## 1 Introduction  
Optical topography sensors such as scanning confocal microscopes (SCM) [1] and coherence scanning interferometers (CSI) [2, 3] are well-established measuring instruments in industry and research for the contactless inspection of surface topographies with height structures in the micro- and nanometer range. However, these topography sensors are sensitive to external disturbances, which distort the corresponding controlled depth scanning procedure. Therefore, a close-to-machine employment is not possible with conventional SCM and CSI instruments. As a consequence, in industrial applications, samples are investigated by these optical sensors under highly controlled conditions on an anti-vibration table. One solution for full-field in situ measurements provides fast measuring methods such as single or dual shot approaches [4, 5, 6]. However, as the depth of field is required to cover the whole height range of the specimen, the lateral resolution and axial accuracy are usually worse compared to CSI, e.g., in case of the approach presented in [5] the lateral resolution is specified by \(30\,\mathrm{\SIUnitSymbolMicro m}\) for an NA of 0.28 and thus exceeds the Rayleigh resolution of the system. Another approach is given by the usage of an additional laser interferometer besides the main measuring system, the output of which is used to actively compensate for deflections caused by environmental vibrations [7, 8, 9, 10]. [PERSON] et al. [9] report a setup where vibrations are measured with respect to the measuring table of the specimen using a quadrature interferometer. The quadrature signal is used to move the entire CSI contrarily to the deflections caused by the vibration using a piezo driven stage. In contrast, [PERSON] et al. [10] present a CSI with a vibration compensation for in situ depth measurements in a deep reactive ion etcher. Besides the light of low temporal coherence used for CSI, a laser beam propagates through the Michelson interferometer in order to detect vibrations. The output of the laser interferometer is used in a closed-loop with a piezo element, which actively compensates for vibrations by moving the reference mirror. Besides these active vibration compensation techniques, passive approaches have also been demonstrated to be suitable for vibration compensation. The recorded interference signals may be postprocessed, as shown by [PERSON] [11] for a phase shifting interferometer, where a so-called phase-error pattern is used to remove deviations caused by vibrations. In order to reduce the effect of noise, [PERSON] et al. [12] correlate the measured interferogram with a nominal one. Another promising approach for passive vibration compensation in CSI is the use of an interferometric distance sensor (IDS) integrated in the optical path of the CSI setup. The changed distance between CSI and surface under investigation caused by a depth scan is measured by the IDS simultaneously to the CSI measurement. This also enables the detection of vibrations, which are represented by an additional change in path length between CSI and specimen. The interference signal obtained by the IDS provides distance measuring values at a high frequency. These are used to correct the CSI datasets subsequent to the measurement. This method is introduced by [PERSON] et al. and is utilized in a [PERSON] [13,14] as well as in a Linnik [15] interferometer setup. The working principle of the IDS is based on an optical path length modulation (OPLM) due to a sinusoidal oscillation of the used reference mirror. If this OPLM is fast enough, distance changes can be monitored with high temporal resolution. Depending on the oscillation frequency of the reference mirror, high measurement speeds of up to 116 kHz can be achieved [16]. This enables the detection of vibrations comprising ultrasonic frequencies. An early report of this approach is given by [PERSON] and [PERSON] [17]. The method is also used in several sensor constellations, which are adapt to other areas of application as reported in [16,18,19,20,21,22].