# Accurate Characterization of the Properties of the Rare-Earth-Doped Crystal for Laser Cooling
## 3 Experimental Set-Up
By calibrating the proportional relationship between pixel intensity and temperature, the change of the target temperature within the thermal image region can be inferred from the change of the pixel intensity. To measure the change in the sample temperature in real time, the thermal image of the sample is recorded for a sufficiently long time (30-50 min) while the ambient temperature is kept constant. In order to minimize the fluctuations, the pixel intensity values of the specified area, as shown by the red dash line box in the thermal image in Figure 3a, are summed and averaged. It is important to specify the temperature scale range of the thermal image, such as 288-302 K for our case here, and establish the mapping relationship between temperature and pixel intensity. The pixel intensity at the lowest temperature of 288 K is 0, and the pixel intensity at the highest temperature of 302 K is 255. The dependence relationship of the reference sample temperature in the copper clamp on the TEC current is affected by both the background pressure of the vacuum and the temperature of the CGTC, as shown in Figure 3b. To minimize the effect of background pressure, the CGTC is maintained in a high vacuum of ~10\({}^{-5}\) Pa during the whole process of the experiment. The pixel intensities of the thermal image of the reference sample (LuLiF\({}_{4}\) crystal) are measured with the temperature of the surrounding CGTC being 295 K and 293 K, respectively. The temperature scale range of the thermal image is chosen from 288 K to 302 K, as shown in Figure 3c. The black and red dots correspond to results for the cases of the CGTC temperature being 295 K and 293 K, respectively. Although the slopes of the two fitting lines are almost the same, the absolute pixel intensities of the reference sample are different for the same sample temperature. Therefore, the temperature of the surrounding CGTC should be kept constant during the whole process of the LITMoS test. Figure 3d shows the relationship between the measured pixel intensity variation \(\Delta\)pixel (\(\Delta\)pixel = P - P\({}_{R}\)) of the thermal image and the temperature variation \(\Delta T(\Delta T\ =\ T-T_{R})\) of the sample. Here, P\({}_{R}\) indicates the pixel intensity of the thermal image at the reference temperature of \(T_{R}\), which is the same as the surrounding CGTC temperature (295 K). The red dots correspond to the case with the temperature scale range of the thermal images being 288-302 K. The red solid line is a linear fit of the measured results. For \(\mid\Delta T\mid\leq 5\) K, the relationship between \(\Delta\)pixel and \(\Delta T\) is rather linear. As the value of \(\mid\Delta T\mid\) grows, the relationship deviates more from being linear. Therefore, the variation of the sample temperature \(\mid\Delta T\mid\) is kept at no more than 5 K in our LITMoS test. The slope of the linear fit, \(\Delta T/\Delta\)pixel, defines the calibration factor, which is 0.07736 for the case here and used for later determination of the sample temperature variation from the pixel intensity of the thermal image.