A-8
A TMS-A-305 Calibration Set
Ambient
temperature
The determined ambient temperature is used to reduce the groove depth to
20 °C, i.e. the groove depth will be calculated that would be the result of a
measurement of the depth setting standard at a temperature of 20 °C. The
linear thermal expansion coefficient of
specified in the
calibration certificate is used. A temperature difference of 3 K (Kelvin) results
in a thermal expansion of 10 nm for the 200 µm groove, for example. To
determine the expanded measurement uncertainty, an uncertainty of the
temperature determination of 2 K is assumed.
Expanded
measurement
uncertainty
The expanded measurement uncertainty displays the statistic uncertainty of
the calibration. It takes into account the uncertainty of the standard as well as
the uncertainty of the measurement. The expanded measurement uncertainty
was determined according to the “Guidelines on specifying uncertainty when
making measurements”.
To calculate the expanded measurement uncertainty, four parameters are
taken into account:
•
The expanded measurement uncertainty of the standard indicated in the
calibration certificate
•
An assumed uncertainty of 1 K when determining temperature of the
depth setting standard
•
The standard deviation of the evaluations of the single profile lines
•
The influence of the uncertainty of the markers determined 1-6 (see
calibration certificate) on the measurement result
All calculation parameters for the expanded measurement uncertainty are
regarded as being statistically independent. The expanded measurement
uncertainty is calculated from the standard measurement uncertainty by
multiplying it with an expansion factor k = 2. When re-measuring, the
expected deviation from a (true) value of the groove depth will be with a
probability of 95% in the
Measurement deviation ± expanded measurement
uncertainty
value range. With a probability of 2.5% each, the deviation will be
above or below this.
The specifications are considered to be complied with if the sum of the
absolute value of the measurement value deviation and the expanded
measurement uncertainty is smaller than the value specified for this step
height.
All calibrated grooves are evaluated groove 1, groove 2, ….
Tolerance value
For every step height, a tolerance value is specified for the measurement
value deviation. To attain a high confidence level on compliance with the
tolerance values, a worst-case consideration is carried out by adding the
absolute value of the measurement value deviation and the expanded
measurement uncertainty together.
You can assume that with a probability of at least 95%, a new measurement
of the same step height will not deviate from the true value by more than the
sum of the absolute value of the measurement value deviation and the
expanded measurement uncertainty.
