## 2 Effect of Surface Force  
Surface forces mainly consist of van der Waals force, electrostatic force, and liquid bridge force. Van der Waals forces are interactions between molecules (or atoms) and are universal, always acting between objects. Liquid bridge force is an adhesion force caused by liquid bridging formed at a contact area. Force between the charged stylus tip and the measured surface is called electrostatic force [22]. When the charged stylus is brought close to the charged surface to be measured and the distance between the stylus tip and the measured surface becomes 10 \(\upmu\)m or below while using the stylus shaft and tips with diameters of 20 and 35 \(\upmu\)m, the stylus tip is attracted to the measured surface by the electrostatic force and may stick to it [21]. The adsorption distance decreases as the diameter of the stylus shaft increases. It is necessary to move the stylus approximately 60 \(\upmu\)m to pull it away from the measured surface due to liquid bridge force and electrostatic force once it is attached to the measured surface. In humid environments, once the stylus tip makes contact with the measured surface, large liquid bridge force acts between the stylus tip and the measured surface. A stylus shaft with a diameter of several tens of micrometers or more can easily pull the stylus tip away from the measured surface due to its high rigidity. However, when the diameter of stylus shaft is less than several tens of micrometers, the deflection of the stylus shaft is larger, and the stylus movement required to pull it away from the measured surface is larger. Surface forces acting on the stylus tip also decrease as the diameter of the stylus decreases. However, the decrease in stylus stiffness with decreasing diameter is greater than the decrease in surface forces; therefore, the stylus deflection (the distance \(\delta\) in Figure 1) increases with the decreasing stylus diameter, leading to increased measurement time and reduced measurement accuracy.  
In addition, once the stylus tip makes contact with the measured surface, it adheres to the measured surface and is difficult to separate. When measuring with the touch-trigger method, this adhesion increases the measurement time because the stuck tip must be pulled away. When measuring in scanning mode, the stylus shaft may deflect due to surface forces, which can worsen the measurement accuracy.  
The van der Waals force and liquid bridge force are sufficiently larger than the electrostatic force when the diameter of stylus tip is approximately 100 \(\upmu\)m or less [21]. However, the van der Waals force drops sharply when surface roughness exists on the contact surface. As an example, the van der Waals force for a surface roughness, RZ, of 100 nm is approximately 1/100 of that for a surface roughness, RZ, of 10 nm. Therefore, the liquid bridge force and electrostatic force are considered to have a large influence on the adhesion of the stylus tip to the measured surface. The effect of liquid bridge force is greater in humid environments, whereas the effect of electrostatic force is greater in low-humidity environments or in the case of measuring easily charged materials such as resins. First, we examine the possibility of reducing the liquid bridge force by applying a water-repellent coating to the stylus tip to reduce the adhesion of moisture from the air to the surface of stylus tip.