## 2 Sensor Configuration  
The proposed sensor setup is based on a Mirau CSI. The temporally low coherent light emitted by an LED and the coherent infrared laser beam with a wavelength of 850 nm emitted by a diode laser are combined by a cold light reflector as shown in Figure 1a to share a common optical path. The laser beam is collimated, whereas the light from the LEDis focused via a condenser lens to the pupil plane of the microscope objective (MO) in order to realize a Kohler illumination. This leads to a collimated illumination of the surface, where each illuminated point in the pupil plane acts a secondary point source. The light reflected from the surface of the reference mirror as well as the scattered light from the sample are superimposed by a beam splitter plate and is then collected by the infinity corrected MO. The resulting interference pattern is then detected in the image plane by the CCD camera. The infrared light is separated from the temporally low coherent light by an IR-cut filter and recorded by a photodiode. Introducing a sinusoidal modulation of the optical path difference (OPD) by an oscillating reference mirror, the laser interferometer works as an IDS [14; 16]. Both CSI and IDS work simultaneously and share the oscillating reference mirror. In order to reduce blurring of the captured camera frames, camera and LED triggering are synchronized  
Figure 1: Schematic illustration (**a**) and photograph (**b**) of the Mirau CSI with a custom-built Mirau attachment comprising the oscillatable reference mirror in front of a commercial MO. with the mirror deflection, so that the camera frame is captured at the turning points of the oscillating reference mirror, where its motion speed is close to zero (visualized in the following Section by a trigger impulse shown in Figure 3). The control of the measurement process is provided by the control-box which is explained in more detail in [13; 24]. As a consequence, a stroboscopic illumination is required to perform the measurement procedure. Short pulses of approximately 5-10 \(\upmu\)s with overvoltage and overcurrent are generated by the LED to illuminate the surfaces of specimen and reference mirror with enough light. The IR-laser source is tilted relatively to the optical axis to be not blocked by the reference mirror located in the center of the optical axis. The interference signal obtained by the superimposed partial laser beams, which are reflected from the reference mirror and the surface to be measured, is detected by a photodiode. Only a small portion of the NA is used to focus and detect the laser spot by the MO. The practical realization of the sensor setup is depicted in Figure 1b. As mentioned before, a MA is developed to realize a Mirau type setup with oscillating reference mirror for the IDS. Figure 2 shows a detailed photograph of the MA. It consists of three parts: the main body, an adjustment head and a clamping ring. In order to avoid dependencies on the manufacturing tolerances, the beam splitter plate is adjustably mounted to balance the interferometer arms. Therefore, the adjustment head including the plate beam splitter and the compensation plate is connected to the main body by a fine-thread, which has a pitch of 0.5 mm according to DIN 13-3. Further, a cover glass thickness compensated MO of Mitutoyo (G Plan Apo) with a magnification of 20\(\times\) is used [25]. This MO provides a long working distance of 30.6 mm (while using a 3.5 mm thick cover glass) and an NA of 0.28. These properties enable an integration of the beam splitter plate and a compensation plate inside the MA avoiding any additional optical aberrations. In order to reduce dispersion, these two components have identical design parameters related to refractive index, geometrical dimensions, and surface quality. Therefore, these glasses are fabricated meeting high requirements. Both components are made of the same glass type (H-K9L) with a refractive index of \(n_{\mathrm{d}}=1.51680\) manufactured by CDGM [26].