## 5 Experiments and Discussion  
A group of experiments were carried out to investigate the capacity of the designed MLDI. Figure 7 shows the experimental setup. The size of the MLDI, including the electric cables and the base plate for mounting the optical components, is 110 mm (x) \(\times\) 100 mm (y) \(\times\) 20 mm (z), which is much smaller than commercial He-Ne laser interferometers, such as LDDM (Optodyne, Rancho Dominguez, CA, USA), which is shown in Figure 7.  
Prior to using the designed MLDI to measure the displacement of a linear stage, the effectiveness of the proposed active wavelength stabilization method was first investigated. As mentioned, before the LD wavelength control, the surface temperature of the LD should be effectively controlled within a commanded range, in which the FWHM is the smallest. The smaller the FWHM, the better the stability of the LD wavelength. Therefore, the FWHM at various temperatures was detected three times by the LWM with the particular temperate stabilized for 10 min, as shown in Figure 8. It can be seen from Figure 8 that when the temperature is set to be 18 \({}^{\circ}\)C and 29 \({}^{\circ}\)C, the corresponding FWHMs are the smallest. Figure 7: Experimental setup. The X- and Y-directional outputs of QPD1 and QPD2 of the LWM, from which the LD wavelength can be evaluated, were then monitored when the temperature of the LD holder was set to be 18 \({}^{\circ}\)C and 29 \({}^{\circ}\)C, respectively. The outputs of QPD1 and QPD2 are shown in Figure 9. It can be seen that when the temperature was set to be 18 \({}^{\circ}\)C, the stability of QPD1 and QPD2 is better than that when the temperature was set to be 29 \({}^{\circ}\)C. Therefore, 18 \({}^{\circ}\)C was selected to be the desired temperature of the active wavelength stabilization method. The accuracy of the LWM will affect the control accuracy of the active wavelength stabilizer and the measurement accuracy of the displacement. Therefore, the accuracy of the LWM was then tested by using a commercial spectrometer (CCS100, ThorLabs, Newton, NJ, USA) which has a wavelength response range from 350 nm to 750 nm and a measurement accuracy of less than 0.5 nm. The measured wavelengths by using the LWM and the commercial spectrometer are shown in Figure 10. The temperature of the LD holder was set around 18 \({}^{\circ}\)C. It can be seen from the figure that the residual between the LD wavelength measured by the LWM and that measured by the spectrograph was less than 4 pm, on the basis of which the effectiveness of the LWM was verified. Figure 8: Full width at half maximum (FWHM) under various temperatures. Figure 10: Wavelength measured by the LWM and the spectrometer under various temperatures. The stability of the LD wavelength was then controlled based on the active wavelength stabilization method proposed in this research and the passive wavelength stabilization method proposed in our previous research [6]. Figure 11a shows the results. It can be seen from the figure that the stability of the LD wavelength was improved from 7.96 \(\times\) 10\({}^{-6}\) to 5.95 \(\times\) 10\({}^{-7}\) by using the active wavelength stabilization method rather than the passive wavelength stabilization method. The Allan deviation of the stability of the LD wavelength is shown in Figure 11b. The short-term stability of the LD wavelength was improved to be 10\({}^{-7}\) from 10\({}^{-6}\), and a long-term stability of the LD wavelength of 10\({}^{-8}\) can be achieved. Finally, the measurement accuracy of the MALDI was investigated by a group of comparison experiments. The displacement of a linear stage with a stroke of 100 mm was simultaneously measured by the designed MALDI and a commercial interferometer (LMMD, Optodyne, CA, USA) with a measurement accuracy of \(\pm\)0.5 ppm and a measurement range of 15 m. Figure 12 shows the experimental results with five times.