TY - JOUR

T1 - Variable transformation of calibration equations for radiation dosimetry

AU - Watanabe, Yoichi

PY - 2005/3/21

Y1 - 2005/3/21

N2 - For radiation dosimetry, dosimetric equipment must be calibrated by using known doses. The calibration is done to determine an equation that relates the absorbed dose to a physically measurable quantity. Since the calibration equation is accompanied by unavoidable uncertainties, the doses estimated with such equations suffer from inherent uncertainties. We presented mathematical formulation of the calibration when the calibration relation is either linear or nonlinear. We also derived equations for the uncertainty of the estimated dose as a function of the uncertainties of the parameters in the equations and the measured physical quantity. We showed that a dosimeter with a linear calibration equation with zero dose-offset enables us to perform relative dosimetry without calibration data. Furthermore, a linear equation justifies useful data manipulations such as rescaling the dose and changing the dose-offset for comparing dose distributions. Considering that some dosimeters exhibit linear response with a large dose-offset or often nonlinear response, we proposed variable transformations of the measured physical quantity, namely, linear- and log-transformation methods. The proposed methods were tested with Kodak X-Omat V radiographic film and BANG® polymer gel dosimeter. We demonstrated that the variable transformation methods could lead to linear equations with zero dose-offset and could reduce the uncertainty of the estimated dose.

AB - For radiation dosimetry, dosimetric equipment must be calibrated by using known doses. The calibration is done to determine an equation that relates the absorbed dose to a physically measurable quantity. Since the calibration equation is accompanied by unavoidable uncertainties, the doses estimated with such equations suffer from inherent uncertainties. We presented mathematical formulation of the calibration when the calibration relation is either linear or nonlinear. We also derived equations for the uncertainty of the estimated dose as a function of the uncertainties of the parameters in the equations and the measured physical quantity. We showed that a dosimeter with a linear calibration equation with zero dose-offset enables us to perform relative dosimetry without calibration data. Furthermore, a linear equation justifies useful data manipulations such as rescaling the dose and changing the dose-offset for comparing dose distributions. Considering that some dosimeters exhibit linear response with a large dose-offset or often nonlinear response, we proposed variable transformations of the measured physical quantity, namely, linear- and log-transformation methods. The proposed methods were tested with Kodak X-Omat V radiographic film and BANG® polymer gel dosimeter. We demonstrated that the variable transformation methods could lead to linear equations with zero dose-offset and could reduce the uncertainty of the estimated dose.

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U2 - 10.1088/0031-9155/50/6/012

DO - 10.1088/0031-9155/50/6/012

M3 - Article

C2 - 15798318

AN - SCOPUS:16444378473

SN - 0031-9155

VL - 50

SP - 1221

EP - 1234

JO - Physics in Medicine and Biology

JF - Physics in Medicine and Biology

IS - 6

ER -