Error analysis in the measurement of x-ray photon fluence: an analysis on the uncertainty from energy calibration

摘要

The measurements of x-ray spectra and photon fluence are of significant importance in medical imaging applications. The complexity of the spectral measurements and photon fluence calculation leads to possible errors which may come from various sources. The focus of this project is to study the mathematical method to determine the uncertainty that is propagated from the energy calibration process into the photon fluence calculation. In order to form a basis for the uncertainty analysis, a straightforward derivation on the calculation of the photon fluence based on spectral and exposure measurements is provided. Then the uncertainty in the determination of the energy-channel linear relationship is calculated. Instead of using this linear relationship to calibrate the measured spectra, we calibrate the mass energy absorption coefficients, in an effort to separate the calibration uncertainty from the measurement uncertainty in the spectra, and to simplify the subsequent derivation on uncertainty propagation. Finally, the formula on the uncertainty in photon fluence that is from the calibration process is derived.