Estimating relationship between the time over threshold and energy loss by photons in plastic scintillators used in the J-PET scanner
Authors: Sharma S. , Chhokar J. , Curceanu C. , Czerwiński E. , Dadgar M. , Dulski K. , Gajewski J. , Gajos A. , Gorgol M. , Gupta-Sharma N. , Del Grande R. , Hiesmayr B.C. , Jasińska B. , Kacprzak K. , Kapłon Ł. , Karimi H. , Kisielewska D. , Klimaszewski K. , Korcyl G. , Kowalski P. , Kozik T. , Krawczyk N. , Krzemień W. , Kubicz E. , Mohammed M. , Niedzwiecki Sz. , Pałka M. , Pawlik-Niedźwiecka M. , Raczyński L. , Raj J. , Ruciński A. , Shivani S. , Shopa R.Y. , Silarski M. , Skurzok M. , Stępień E.Ł. , Wiślicki W. , Zgardzińska B. , Moskal P. 
Published: June 2020

Abstract
Purpose
The time-over-threshold (TOT) technique is being used widely due to itsimplications in developing the multi-channel readouts, mainly when fast signal processing is required. Using the TOT technique, as a measure of energy loss instead of charge integration methods, significantly reduces the signal readout costs by combining the time and energy information. Therefore, this approach can potentially be utilized in J-PET tomograph which is built from plastic scintillators characterized by fast light signals. The drawback in adopting this technique lies in the non-linear correlation between input energy loss and TOT of the signal. The main motivation behind this work is to develop the relationship between TOT and energy loss and validate it by the J-PET tomograph setup.

Methods
The experiment was performed using a 22Na beta emitter source placed in the center of the J-PET tomograph. This isotope produces photons of two different energies: 511 keV photons from the positron annihilation (direct annihilation or through the formation of a para-positronium atom or pick-off process of ortho-positronium atoms) and a 1275 keV prompt photon. This allows the study of the correlation between TOT values and energy loss for energy ranges up to 1000 keV. Since the photon interacts predominantly via Compton scattering inside the plastic scintillator, there is no direct information of the energy deposition. However, using the J-PET geometry, one can measure the scattering angle of the interacting photon. Since the 22Na source emits photons of two different energies, it is necessary to know unambiguously the energy of incident photons and their corresponding scattering angles in order to estimate energy deposition. In summary, this work presents a dedicated algorithm developed to tag photons of different energies and studying their scattering angles to calculate the energy deposition by the interacting photons.

Results
A new method was elaborated to measure the energy loss by photons interacting with plastic scintillators used in the J-PET tomograph. We find the relationship between the energy loss and TOT is non-linear and can be described by the functions TOT = A0 + A1 * ln(E dep + A2) + A3 * (ln(E dep + A2))2 and TOT = A0 - A1 * A2$^{E_{dep}}\phantom {\dot {i}\!}$

E

dep

. In addition, we also introduced a theoretical model to calculate the TOT as a function of energy loss in plastic scintillators.

Conclusions
A relationship between TOT and energy loss by photons interacting inside the plastic scintillators used in J-PET scanner is established for a deposited energy range of 100–1000 keV.