On the measurement uncertainty of microdosimetric quantities using diamond and silicon microdosimeters in carbon-ion beams

Purpose The purpose of this paper is to compare the response of two different types of solid-state microdosimeters, that is, silicon and diamond, and their uncertainties. A study of the conversion of silicon microdosimetric spectra to the diamond equivalent for microdosimeters with different geometry of the sensitive volumes is performed, including the use of different stopping power databases. Method Diamond and silicon microdosimeters were irradiated under the same conditions, aligned at the same depth in a carbon-ion beam at the MedAustron ion therapy center. In order to estimate the microdosimetric quantities, the readout electronic linearity was investigated with three different methods, that is, the first being a single linear regression, the second consisting of a double linear regression with a channel transition and last a multiple linear regression by splitting the data into odd and even groups. The uncertainty related to each of these methods was estimated as well. The edge calibration was performed using the intercept with the horizontal axis of the tangent through the inflection point of the Fermi function approximation multi-channel analyzer spectrum. It was assumed that this point corresponds to the maximum energy difference of particle traversing the sensitive volume (SV) for which the residual range difference in the continuous slowing down approximation is equal to the thickness of the SV of the microdosimeter. Four material conversion methods were explored, the edge method, the density method, the maximum-deposition energy method and the bin-by-bin transformation method. The uncertainties of the microdosimetric quantities resulting from the linearization, the edge calibration and the detectors thickness were also estimated. Results It was found that the double linear regression had the lowest uncertainty for both microdosimeters. The propagated standard (k = 1) uncertainties on the frequency-mean lineal energy y over bar F${\bar{y}}_{\rm{F}}$ and the dose-mean lineal energy y over bar D${\bar{y}}_{\rm{D}}$ values from the marker point, in the spectra, in the plateau were 0.1% and 0.2%, respectively, for the diamond microdosimeter, whilst for the silicon microdosimeter data converted to diamond, the uncertainty was estimated to be 0.1%. In the range corresponding to the 90% of the amplitude of the Bragg Peak at the distal part of the Bragg curve (R-90) the uncertainty was found to be 0.1%. The uncertainty propagation from the stopping power tables was estimated to be between 5% and 7% depending on the method. The uncertainty on the y over bar F${\bar{y}}_{\rm{F}}$ and y over bar D${\bar{y}}_{\rm{D}}$ coming from the thickness of the detectors varied between 0.3% and 0.5%. Conclusion This article demonstrate that the linearity of the readout electronics affects the microdosimetric spectra with a difference in y over bar F${\bar{y}}_{\rm{F}}$ values between the different linearization methods of up to 17.5%. The combined uncertainty was dominated by the uncertainty of stopping power on the edge.