Implementation of sub-nanosecond time-to-digital convertor in field-programmable gate array: applications to time-of-flight analysis in muon radiography

Abstract

Time-of-flight (TOF) techniques are standard techniques in high energy physics to determine particles’ propagation directions. Since particle velocities are generally close to c, the speed of light, and detector typical dimensions at the metre level, the state-of-the-art TOF techniques should reach sub-nanosecond timing resolution. Among the various techniques already available, the recently developed ring oscillator time-to-digital converter (TDC) ones, implemented in low-cost programmable logic circuits like FPGA (field programmable gate array), feature a very interesting figure of merit since a very good timing performance may be achieved with limited processing resources. This issue is relevant for applications where unmanned sensors should have the lowest possible power consumption. Actually this paper describes in detail the application of this kind of TOF technique to muon tomography of geological bodies. Muon tomography aims at measuring density variations and absolute densities through the detection of atmospheric muon flux’s attenuation, due to the presence of matter. When the measured fluxes become very low, an identified source of noise comes from backwards propagating particles hitting the detector in a direction pointing to the geological body. The separation between through-going and backward-going particles on the basis of the TOF information is therefore a key parameter for the tomography analysis and subsequent forecasts. This paper describes a TDC implementation fulfilling the requirements of a TOF measurement applied to muon tomography.