Linearity correction of energy response
Why an energy response point irradiated at a different dose rate from the reference needs correcting, how the correction factor is derived from the linearity curve, its preconditions, and what the tool does when it cannot be applied.
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The energy response evaluation assumes that the only variable changing between rows is photon energy. In a real calibration laboratory that assumption frequently does not hold, and the correction described here is what recovers the evaluation when it does not.
The confounded measurement
The available dose rate differs between radiation qualities. An X-ray tube at N-40 and a ¹³⁷Cs source do not produce comparable output at a fixed distance, and matching them may require a distance or an attenuator that is not available.
If each energy point is irradiated at whichever dose rate is convenient, the computed relative response contains two effects:
- the energy dependence, which is the quantity being measured;
- the dose rate dependence, which is not.
The result is a single number in which the two are not separable. It is not incorrect as an observation; it does not answer the question the test asks.
Derivation of the correction
The dose rate dependence is already known: it is what the linearity evaluation measures. The linearity curve L(H) gives the response as a function of dose rate H.
If an energy point was irradiated at dose rate H while the reference point was irradiated at Href, the ratio of the curve at those two dose rates is the factor by which the observed relative response was displaced:
The correction is applied automatically to any row whose dose rate differs from the reference row. The factor k is displayed on that row, so the correction is visible in the output rather than absorbed into the value.
Preconditions
The correction is only valid where the linearity curve characterises the dose rate region being corrected across. Two conditions must hold.
Bracketing points
The linearity dataset must contain points that bracket both H and Href. Extrapolating the curve beyond its measured range assumes behaviour that was not measured, which is the failure the correction exists to avoid.
Compatible units
The linearity points and the energy point must be in units that convert to one another. Dose equivalent and air kerma are different physical quantities and do not convert, so a linearity dataset in Sv/h cannot correct an energy point recorded in Gy/h.
Behaviour when the correction cannot be applied
Where either precondition fails, the tool does not extrapolate and does not silently skip the correction. It marks the row and judges the uncorrected relative response.
That is a reportable result, with a stated limitation: the row’s relative response includes an unquantified dose rate contribution. The limitation must be carried into the report. A row that was judged uncorrected and a row that needed no correction are not equivalent, and the output distinguishes them.
Effect on uncertainty
The correction factor is derived from measured linearity points and therefore has its own relative uncertainty. That component is combined into the uncertainty of the corrected row.
A corrected row consequently has a larger reported uncertainty than an uncorrected one. This is the expected outcome: the correction improves the accuracy of the value and reduces the confidence in it, and both changes are represented in the output. See the uncertainty guide.
Practical consequences
Linearity quality determines energy result quality
A sparse or incomplete linearity dataset limits the energy evaluation. Where linearity has few points or does not span the dose rates used for the energy campaign, corrections cannot be applied and the energy result carries the limitation described above. Plan the linearity points with the energy campaign in mind.
Record the dose rate on every energy row
A report that lists radiation qualities and relative responses without the dose rate used at each point cannot be checked. A reviewer cannot determine which rows carried a correction, how large it was, or whether it was applicable.
The correction is not a substitute for matching the dose rate
Where the dose rate can be matched to the reference, match it. The correction recovers a usable result from a confounded measurement; it does not produce a result equivalent to one that was not confounded, because it introduces a dependence on a second dataset and its uncertainty.