## 2 Measurement Principle  
Figure 2 shows a diagram of the developed optical measurement system. The stylus consists of a 2.5-\(\upmu\)m-diameter optical fiber to which a 5-\(\upmu\)m-diameter glass stylus tip is attached. The total length of the stylus is 0.38 mm. The probing system consists of the fiber stylus, two laser diodes with a 650 nm wavelength (LDX and LDY in the \(X\)- and \(Y\)-directions, respectively), and two dual-element photodiodes (PX and PY in the \(X\)- and \(Y\)-directions, respectively). The stylus shaft is fixed to a tube-type piezo driver element in order to perform attitude adjustment of the stylus shaft; the stylus shaft is installed between the laser diodes and the dual-element photodiodes, which are oriented orthogonally. The laser diodes are mounted above the stylus tip, and the focused laser beams irradiate along the \(X\)- and \(Y\)-directions onto the stylus shaft. The two dual-element photodiodes are located opposite the laser diodes beyond the stylus. The laser beams that pass through the stylus shaft are received by these dual-element photodiodes. The beam intensities detected by the photodiodes are converted into voltages; hereafter, these intensities are denoted as \(I_{\text{PX1}}\), \(I_{\text{PX2}}\), \(I_{\text{PY1}}\), and \(I_{\text{PY2}}\) (V). The output signal \(I_{\text{X}}\) in the \(X\)-direction obtained using \(I_{\text{PY1}}\) and \(I_{\text{PY2}}\) and the output signal \(I_{\text{Y}}\) in the \(Y\)-direction obtained using \(I_{\text{PY1}}\) and \(I_{\text{PY2}}\) are defined as given in Equations (1) and (2), respectively. A charge-coupled device is employed to monitor the positions of the stylus and test piece during the setting up of the equipment and the measurement. \[I_{\text{X}} = I_{\text{PY1}}\ - I_{\text{PY2}} \tag{1}\] \[I_{\text{Y}} = I_{\text{PX1}}\ - I_{\text{PY2}} \tag{2}\]  
To illustrate the measurement principle of the optical fiber probe, Figure 3 shows a cross-sectional diagram of the \(X\)-\(Y\) plane of the optical system shown in Figure 2. Before the stylus tip comes into contact with the measured surface, the light intensities measured by each element of the dual-element photodiode are equal (_i.e._, \(I_{\text{PX1}}\) = \(I_{\text{PY2}}\) and \(I_{\text{PY1}}\) = \(I_{\text{PY2}}\)), as shown in Figure 3a. When the stylus tip comes into contact with the measured surface in the \(X\)-direction, the laser-irradiated part of the stylus shaft is displaced, and the light intensities measured by each element of the dual-element photodiode are no longer equal to each other (_i.e._, \(I_{\text{PY1}}\) = \(I_{\text{PY2}}\) and \(I_{\text{PY1}}\) = \(I_{\text{PY2}}\)), as shown in Figure 3b. When the stylus shaft is displaced in the \(+X\)-direction, the angle of refraction of the laser beam passing through the stylus shaft in the \(Y\)-direction changes owing to a shift in the part of the stylus shaft being irradiated. Additionally, when the stylus tip comes into contact with the measured surface in the \(Y\)-direction, the light intensities measured by each element of the dual-element photodiode are no longer equal to each other (_i.e._, \(I_{\text{PY1}}\) < \(I_{\text{PY2}}\) and \(I_{\text{PY1}}\) = \(I_{\text{PY2}}\)), as shown in Figure 3c. As a result, the contact direction and  
Figure 2: Measurement system using optical fiber probe. the magnitude of displacement of the stylus tip can be obtained from the output signals \(I_{\mathrm{X}}\) and \(I_{\mathrm{Y}}\). When the stylus tip comes into contact with the measured surface in the \(Z\)-direction, the stylus shaft is buckled and deflected. This deflection is also measured using the above-mentioned method. Because the proposed probe measures the deflection amplitude of the stylus shaft by using a laser-based non-contact method, the stylus shaft does not need to be rigid; this principle also applies to a stylus with a much smaller diameter. This measurement system measures the deflection of the stylus shaft; however, it does not directly measure the displacement of the stylus tip.