A mathematical formalism for hyperspectral, multipoint plastic scintillation detectors

The aim of this paper is to generalize and extend the mathematical formalism used with plastic scintillation detectors (PSDs). By doing so, we show the feasibility of multi-point PSD. The new formalism is based on the sole hypothesis that a PSD optical signal is a linear superposition of spectra. Two calibration scenarios were developed. Both involve solving a linear equation of the form Y = XB, but the process and input data depend on the information available on the detector system. Simulations were carried out to validate both scenarios and demonstrate the advantages of the new formalism. In this paper, we prove the following results. (1) Multi-point PSDs are feasible. Simulations have shown that six different spectra could be resolved accurately even in the presence of up to 10% Gaussian noise. (2) The new formalism leads to more precise PSD measurements. (3) By using the condition number of the measurement matrix, the ideal sets of calibration measurements can be identified. (4) By using principal component analysis it was possible to identify the best set of wavelength filters. We have shown through numerical simulations that multi-point detectors are feasible. This has potential for applications such as in vivo dose verification. Furthermore, our new formalism can be used to improve the robustness and ease of use of PSDs.