Implementation of sub-nanoseconds TDC in FPGA: applications to time-of-flight analysis in muon radiography

TLDR: In this paper, the application of ring oscillator TDC to muon tomography of geological bodies is described in detail, which aims at measuring density variations and absolute densities through the detection of atmospheric muons flux's attenuation, due to the presence of matter.

Abstract: Time-of-flight (tof) techniques are standard techniques in high energy physics to determine particles propagation directions. Since particles velocities are generally close to c, the speed of light, and detectors typical dimensions at the meter 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 TDC ones, implemented in low cost FPGA, feature a very interesting figure of merit since a very good timing performance may be achieved with limited processing ressources. This issue is relevant for applications where unmanned sensors should have the lowest possible power consumption. Actually this article describes in details 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 muons 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 previsions.