## 3 Experiment Results
### Measurement Accuracy and Repeatability Verification  
The purpose of this experiment was to check the measurement accuracy and stability of the measuring device. The selected depths of holes are from 3 mm to 30 mm with an interval of 1 mm and the diameters of these holes are all 6 mm. We selected 28 holes with different depths as measured objects. The feed speed of the probe was fixed at 4 mm/s, and the white pixel threshold was set to 100. Each hole with a certain standard depth was repeatedly measured 50 times; thus, a total of 50 sets of measurement data were obtained. Table 1 intercepts part of the measurement data in this experiment; five groups of actual measured value were randomly selected for each hole with standard depth.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Standard**} & \multicolumn{4}{c}{**Five sets of Actual Measured Value (mm)**} \\ \cline{2-6}  & **First** & **Second** & **Third** & **Fourth** & **Fifth** \\ \hline
3 & 3.03 & 3.08 & 2.98 & 2.93 & 2.90 \\
4 & 4.00 & 4.01 & 3.98 & 4.07 & 4.10 \\
5 & 5.01 & 5.10 & 5.06 & 5.03 & 5.07  
In order to analyse the measurement accuracy and stability of the device, Figure 9a gives the interpolated curves of average value and difference value under different standard depths, and Figure 9b shows the standard deviation under different standard depths in the repeatability experiment. As shown in Figure 9a, it can be seen from the curve average value that the measured results of this device can better fit the real value of hole depth, and its measuring structure is approximately a straight line. The average value of each node in the average value curve can be calculated by:  
\[\mu=\frac{\sum_{n=1}^{50}S_{n}}{50} \tag{4}\]  
The difference value curve in Figure 9a reveals the measurement error between the measured value and the true value under different standard depths. The horizontal axis is the standard depth of real hole, and the vertical axis is the error value. The error value fluctuates with the change of standard depth. The minimum error is 6 microns and the maximum error is 34 microns.  
To verify the repeatability of the designed device, Figure 9b shows the standard deviation curve of the repeatability experiment. Its horizontal axis is the standard depth of the measured hole, and its vertical axis is the standard deviation of 50 sets of actual measured data. The standard deviation at each standard depth can be calculated by the following formula:  
\[\delta=\sqrt{\frac{\sum_{n=1}^{50}(X_{n}-\mu)^{2}}{50}} \tag{5}\]  
According to Figure 9a, standard deviation fluctuates continuously with the change of the standard hole depth. Its maximum value is 0.073 mm and its minimum value is 0.038 mm. In order to further verify the reliability of the device and determine whether the deviation is systematic, we can calculate the standard error of mean using the following formula:  
\[\text{SE}=\frac{\text{S}}{\sqrt{\text{N}}}=\frac{0.073}{\sqrt{50}}=0.010\text { mm} \tag{6}\]  
where SE is the standard error of mean; S is the standard deviation; N is the number of measurements. The value of S = 0.073 mm is the maximum value of standard deviation, which is more able to explain the reliability of the device.  
Figure 9: Measurement accuracy and repeatability analysis: (**a**) the average value and difference values under different standard depths; (**b**) the standard deviation curve of the repeatability experiment.  
After the above calculation, the maximum value of standard error of mean was only 0.01 mm, judging by which the new approach and the device have high reliability. We will further explore ways to improve measurement repeatability in subsequent studies.