## 3 Comparison and Simulation Results  
The traditional zoom lens structure is based on a front group with a fixed structure, zoom group, back group with a fixed structure, and compensated group. Using a liquid lens as a compensating lens enables complex optical systems to be improved easily, because the focal length of liquid lenses can be varied by adjusting the applied voltage, and, thus, zoom systems featuring various focal lengths and zoom ratios can be developed. The liquid lens parameters after CODE V optimization are listed in Table 6. Two-dimensional plots of the optimized structure of the proposed lens are shown in Figure 9. Figures 10 and 11 respectively show the MTFs and spot plots of the proposed lens.  
Comparing conventional intermediate optics design of Figure 5 with proposed compensating lens scheme of Figure 10, the average MTF curves are superior than conventional intermediate optics design, hence the better image performance can be obtained. Besides, the third aberrations in the proposed zoom structure are also improved of smaller spot size as shown in Figures 6 and 11.  
\begin{table}
\begin{tabular}{c c c} \hline
**Wavelength (mm)** & **PC100 (Liquid A)** & **H100 (Liquid B)** \\ \hline
400 & 1.41178 & 1.51297 \\
448 & 1.40729 & 1.50340 \\
489 & 1.40451 & 1.49772 \\
541 & 1.40180 & 1.49250 \\
589.3 & 1.39988 & 1.48894 \\
654.6 & 1.39791 & 1.48535 \\
703 & 1.39671 & 1.48332 \\ \hline \end{tabular}
\end{table}
Table 5: Liquid index at 20 \({}^{\circ}\)C.  
Figure 9: Two-dimensional plots of the optimized design: (**a**) Zoom 1; (**b**) Zoom 2; (**c**) Zoom 3; (**d**) Zoom 4; (**e**) Zoom 5; (**f**) Zoom 6.  
Figure 10: MTFs of the proposed lens: (**a**) Zoom 1; (**b**) Zoom 2; (**c**) Zoom 3; (**d**) Zoom 4; (**e**) Zoom 5; (**f**) Zoom 6.  
Figure 11: Spot plots of the proposed lens: (**a**) Zoom 1; (**b**) Zoom 2; (**c**) Zoom 3; (**d**) Zoom 4; (**e**) Zoom 5; (**f**) Zoom 6.  
In general, optical design with a liquid lens element is difficult to optimize, mainly because of the extreme spherical aberration, coma aberration and the axial chromatic aberrations. These severe axial aberrations are generated mainly from oblique incident rays close to the liquid lens element. In the study, first, we demonstrate a methodology for the optical design of intermediate zoom optics, which may not only mitigate some aberration problems but also further reduce the volumetric size of the 9\(\times\) zoom system. Second, in this newly developed design, the liquid lens technology used as compensating lens to reduce the error of effective focal length and several aberrations especially on TCO, LAT and PTZ, thanks to the assistance of a new design methodology for liquid lens elements in particular.  
The simulation results revealed that the performance of the proposed lens design is superior to the standard 9\(\times\) zoom lens design; the zoom ratios are listed in Table 6, and an MTF comparison is in 40 1p/mm. In Table 7, we can find the average performance of TCO, LAT, PTZ and MTF are also improved in the proposed compensating liquid lens technology, but got the worse performance in SA. This is because the optical design is a tradeoff between all aberrations.