## 4 Results and Discussion
### Functioning of the Mirau Configuration
The standard deviation is reduced to 0.995 nm for a subtraction of the two topographies from each other and a predominantly uniform shape occurs. Consequently, deviations in flatness of the Mirau CSI are not mainly caused by dispersion and can be attributed to other influences such as flatness deviations or contaminations of the reference mirror or other system-related wavefront errors. The residual flatness can be used for the calibration of the system by pixel-wise subtracting the residual flatness from each performed topography measurement. An application is shown in Figure 6c, where an additional measurement of the aluminum mirror is calibrated by subtracting the residual flatness shown in Figure 6a from the measured topography. As depicted in the Figure 6c a nearly uniform topography occurs with a standard deviation of \(\sigma_{corr}=0.62\,\text{nm}\). Consequently, subtracting the residual flatness is a suitable approach for correcting the measured topography data. Therefore, this correction approach is considered in all following results in order to reduce systematic errors of the measured surface topographies. Figure 5: Interference signals obtained from an aluminum mirror using the custom-built (**a**,**c**) as well as the commercial Mirau objective (**b**,**d**). In addition, a resolution standard (type RS-M from Simetrics GmbH) comprising several gratings of period lengths from 4 \(\upmu\)m to 800 \(\upmu\)m with a nominal step height of 90 nm is used [37]. The results are shown in Figure 7.  
The gratings with a period length of 40 \(\upmu\)m and 20 \(\upmu\)m (blue profile) are well resolved with minor measurement deviations apart from rounded edges. The step height determined following the procedure described in DIN EN ISO 5436-1 is 85.9 nm for the 40 \(\upmu\)m and 81.5 nm for the 20 \(\upmu\)m structure. In the red profile an asymmetric constriction is observable for the grating of \(\Lambda=8\,\upmu\)m leading to a measured step height of 50.3 nm. This asymmetry occurs due to a sharp-combed structure, where the width of the upper plateaus are smaller than those of the lower plateaus [37]. Consequently, a low pass filtering due to the NA of 0.28 for the MA setup has a stronger effect on the upper plateaus compared to the lower ones. According to the Rayleigh criterion, the lateral resolution of the Mirau objective is 1.36 \(\upmu\)m for an evaluation wavelength of 625 nm and an NA of 0.28. Therefore, the smallest grid with a period length of 4 \(\upmu\)m (green profile) is still well resolved as expected. However, the step height for the 4 \(\upmu\)m grating is clearly decreased to 18.3 nm. Obviously, the low-pass filtering effect is strongest for the 4 \(\upmu\)m structure. In addition, an asymmetric constriction similar to the grating of \(\Lambda=8\,\upmu\)m appears, which is again a result of a sharp-combed structure. Figure 6: Residual flatness obtained by averaging nine slightly shifted measured topography data sets (**a**) acquired with a white and (**b**) with red light illumination and (**c**) corrected topography of an additionally measured mirror surface by subtracting the residual flatness. Figure 7: Profiles of RS-M standard obtained by 20x Mirau with different grating periods \(\Lambda\) of 40 \(\upmu\)m and 20 \(\upmu\)m (blue curve), 20 \(\upmu\)m and 8 \(\upmu\)m (red curve) and 8 \(\upmu\)m and 4 \(\upmu\)m (green curve). In an industrial context, rough surfaces often are encountered in topography measurement applications. For this reason, roughness standards are frequently used for the realistic characterization of a measuring system. Accordingly, the system is also characterized using the superfine roughness standard KNT4070/03 by Halle GmbH [38]. According to DIN EN ISO 4288, the roughness parameters \(R_{a}\), \(R_{q}\), and \(R_{z}\) are convenient to characterize surface roughness.