## 3 Analysis and Results
This strategy leads to a degradation of the imaging quality, which can be observed by relatively poor values of the MTF. Nevertheless, this setup is suitable to evaluate our approach to enhance the optical simulation model by means of measurement surface data. The MTF of the central field was calculated using the nominal surface of the Alvarez-optics and the fitted function corresponding to the \(\upmu\)IM process. Five different settings of the varifocal optics were used in the calculation corresponding to different states of refraction power, respectively. Table 2 depicts the MTF of the fitted functions with respect to the nominal values and the central field. The optical subsystem used suffers from a dependency of the imaging quality (depicted by the MTF value) on the adjustment of focal length. This effect can be observed in the nominal design as well as for the manufactured optics. The injection-molded optics shows a non-acceptable decline in performance in particular at the infinite focus length. \begin{table}
\begin{tabular}{c c c c} \hline \hline \((\mathbf{x},\mathbf{y})=\mathbf{a_{1}}\)\(\mathbf{x^{4}}+\mathbf{a_{2}}\)\(\mathbf{x^{3}}\mathbf{y}+\mathbf{a_{3}}\)\(\mathbf{x^{2}}\mathbf{y^{2}}+\mathbf{a_{4}}\)\(\mathbf{x^{3}}+\mathbf  
Figure 3 shows the graph of the MTF. Again, the central field is displayed in an adjustment of an infinite focal length. The splitting of the curves in two parts is due to the non-rotationally symmetric shape of the freeform optics. The transversal part is shown as solid line; the sagittal part is represented as dashed line. The red curves describe the MTF of the nominal design, the blue curves represent the MTF of the simulation based on the measurement data of the manufactured Alvarez-optics. The reduced MTF of the manufactured optics is caused by geometrical part deformation occurring in the \(\upmu\)IM process. An uneven refractive index distribution may also contribute to the poor MTF. An optimization of the \(\upmu\)IM process was conducted to compensate for these two limiting factors. Optimization of the molding process lead to different settings of the process parameters and is described in detail in [28]. Figure 4 presents RMS and PV values of intermediate states of the optimization for four samples, respectively. The initial setting is depicted as \"original\". Several corrections led eventually to the final process settings (\(\upmu\)IM/comp) featuring a smooth characteristic over all four samples. Based on the \(\upmu\)IM/comp-process, modified Alvarez-optics were manufactured. Figure 5 shows the surface residuals for the compensated Alvarez-lens parts manufactured by means of the \(\upmu\)IM/comp-process. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Focal Length [m]** & **MTF Nominal** & **MTF Manufactured** & **Relative MTF [\%]** \\ \hline \(\infty\) & 0.34 & 0.2 & 59 \\
4 & 0.49 & 0.43 & 88 \\
0.667 & 0.66 & 0.64 & 97 \\
0.364 & 0.63 & 0.54 & 86 \\
0.263 & 0.55 & 0.43 & 78 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Modulation transfer function (MTF) of the manufactured optics compared with the nominal design (central field, evaluated at 40 cyc/mm). Figure 4: RMS and PV-values of intermediate states of the process optimization for four samples, respectively. “original” means the initial setting. Figure 3: MTF of the manufactured optics compared with the nominal design. Noticeable is the smooth surface. The improvement of the surface form deviation can be seen clearly by comparing Figures 2 and 5. Of course, this aspect can also be seen regarding the PV and RMS errors, resulting in 4.1 \(\upmu\)m and 0.34 \(\upmu\)m, respectively. Figure 6 shows the PV and RMS value of the Alvarez-surface manufactured by the two microinjection molding processes. The improvement of the compensated surface manufactured by means of the \(\upmu\)IM/comp-process is obvious.