## 3 Results
The minimum value of the telephoto end (Table 2c) was 0.096 mm for 0.5 fields, and the maximum value was 0.297 mm for 1 field. For an infinite object point, the maximum value of the spot was 0.297 mm at the telephoto end, which was smaller than the sensor pixel size of 1 mm. Figure 12b,d,f show the diffraction MTF at infinite points. When the pixel size is 1 mm, the Nyquist frequency is 0.5 cycles/mm, which is close to the diffraction limit of 0.45 at that frequency. Figure 11: Distortion grid at an object distance of 6 m at (a) wide, (b) middle, and (c) tele ends. Figure 12: (**a**) Spot diagrams and (**b**) diffraction MTF at infinite object distance for the wide end, (**c**) spot diagrams and (**d**) diffraction MTF at infinite object distance for the middle end, and (**e**) spot diagrams and (**f**) diffraction MTF at infinite object distance for the telephoto end. Figure 13: (**a**) Spot diagrams and (**b**) diffraction MTF at an object distance of 3 m for the wide end, (**c**) spot diagrams and (**d**) diffraction MTF at an object distance of 3 m for the middle end, and (**e**) spot diagrams and (**f**) diffraction MTF at an object distance of 3 m for the telephoto end. Figure 14: (**a**) Spot diagrams and (**b**) diffraction MTF at an object distance of 6 m for the wide end, (**c**) spot diagrams and (**d**) diffraction MTF at an object distance of 6 m for the middle end, and (**e**) spot diagrams and (**f**) diffraction MTF at an object distance of 6 m for the telephoto end. Figure 13 shows the spot diagrams for each zoom at an object distance of 3 m. The minimum value of the wide-angle end (Table 3a) based on a defocusing of 0 was 0.063 mm at 0.3 field, and the maximum value was 1.90 mm in 1 field. The minimum value for the middle stage (Table 3b) was 0.041 mm in 1 field, and the maximum value was 0.197 mm in 1 field. Further, the minimum value of the telephone end (Table 3c) was 0.051 mm in 0.3 fields, and the maximum value was 0.326 mm in 1 field. For an object distance of 3 m, the maximum value of the spot was 0.326 mm at the telephone end, which was smaller than the sensor pixel size of 1 mm. Figure 13b,d,f show the diffraction MTF at 3 m. The performance is close to the diffraction limit of 0.45 at 0.5 cycles/mm. Figure 14 shows a spot diagram for each zoom at an object distance of 6 m. Based on a defocusing of 0, the minimum value of the wide-angle end (Table 4a) was 0.058 mm in 0.3 field, and the maximum value was 0.175 mm in 0.8 field. The minimum value of the middle stage (Table 4b) was 0.06 mm in 1 field, and the maximum value was 0.14 mm in 1 field. The minimum value of the telephone end (Table 4c) was 0.082 mm in 0.3 field, and the maximum value was 0.216 mm in 1 field. For an object distance of 6 m, the maximum value of the spot was 0.216 mm at the telephone end, which was smaller than the sensor pixel size of 1 mm. Figure 14b,d,f show the diffraction MTF at 6 m. The performance is close to the diffraction limit of 0.45 at 0.5 cycles/mm. By checking the spot diagrams in Figures 12-14, the spot root mean square (RMS) size was found to be smaller than the pixel size in all zooms, thereby satisfying the target performance. The aberration of the optical system was confirmed at the millimeter level using a spot diagram, and the performance was confirmed using light tools and optical  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Field Position** & **(a) RMS (mm)** & **(b) RMS (mm)** & **(c) RMS (mm)** \\ \hline
1 & 0.1546 & 0.1401 & 0.2161 \\ \hline
0.8 & 0.1746 & 0  
software (Synopsys Inc.). The designed optical system can show that the diffraction MTF performance values are close to the diffraction limit at all zooms. An analysis was conducted for object distances of 6 and 3 m. Six zooms were confirmed for the wide-angle, middle, and telephoto ends. The illuminated area resulting from the light-source arrangement was determined according to the magnification of the optical system. The equation for the optical system magnification is derived from the paraxial [PERSON]'s law in Equation (8).