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Table 1. Results of the repeated specimen positioning measurements for the four tested specimens.
Specimen r z / nm r x / lm r y / lm Dz 95 %( x, y)/ nm
Asphere |
27.058 |
0.807 |
1.534 |
0.581 |
Sphere with radius 15 mm |
20.674 |
0.774 |
2.633 |
0.162 |
Sphere with radius 40 mm |
16.230 |
5.221 |
34.329 |
5.911 |
Toroid |
25.837 |
5.124 |
2.705 |
1.242 |
Figure 10. Repeated positioning of the test specimen along lateral axes( x and y) in the plane of the Cat’ s Eye reference with mean value subtracted:( a) asphere,( b) sphere with radius 15 mm,( c) sphere with radius 40 mm, and( d) toroid.
measured deviations from the mean are used together with the design topography of the measured specimens. The point-wise axial offsets are calculated and ordered by magnitude. The highest offset of 95 % of the data points( Dz 95 %( x, y)) is used as an estimate of the axial error due to lateral misalignment. For all but the sphere with radius 40 mm, the expected axial error Dz 95 % due to the lateral alignment is small against the axial error due to the axial adjustment r z. Using the design, one can estimate a maximum axial displacement due to the lateral displacement of about 4 nm. This error appears reasonably low. Nevertheless, these effects will be further minimized by the alignment correction, including both lateral specimen position and specimen tilt, in measurement position( which is much more sensitive to alignment errors), and respective repositioning of the Cat’ s Eye. These next steps will be investigated in more detail in future work. It has to be further noted that the lateral displacement and the tilt of the specimen are parameters that are estimated during the surface reconstruction. This makes the measurement to a certain extent robust against alignment errors of these parameters.
In order to estimate the influence of the axial deviation of the specimen position from the Cat’ s Eye position on the final form reconstruction, a virtual experiment was carried out: The maximum standard deviation of the axial position deviation of a specimen is estimated to r z 31 nm( 27 nm for direct z-repeatability, compare Table 1, and4 nm forthe influence of the lateral misalignment). In a virtual experiment, the asphere was used as a test specimen and an axial misalignment of the specimen of twice the estimated standard deviation was used to simulate the measurement data. After form reconstruction from these simulated data, this results in a surface form reconstruction error of 4.5 nm RMS.
4 Conclusion
Surface alignment plays an important role in interferometric form measurement and misalignment can lead to measurement errors that are not obvious by the measurement results themselves. In tilted-wave interferometry, the form