# Design of an Internal Focusing Tube Lens for Optical Inspection Systems
## 4 Conclusions  
In recent years, inspection optical systems have required an increasingly high resolution owing to the growth of the semiconductor market. To increase the resolution, a method of increasing the NA of the objective lens was considered. However, as the objective lens's NA increases, the depth of focus decreases. To focus within the shortened depth of focus, the entire optical lens group has to be moved to maintain the resolution. As the size and weight of the lens-holding mechanism increase, so do the focusing time and the problems with inertial control and accuracy. However, to achieve a high resolution, the inspection optical system must be large and heavy, reducing the focusing speed and necessitating significant energy in the driving device to increase the speed. To compensate for this, an internal focusing method was used rather than moving the entire optical system. A lens group for focusing was placed within the tube lens to \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sample Height (mm)** & **(a) Distortion (\%)** & **(b) Distortion (\%)** & **(c) Distortion (\%)** \\ \hline
3.500 & \(-\)0.0192 & \(-\)0.0421 & 0.0041 \\
3.400 & \(-\)0.0132 & \(-\)0.0346 & 0.0085 \\
2.720 & 0.0094 & \(-\)0.0035 & 0.0224 \\
1.190 & 0.0125 & 0.0056 & 0.0195 \\
0.340 & 0.0062 & 0.0039 & 0.0085 \\
0.000 & 0.0000 & 0.0000 & 0.0000 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Distortion of the 5\(\times\) optical system. Figure 12: Distortion aberration diagram of the 5\(\times\) optical system when the sample moves (**a**) \(-\)0.36 mm from the reference point, (**b**) when the sample is located at the reference point, and (**c**) when the sample moves +0.36 mm. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sample Height (mm)** & **(a) RMS (mm)** & **(b) RMS (mm)** & **(c) RMS (mm)** \\ \hline
3.500 & 0.00866 & 0.00708 & 0.00645 \\
3.400 & 0.00900 & 0.00722 & 0.00621 \\
2.720 & 0.00973 & 0.00775 & 0.00618 \\
1.190 & 0.00966 & 0.00705 & 0.00602 \\
0.340 & 0.00920 & 0.00657 & 0.00596 \\
0.000 & 0.00819 & 0.00674 & 0.00593 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Image RMS data of the 5\(\times\) optical system. widen its focus adjustment range. Thus, even when the sample's position is changed, the internal focusing group moves to form an image on the image pickup device. However, when using this focusing method, the magnification may change depending on the object distance and optical system data change. Therefore, the optical system was designed as a telecentric collimator system in combination with objective and tube lenses. Using this setup, we confirmed that the magnification remained constant when the focus was adjusted based on sample movement. In addition, a resolution analysis and performance evaluation were conducted using spot diagrams. As listed in Tables 1 and 3, we confirmed that the spot size was similar to that of an airy disk. This design ensured that the distortion was offset when the objective and tube lenses were combined. This is because there should be no distortion aberration, owing to the characteristics of the optical inspection system. As listed in Tables 2 and 4, the distortion aberration values were close to zero. The optical system's resolution was set to be lower than that of the airy disk of 13.29 \(\upmu\)m.  
In the optical system, the weights of the objective lenses with focal lengths of 30 and 60 mm were calculated to be approximately 844 and 570 g, respectively, and the focusing group of the tube lens weighed approximately 22 g. These values confirm that the weight of the moving group can be significantly reduced, thereby reducing the inertial control by the weight of the focusing lens or the size of the actuator. The internal focus control method allows for faster and more accurate inspections than the current inspection optical system, which adjusts the entire optical lens group for focus. Therefore, we expect that the overall length of the optical system can be fixed, and the inspection device can be miniaturized.