# Improved Design of Imaging System for Online Detection of Large-Sized Step-Shaft Runout Errors
## 3 Experimental Validation of Runout Detection Optical System  
In this section, a test platform is built for the runout detection optical system designed above in order to measure the stepped shaft with a diameter of 65-750 mm, and the block diagram of the test platform is shown in Figure 11. The optical power meter evaluates the output power of the laser beam received by the PSD, and the evaluation results show that the laser emitted from the semiconductor laser emitter reaches the level of about 50% of the light energy remaining on the PSD, and the optical power required is at 10 mW or more, and the adopted ML10124P semiconductor laser transmitter (Mitsubishi Group, Shanghai, China) is 100 mW, which meets the requirements. The position of the imaging spot in the receiving area of the PSD was captured using image capture, the captured data were fitted using a computer, and the test platform is shown in Figure 12. The test platform mainly consists of a semiconductor laser transmitter, a beam-expanding collimating optical system, an imaging optical system, a PSD, a base, and a computer. Regarding these components, the parameters of the expanded beam \begin{table}
\begin{tabular}{c c} \hline \hline
**Geometric Mean MTF** & **Result** \\ \hline
90\%\(\geq\) & 0.33013253 \\
80\%\(\geq\) & 0.36453406 \\
50\%\(\geq\) & 0.43950725 \\
20\%\(\geq\) & 0.52218292 \\
10\%\(\geq\) & 0.54527571 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Monte Carlo analysis results. Figure 11: Block diagram of runout detection optical system. collimation optical system are as follows: \(f\) = 7 mm, the numerical aperture NA of the object square is 0.15, and the total length of the system is 20 mm. It can be seen from Equation (6) that y and y\({}^{\prime}\) have a linear relationship, i.e., when the object under testing moves along the incident light, the imaging spot received on the PSD is a straight line. The measured step axis of the reference surface is a reference for up and down movement, the imaging optical system in the PSD forms the image point, the step-axis displacement is recorded as x, the image point position is recorded as y, and the test results are shown in Figure 13. The displacement is positive for the step-axis upward jump, and negative for the downward jump. From the fitting curve, it can be seen that the primary coefficient of 2.3091 is close to the magnification of 2.33 shown by the beating-detection imaging system, indicating that the output of the PSD has a good linear relationship with the input. When using the runout detection optical system to measure the step shafts, KEYENCE laser displacement sensors were used to detect the radial runout and end-face runout of stepped-shaft standards, with diameters ranging from 65 mm to 750 mm. Five cross  
Figure 12: Jump detection test bench diagram. Figure 13: Fitting curve of test results. sectional positions were selected for end-face runout detection, and the diameter of 750 mm was selected for radial runout detection, with the measured values of the KEYENCE displacement sensor (KEYENCE, Shanghai, China) used as the true value. Among these values, the repeatability of KEYENCE radial runout error measurement was 10 \(\upmu\)m; the repeatability of the radial runout error measurement of the runout detection system designed in this paper was 10 \(\upmu\)m. Then, we used the stepped-axis motion control to adjust the tilt angle of the stepped-axis to 5\({}^{\circ}\) to carry out the measurement of the end-face runout, and the runout error derived from this is shown in Figure 14.  
The results of the end-face runout measurement show that, when the measured stepped shaft is not tilted, the runout detection optical system designed in this paper has a similar measurement accuracy to the KEYENCE displacement sensor, being just 0.01 mm lower.