## 2 Materials and Methods
### Retrofocus Lens  
A third example of desensitizing a lens is the retrofocus lens in example 1 of US Patent 2,824,495 to [PERSON]. [PERSON] [18] with a field of view of \(\pm 31^{\circ}\), focal length of 50 mm, and an optical speed of F/4. This lens is shown in Figure 3 at left where the lens was reoptimized with modern lens design software. At right in Figure 3 is the lens desensitized for linear astigmatism as discussed above. Monte Carlo analysis of both lenses using only surface tilts of 0.1\({}^{\circ}\) as lens errors, were performed as also illustrated at bottom in Figure 3 with histograms of 1000 trials. This retrofocus lens case highlights better the results of desensitizing a lens for a given effect, in this case linear astigmatism. The desensitized lens has a nominal performance degraded almost by a factor of two. However, the trials mean for both lenses is about the same but the desensitized lens has about half the standard deviation. In addition the desensitized lens does not produce either very good performing trials, or very bad performing trials. Thus for mass production and quality control a desensitized lens might be preferable to one optimized solely for image quality.  
Figure 2: **Left, triplet lens; right, desensitized triplet lens. Histograms for 1000 Monte Carlo trials of rms wavefront error across the field of view.**  
Tables 3 and 4 provide the sensitivities of lenses in Figure 3. In the desensitizing process the sensitivity to linear astigmatism was reduced from 9.91 waves to 5.63 waves. In addition, the sensitivities to uniform coma and field tilt were also reduced.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{3}{c}{**Dessentized Retrofocus Lens Surface Sensitivities in Waves**} \\
**Surface** & \(W_{ULA}\) & \(W_{UC}\) & \(W_{LA}\) & \(W_{FT}\) \\ \hline
1 & 0.0 & \(-\)0.06 & \(-\)0.17 & 0.29 \\
2 & 0.0 & 0.19 & 1.24 & 0.40 \\
3 & 0.00 & \(-\)0.07 & 0.67 & 0.24 \\
4 & 0.00 & 0.32 & 1.73 & 1.08 \\
5 & \(-\)0.01 & \(-\)0.94 & \(-\)0.36 & \(-\)0.68 \\
6 & 0.00 & 0.43 & 1.04 & 0.58 \\
7 & 0.00 & \(-\)0.63 & 0.06 & 0.90 \\
8 & 0.00 & 0.27 & 0.50 & \(-\)0.71 \\ STOP & 0.00 & 0.00 & \(-\)0.02 & 0.00 \\
10 & 0.00 & \(-\)0.43 & \(-\)2.43 & 0.00 \\
11 & 0.00 & \(-\)0.16 & \(-\)0.08 & 0.07 \\
12 & 0.00 & 0.89 & \(-\)0.97 & \(-\)0.75 \\
13 & 0.00 & \(-\)0.26 & 1.12 & \(-\)0.08 \\
14 & \(-\)0.01 & 0.34 & 4.13 & 1.64 \\ RSS & 0.01 & 1.69 & 5.63 & 2.66 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Desensitized retrofocus lens. Surface sensitivities in waves.  
Figure 3: **Left**, retrofocus lens; **right**, desensitized retrofocus lens. Histograms for 1000 Monte Carlo trials of rms wavefront error across the field of view.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{3}{c}{**Retrofocus Lens Surface Sensitivities in Waves**} \\
**Surface** & \(W_{ULA}\) & \(W_{UC}\) & \(W_{LA}\) & \(W_{FT}\) \\ \hline
1 & 0.00 & \(-\)0.05 & \(-\)0.05 & \(-\)0.05 \\
2 & 0.00 & 0.19 & 1.11 & 0.48 \\
3 & 0.00 & \(-\)0.08 & 0.82 & 0.15 \\
4 & 0.00 & 0.38 & 2.46 & 1.48 \\
5 & \(-\)0.01 & \(-\)1.43 & \(-\)3.03 & \(-\)1.85 \\
6 & \(-\)0.01 & 0.58 & 2.01 & 0.95 \\
7 & 0.00 & \(-\)0.71 & \(-\)0.53 & 0.64 \\
8 & 0.00 & 0.38 & 1.67 & \(-\)0.28 \\
9 & 0.00 & \(-\)0.90 & \(-\)5.97 & \(-\)1.58 \\
10 & 0.00 & \(-\)0.15 & \(-\)0.27 & \(-\)0.04 \\
11 & 0.00 & 1.31 & 0.95 & 0.42 \\
12 & 0.00 & \(-\)0.45 & 0.34 & \(-\)0.95 \\
13 & \(-\)0.01 & 0.46 & 6.10 & 2.43 \\ STOP & 0.00 & 0.00 & \(-\)0.01 & 0.00 \\ RSS & 0.02 & 2.49 & 9.91 & 4.11 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Retrofocus lens. Surface sensitivities in waves.