| Zusammenfassung |
Compared to the classical instrument calibration procedure requiring separate lateral and vertical
calibration standards, the “nanomarker”-based 3D standard with the shape of cascade step-slope
pyramids can calibrate three scale factors of the measurement instrument as well as three coupling
factors using only one piece of sample and in one measurement, thus offering great application
convenience. To verify the calibration performance of 3D standards, a pilot study aimed to
investigate the calibration performance of 3D standards is currently being carried out among several
NMIs including PTB, NMIJ, and NPL. In this pilot study, it is agreed that the data evaluation algorithm,
which was delicately developed by Point electronic GmbH and offered as an essential part of the
solution package, is applied for the data evaluation. However, from the quality management point of
view, it is of high importance to validate the error attributable to the data evaluation algorithm
beyond the comparison, as such error cannot be validated by the comparison itself
A software validation method for the calibration of 3D standards has been developed. The method
applies two different kinds of reference data:
(i) simulated AFM images, which are generated from the given feature geometries (i.e.,
ground true values) of 3D standards using a virtual AFM developed at the PTB [1]. After
the simulated AFM images are evaluated by the to-be-validated software/algorithm, its
output (i.e., the x-, y- and z- coordinates of nanomarkers) can be compared to the ground
true values for evaluating its performance. Possible measurement influences such as
noise, drift, and tip contribution can be introduced in the simulation process so that the
validation process fits better to real measurement conditions.
(ii) a real AFM image of a 3D standard from e.g., a metrological AFM. In the validation, we
simulate the deformation of the real AFM image for different scenarios if the AFM has
certain scaling or coupling factors (ground trues). Then, by inputting the deformed AFM
image as measurement data and the real AFM image as the reference data, the output of
the software (i.e., the calculated scaling and coupling factors) can be compared to the
ground true values for validation.
As an example, simulated images of a 3D standard (Fig. 1) are generated and transformed by a firstorder
linear calibration matrix. The three linear scale factors and three coupling factors in the
calibration matrix are random values acquired by the Monte Carlo method. The transformed images
are then evaluated by the to-be-validated algorithm. Comparing the evaluation results with the input
calibration matrix, the accuracy of the evaluation algorithm can be proved. This investigation also
indicates the influence of 3D standard type and imaging parameters, such as the scan range and pixel
number. It makes the calibration results from images with different parameters more comparable.
In the validation example, the linear scale factors Cx, Cy and Cz in the input first-order linear
calibration matrix vary between [0.99, 1.01], the coupling factor Cxy between [-0.01, 0.01], and Cxz
and Cyz between [-0.05, 0.05]. All the above factors vary with a uniform distribution. The mean
values ± standard deviation of the difference between the input and the evaluated results by the tobe-
validated algorithm are drawn in Fig.2. The difference ΔCx, ΔCy and ΔCxy are smaller than 10-4,
and ΔCz, ΔCxz and ΔCyz are smaller than 3 x 10-3. The evaluation error of Cz, Cxz and Cyz in the
simulation measurement of artifact MMC80 with 512 x 512 pixels is noticeably larger than the other
three simulation measurements |
