Multiple detectors

Data from multiple detectors can be added before or after fitting.

Add after fitting

Compute the weighted sum of the peak areas, associated uncertainties and mass fractions for several detectors.

For elemental peak areas

\[A(\mathrm{Fe}) = \sum_i{\left[ W_i A_i(\mathrm{Fe}) \right] }\]

The variable \(W_i\) is the weight for detector \(i\) which is typically the inverse of the live time multiplied by the target live time.

For the associated uncertainties (linear error propagation)

\[\sigma_{A}(\mathrm{Fe}) = \sqrt{ \sum_i\left[ W_i^2 \sigma_{A_i}^2(\mathrm{Fe}) \right] }\]

For elemental mass fractions, in addition to the detector weight we also weight for the peak area

\[M(\mathrm{Fe}) = \sum_i{\left[ W_i M_i(\mathrm{Fe}) \frac{W_i A_i(\mathrm{Fe})}{A(\mathrm{Fe})} \right] }\]

Add before fitting

Warning

When adding XRF spectra from multiple detector, quantification can never be strictly correct since the combined response of multiple detectors cannot be replaced by the response of a single theoretical detector.

The weighted sum of XRF spectra from multiple detectors is

\[\mathrm{MCA}_{\mathrm{sum}} = \sum_i\left[ W_i\mathrm{MCA}_{i} \right]\]