Linearity
How to run the linearity evaluation of IEC 60846-1:2009 §8.7 — choosing test points across the decades, taking repeated readings, and why the same readings also serve the statistical fluctuation test.
Last reviewed
Linearity establishes whether an instrument calibrated at one point remains within the acceptance band across the rest of its measuring range. A detector that is accurate at 10 µSv/h and reads 30 % low at 10 mSv/h fails this test, and the deviation is not detectable from the instrument’s appearance or from a single-point check.
Measured quantities
At each test point you irradiate the instrument at a known dose rate — the reference value — and take repeated readings. The mean of those readings, after subtracting background, is the indication. Divide it by the reference value and you have the response at that point.
Response on its own is not the acceptance quantity, because it carries the instrument’s overall calibration factor. What matters is whether it changes across the range. So every point’s response is divided by the response at the reference point, giving the relative response. The reference point is by definition 1,00; everything else is measured against it, and the acceptance band applies to that ratio.
This is worth being clear about, because it has a practical consequence: an instrument that reads uniformly 20 % low passes linearity. Linearity is not accuracy. A systematic offset is a calibration problem and this test is deliberately blind to it.
Test point selection
Work at the reference radiation quality, then set a reference dose rate in each decade of the effective measuring range. The conventional layout is three points per decade — roughly 20 %, 40 % and 80 % of each decade — which gives you enough points to see curvature rather than just a slope.
Two conditions determine whether the dataset is usable:
- If the instrument switches display units across decades, record the unit per row. Reading “8,5” without noting whether the display had flipped from µSv/h to mSv/h is the single most frequent cause of an unusable linearity dataset.
- Distribute the points across decades. Five points in one decade and one in the next characterises only the populated decade. The deviations this test detects occur at the range extremes and at range-switching boundaries.
Repeated readings and shared data
At each point, take repeated readings rather than one. The standard leaves the count open within a range; something in the region of ten to twenty at every point is the usual working choice, and the count must be the same at every point.
Those repeated readings are also the statistical fluctuation dataset. IEC 60846-1 evaluates fluctuation from the same measurements as linearity (§8.7.1). A second irradiation campaign is not required. Linearity evaluates the means across points; fluctuation evaluates the variation within each point. Running them separately doubles the beam time without adding information.
The reading count is therefore not a free parameter. Selecting four readings per point because linearity requires no more weakens the fluctuation evaluation, which uses the same data.
Reading interval
Readings must be separated by enough time to be statistically independent. With an instrument whose integration time is long relative to the interval, successive readings are correlated and the computed variation is lower than the true value. The manufacturer’s response time is the reference; three times that interval is a practical minimum.
Acceptance criterion
Rule
Every point’s relative response must fall inside the acceptance band. One point outside it fails the test — there is no averaging, and no “most points passed”.
Failure patterns
The distribution of the failing points normally identifies the cause. A single bad point in the middle of an otherwise flat set is normally a setup error: wrong distance, wrong attenuator, a reference value entered in the wrong unit. A progressive drift towards the top of the range is detector saturation or dead-time behaviour. A drift at the bottom is background subtraction — check what background you actually measured, and whether it was measured with the same instrument settings.
Relationship to the energy response test
Linearity is not only a test in its own right. Its result is used to correct the energy response evaluation when an energy test point could not be irradiated at the same dose rate as the reference — the linearity curve is what tells you how much of the observed difference was energy and how much was dose rate. A weak or incomplete linearity dataset therefore weakens the energy result too.