Calibration and uncertainties

Calibration data

Calibration data can be used to provide correction of measured data or perform uncertainty calculations. Generally, calibration data can be of different types and different levels of complexity. For most of the cases user acquires error in each axis, e. g. using a calibrated standard. This value can be used for data correction. Similarly, the value of uncertainty is mostly determined for each axis from calibrated standard certificate and from measurement process uncertainty budget.

In more complex cases, calibration data can be determined locally. Scanner error cannot always be described by only three parameters (one for each axis) and its uncertainty is not necessarily the same in whole range. For precise measurements it is therefore practical to determine local errors and namely local uncertainties that can be used for further calculations. By "local" we mean here uncertainties that are related to certain location in the complete volume that can be reached by the scanner.

To obtain local errors and uncertainties, one can use a calibration standard again or use a more complex instrument, like interferometer for scanning stage calibration. This is usually done in metrology institutes.

In Gwyddion, there is a set of tools helping local uncertainty processing. Primary calibration data, related to a scanning stage, can be determined or loaded. They can be assigned to a certain SPM measurement data creating a set of calibrations. These are used automatically in tools and modules where uncertainty propagation calculation can be performed in order to provide measurement uncertainty.

Calibration data acquisition

Data ProcessCalibration3D calibration

Calibration data can be acquired in the following ways:

The module 3D calibrationCreate... can be used for creating simplest primary calibration data - based only on knowledge of xyz errors and uncertainties and on scanner volume geometry. We also need to specify calibration name. Primary calibration data will be accessible under this name module for its data application to SPM measurements.

Using 3D calibrationGet simple error map... module, we can determine primary xyz calibration data from a set of calibration grating measurements. Here we need to provide several measurements of calibration grating for different z-levels of the scanner. This forms several cross-sections of the full scanner volume. Providing single grating detail, nominal grating pitch and assuming that the grating planarity and orthogonality is much higher than that of scanning stage we can determine primary calibration data on the basis of correlation. Note that this way of calibrating a microscope is only very approximate and its use for metrology purposes is very limited. However, it can provide a lot of useful information about our scanner properties if we are unable to perform more complex analysis.

Finally, using 3D calibrationLoad from file... we can load any primary 3D calibration data determined by an external device, like set of interferometers. Data should be a plain text file containing number of calibration sets and sets (x, y, z, x_err, y_err, z_err, x_unc, y_unc, z_unc).

Calibration data application and further use

Data ProcessCalibration3D calibration

Primary calibration data obtained in previous steps are related to a scanning stage, not to concrete SPM measurements. We can use primary calibration data for different measurements. To use primary calibration data for our measured data processing, we need to apply them first. Using module 3D calibrationApply to data... we can review and select calibration data applied on our height field measurements. After applying calibration data a set of calibration datafields is created and attached to selected data. A ‘C’ character appears in data browser as a sign of data with attached calibration. Note that the calibration attached to SPM measurement is no more related with primary calibration data (that were used for its creation).

When there is calibration attached to data, data reading and statistical quantities evaluation modules and tools recognize it automatically. Measurement uncertainty is then added to the measurement results. Uncertainty is calculated using uncertainty propagation law.