The calibration certificate and your own setup state two different numbers
Measurement uncertainty in UV measurement
Data sheets for UV sensors and UV radiometers state a percentage, usually followed by k = 2. It comes from the calibration and describes how accurate the instrument was in the laboratory, at the calibration source. At your own measuring position the uncertainty is larger – often considerably. This page explains where the difference comes from, what k = 2 means and how the individual contributions add up to a defensible figure for your own measuring task.
Calibration uncertainty is not measurement uncertainty
Calibration uncertainty applies to a narrowly defined state: the calibration source of the laboratory, the calibrated spectral range, the calibrated measuring range, room temperature and the day of calibration. It is stated in the calibration certificate and is the smallest uncertainty the instrument will ever have.
Measurement uncertainty is the figure that applies to your own result. It contains the calibration uncertainty plus everything that is added afterwards: a source other than the calibration source, a different sensor temperature, ageing since calibration, distance and alignment to the source, and the scatter of the measurement itself.
Quoting the certificate figure as the measurement uncertainty understates it. For a process release, a proof of capability or evidence of conformity with a standard it is the wrong number.
What k = 2 means
What is stated is not the standard uncertainty u but the expanded uncertainty U = k · u. The coverage factor k determines how confidently the true value lies within the stated interval:
- k = 1 – approx. 68 % confidence level
- k = 2 – approx. 95 % confidence level; the usual value in calibration certificates to DIN EN ISO/IEC 17025
- k = 3 – approx. 99.7 % confidence level
A percentage without k therefore cannot be evaluated: 5 % at k = 1 and 5 % at k = 2 differ by a factor of two. If a data sheet states a figure without a coverage factor, the specification is incomplete.
The uncertainty budget of a UV measuring setup
Every contribution is estimated separately, converted into a standard uncertainty and only then combined. The orders of magnitude below apply to Opsytec sensors and radiometers; the figures for an individual case are given in the calibration certificate and in the technical data of the respective product.
Contributions to measurement uncertainty
| Contribution | Order of magnitude | Where the figure comes from, what reduces it |
|---|---|---|
| Factory calibration | 4.5–6.0 % (k = 2) | calibration certificate; typical value of Opsytec sensors |
| ISO 17025 calibration | from 2.8 % (k = 2) | accredited calibration laboratory to DIN EN ISO/IEC 17025 |
| Spectral mismatch | up to several tens of percent | largest single item at an unfamiliar source; calibrate against the actual source or apply a mismatch factor |
| Linearity | below 1 % | technical data of the sensor |
| Ageing | below 3 % per year | grows with the time since the last calibration; define a calibration interval |
| Temperature drift | below 0.1 % per °C | limit the sensor temperature, provide cooling |
| Distance and alignment | application-dependent | define a repeatable measuring geometry; observe cosine correction |
| Repeatability | application-dependent | determine from repeated measurements at your own setup |
From the budget to a figure
The contributions are added in quadrature, not summed – they are independent of one another. The combined standard uncertainty follows from the standard uncertainties ui:
uc = √(u1² + u2² + … + un²)
Before adding, every contribution is converted back to k = 1: a value stated with k = 2 is halved, a limit value without a stated distribution is treated as a rectangular distribution and divided by √3. At the end the result is expanded again with k = 2.
Worked example: UVA LED curing, sensor calibrated against the actual source
| Contribution | Input value | u (k = 1) |
|---|---|---|
| Factory calibration | 6 % (k = 2) | 3.0 % |
| Residual mismatch after source-specific calibration | 4 % (k = 2) | 2.0 % |
| Ageing, one year since calibration | below 3 %, rectangular distribution | 1.7 % |
| Sensor temperature 20 °C above calibration temperature | 2 %, rectangular distribution | 1.2 % |
| Repeatability at the measuring position | from repeated measurements | 1.0 % |
| combined standard uncertainty | individual contributions added in quadrature | 4.3 % |
| expanded measurement uncertainty (k = 2) | combined standard uncertainty × 2 | 8.6 % |
The calibration certificate alone would have stated 6 %. Realistically this setup reaches 8.6 % – and that is already with a sensor calibrated against the LED actually used. Without source-specific calibration, spectral mismatch dominates the budget and the figure reaches double digits.
What this means for process control
For ongoing process monitoring it is not the absolute reading that counts but repeatability: is today's dose measured the same way as last week's? The systematic part – calibration and mismatch – enters as a fixed factor and cancels out when two measurements are compared. What remains is the scatter.
This is why the suitability of a measuring system is established through the proof of capability with the indices Cg and Cgk, not through the figure in the calibration certificate. For absolute evidence towards customers, auditors or a standard, however, the complete measurement uncertainty from the budget applies.
Two levers reduce it most effectively: calibration against the actual source and an observed calibration interval. The calibration laboratory offers both, ISO 17025-accredited on request.
Frequently asked questions about measurement uncertainty
What is the difference between calibration uncertainty and measurement uncertainty?
Calibration uncertainty is stated in the calibration certificate and applies only to the calibration source, the calibrated spectral and measuring range and the day of calibration. Measurement uncertainty applies to your own result: it contains the calibration uncertainty plus the spectral mismatch at the source actually used, the sensor temperature, ageing since calibration, distance and alignment, and the scatter of the measurement. It is therefore always larger than the figure in the certificate.
What does k = 2 mean in an uncertainty statement?
k is the coverage factor. What is stated is the expanded uncertainty U = k · u, not the standard uncertainty u. k = 2 corresponds to a confidence level of approximately 95 % and is the usual value in calibration certificates to DIN EN ISO/IEC 17025. A percentage without k cannot be evaluated, because 5 % at k = 1 and 5 % at k = 2 differ by a factor of two.
How large is the measurement uncertainty of a UV measurement in practice?
That depends on the measuring setup and is determined through an uncertainty budget. For UVA LED curing with a sensor calibrated against the actual source, factory calibration, residual mismatch, one year of ageing, raised sensor temperature and repeatability together give roughly 8.6 % (k = 2) – compared with 6 % from the calibration certificate alone. Without source-specific calibration the figure reaches double digits.
Which contribution to measurement uncertainty is the largest?
As a rule spectral mismatch, as soon as measurements are taken at a source other than the one calibrated against. It can reach several tens of percent and thus exceed all other contributions combined. Because the deviation is systematic and reproducible, it can largely be removed by calibrating against the actual source or by applying the mismatch factor.
