## 4 Methodology: Optical Design of the Prime System
### Design and Verification of the Underwater Optical Camera
So far, there is no similar software or digital signal processing to overcome this kind of \"ocean aberration\" but minimization of chromatic aberration might be successful in minimizing such types of time-domain aberrations; similar optical software is used in the air in order to overcome air turbulence. In this section, we propose an extended optimization method via genetic algorithm specific for chromatic aberration applied to photogrammetry. This extended optimization method will efficiently eliminate the chromatic aberration although it might be not of help in improving MTF. The optical design of zoom lenses for underwater is different from that of prime lenses. First, changes in light spectra increase the chromatic aberration and focus-point displacement for zoom lenses compared with prime lenses. The various optical aberrations generated by zoom magnification are difficult to control. Second, zoom lenses generally have lower resolving power than prime lenses and produce more complex optical aberrations with changes in magnification [17]. Therefore, designing a zoom lens with a  
Figure 23: Flowchart of the genetic algorithm calculation. high resolving power for underwater photography and the ability to adjust with changes in water depth is difficult. In accordance with Polaris specifications, we developed a zoom lens with three times zoom ratio. The specifications are listed in Table 6. The half-angles of view and their weight ratios are listed in Table 7. All optical layouts are demonstrated on Figure 24 optimized by Zemax with genetic algorism. Its MTF performance is illuminated by Figures 25-27 according to difference zoom ratio 5 mm, 10 mm, and 15 mm. Zoom optics has its inherent difficulties in optical performance compared to prime lenses especially in astigmatism, distortion, and MTF performance. In this case, fixed overall length complicates optical design and optimization so that its performance is not as good as fixed focal optics. There are some alternatives to improve the performance of zoom optics although their performance is not equivalent to optics with fixed focal length. Generally speaking, one is the employment of very-high-index optical glass and another is employment of more optical elements. Unfortunately, both methods are not feasible in this specification from Polaris as optical glass with high index might have poor physical and chemical characteristics so that it is not a good choice for optics under water and employment of more optical glass will make optics longer than expected, which is also not good for optics under water. Despite the two concerns of optical aberrations and resolving power, zoom lenses have more degrees of freedom than prime lenses. Therefore, we used the genetic algorithm for optimization and conducted optical design in Zemax as follows: the optimal glass lens sets were initially selected in Zemax based on the genetic algorithm to significantly reduce chromatic aberration, particularly axial chromatic aberrations [18; 19]. Various approaches can be used to reduce axial chromatic aberration; however, the most direct and efficient method is to select an appropriate optical glass. Neither the least damping square in Zemax nor CODEV could reduce the chromatic aberration of the zoom lens to a low value [17; 20]. However, we incorporated the high-level language of the genetic algorithm into Zemax for optimization and obtained a set of lenses that produced relatively low axial chromatic aberration. We made minute adjustments to the zoom lenses and further identified the \begin{table}
\begin{tabular}{c c} \hline Resolving power & 2100 K pixels \\ \hline Sensor size & 12.8 mm \(\times\) 9.6 mm (CMOS) \\ \hline Diagonal length & 14.6 mm \\ \hline Actual image height & 7.3 mm \\ \hline Object distance & Infinity \\ \hline Spatial cutoff frequency & 70 lp/mm \\ \hline Angle of view & 72.20\({}^{\circ}\) \\ \hline Focal length & 5 mm to 15 mm 3x \\ \hline Aperture & f/2.8 to f4.5 \\ \hline \end{tabular}
\end{table} 
Table 6: Specifications of the novel underwater zoom lens.