## 3 Reduction in Liquid Bridge Force by Applying a Water-Repellent Coating to the Stylus Tip  
When moisture is present on the stylus tip or the measured surface, liquid bridges are formed between the contacting surfaces at the moment of contact. This liquid bridge generates a liquid bridge force when the stylus tip is pulled away from the measured surface. One possible method to reduce the liquid bridge force is to create a vacuum or low humidity in the measurement environment to prevent water from adhering to the stylus tip [21]; however, it is difficult to create such an environment at the actual measurement site. Therefore, a water-repellent coating was investigated to change the contact angle with the liquid as a method to reduce the influence of liquid bridge force.  
This fluoropolymer coating (Fluoro Technology Co., Ltd., Japan, Fluoro Surf FG-5084) shown in Figure 2a reduces the adhesion of water by forming a fluorinated resin layer on the surface. Fluorine-based coatings were selected because of their higher water repellency and durability compared with silicone-based coatings [23]. Figure 2b shows a photograph of a drop of water observed from the horizontal direction on a glass substrate with the fluororesin coating. From this photograph, the contact angle with the fluororesin coating can be determined as 105\({}^{\circ}\).  
To evaluate the performance of a stylus coated with a water-repellent coating, the performance test was conducted using styluses with and without the fluororesin coating (tip diameter 35 \(\upmu\)m, shaft diameter 20 \(\upmu\)m, shaft length 2 mm). The stylus was dipped into the coating solution and then dried in a furnace at 80 \({}^{\circ}\)C for 60 min to form a fluorinated resin layer. As shown in Figure 3a,b, the stylus was moved at a pitch of 100 nm by the fine movement positioning XYZ piezo stage (P-562.3 CD, Physik Instrument) [16] away from the measured surface in contact with the stylus tip. The closed-loop resolution of the stage travel was 1 nm, and repeatability in the X-, Y-, and \(Z\)-directions was 2.2, 2.2 and 4 nm, respectively. A capacitive displacement sensor was integrated into the stage. The experiment was conducted in a chamber controlled at 20 \(\pm\) 0.1 \({}^{\circ}\)C.  
When the stylus is moved further, the stylus tip separates from the measured surface at a certain distance, \(D_{\text{S}}\) (Figure 3c). The distance, \(D_{\text{S}}\), was measured 10 times repeatedly. To eliminate the effect of static electricity, the stylus and the measured surface were ionized with an ionizer before the experiment.  
The film thickness of a fluorinated resin layer was estimated to be 10-20 nm from the specifications in the manufacturer's catalog. The film thickness was assumed to have no effect on the stylus dimension and measurement accuracy because its thickness was below the resolution of this measurement system. The relative humidity during the measurement was 27%. The average separation distances for styluses with and without the fluororesin coating are shown in Figure 4. The results show that the average separation distance without a coating is 61.2 \(\upmu\)m and with a fluororesin coating it is 13.8 \(\upmu\)m, indicating that the fluororesin-coated stylus reduces the separation distance by approximately 78%. These results confirm that the liquid bridge force is reduced by improving water repellency of the stylus tip. This is thought to be due to a decrease in capillary condensation between  
Figure 2: Coating composition and contact angle of the droplet.  
the stylus tip and the measured surface by changing the stylus surface from hydrophilic to hydrophobic.