing region of the pulse, either on its leading edge or near its peak, and uses this ratio with a preconstructed lookup table to generate the arrival time. We examine the algorithms' improved timing capability by comparing their coincidence timing resolutions to those from three standard algorithms, all applied to three data sets of pulses with different characteristics. At 500 MSps, the interpolation technique achieves about 7-ps full-width at half-maximum (FWHM) for an analog trigger pulse split between two ADC channels; for a fast laser pulse illuminating two ADIT L25D19 PMTs, better than 50-ps FWHM, and at 250 MSps, for two $\phi ~25$ mm $\times25$ mm LaBr3 crystals exposed to
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Co, 137-ps FWHM for gamma rays in a 0.95- and 1.33-MeV window.