## 5 Conclusions and Outlook  
In this contribution, a CSI comprising a Mirau objective is introduced, where a custom-built interference device is attached to a commercial microscope objective. An oscillating reference mirror inside the Mirau objective's attachment enables the IDS measuring process in parallel to the conventional CSI depth scan. Thus, the changed distance between CSI and surface under investigation including influences caused by external vibrations are measurable by the IDS. This enables a correction of the disturbance as shown for a sinusoidal standard. Due to its advantages, the Mirau setup is the preferred and most frequently used interferometer type in industry. Thus, to the best of the authors knowledge, this is a novel combination, enabling the industrial application of the previously developed method for vibration compensation. Furthermore, the proper optical functioning of the  
Figure 10: Measured IDS signal of a depth scan of \(10\,\mathrm{\SIUnitSymbolMicro m}\) disturbed by a sinusoidal oscillation. Figure 9: Measured sinusoidal standard with \(1\,\mathrm{\SIUnitSymbolMicro m}\) peak-to-valley amplitude and \(100\,\mathrm{\SIUnitSymbolMicro m}\) period length. (**a**) Topographies obtained without disturbances on a vibration-damping table, (**b**) disturbed by a sinusoidal vibration with an amplitude of \(200\,\mathrm{nm}\) and an oscillation frequency of \(8\,\mathrm{Hz}\), (**c**) same topography as shown in panel (**b**) but corrected according to the described compensation method, (**d–f**) the corresponding profiles marked by the blue dashed line in the (**a–c**) surface topographies. custom-built Mirau objective is investigated by comparative measurements on various surface structures using different LEDs and reference instrumentation such as a tactile stylus instrument and a 10x Mirau objective lens from Nikon Inc. The measured surface structure of the superfine roughness standard and the gratings of the RSM standard are well resolved as expected for a CSI with an NA of 0.28. A comparison between interference signals obtained by the custom-built Mirau objective using different LEDs of different spectral bandwidth reveals that interference signals obtained for a white LED illumination suffer from dispersion. Moreover, low systematic deviations in the range of \(\pm\)10 nm occur, which are basically independent from the dispersion effect. Since these systematic deviations are reproducible, it can be eliminated from the measured surface structure after calibration. These deviations and disturbances might be a result of misalignment in the custom-built objective. In further investigations, the alignment of the optical elements will be measured in a custom-built interferometric setup. In this work, a disturbance affecting the interference signals of each camera pixel in the same way is assumed. However, the influence of external vibrations might be different across the surface to be measured. Therefore, multiple IDS can be applied to measure vibrations on laterally shifted locations on the surface under investigation. This is part of future developments. The laser beam of the IDS is currently tilted to be able to pass the reference mirror of the Mirau objective. Consequently, a decreased intensity of the reflected laser light occurs with increasing surface slope. This can probably be optimized using critical illumination for the IDS. Conceptualization, H.S. ; investigation, H.S. methodology, H.S. ; software, P.G. ; validation, H.S., P.G. and S.H. ; formal analysis, H.S. and S.H. writing--original draft preparation, H.S. ; writing--review and editing, H.S., P.G., S.H. and P.L. ; supervision, P.L. ; funding acquisition, P.L. All authors have read and agreed to the published version of the manuscript. The support of this project under the WIPANO program (grant number 03 THW10K24) by the German Ministry of Economy and Energy is gratefully acknowledged. Not applicable. The data presented in this study are available on request from the corresponding author.