# Non-Rotationally Symmetric Field Mapping for Back-Scanned Step/Stare Imaging System
## 5 Conclusions and Future Work  
Addressing the problems of off-axis field point wander and image blurring caused by the use of FSM in back-scanned step/stare imaging system, this manuscript proposes a non-rotationally symmetric field mapping method for back-scanned step/stare imaging system, which can make all field points  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Characteristics**} & **Maximum Distortion When FSM** & **Maximum Image Wander during** \\  & **Does Not Move** & **Back-Scanning** \\ \hline Optical system under \(h=f^{\prime}\tan\theta\) & \textless{}0.02\% & 3.13 pixels \\ Optical system under \(h=f^{\prime}\theta\) & \textless{}0.012\% & 3.18 pixels \\ Optical system under & & \\ \(h_{x}=f^{\prime}\delta_{x},h_{y}=f^{\prime}\theta_{y}\) & \textless{}0.46\% & 0.22 pixels \\ \hline \hline \end{tabular}
\end{table}
Table 2: Distortion characteristics and image wander.  
Figure 12: Image points wander during back-scanning under field mapping condition \(h=f^{\prime}\theta\): \(-0.4\) deg to \(+0.4\) deg back-scan in object space.  
stable on the FPA during back-scanning. The mathematical model of non-rotationally symmetric field mapping between object space and image space is established. Meanwhile, a back-scanned step/stare imaging system based on the model is designed, in which this non-rotationally symmetric mapping can be implemented with an afocal telescope including freeform lenses. Experimental results show that this non-rotationally symmetric field mapping can provide the highest contrast images for back-scanned step/stare imaging system.  
The future work includes three aspects. Firstly, the actual optical imaging systems will be utilized to verify the impact of image wander on SNR through quantitative imaging experiments. Secondly, due to the fact that the application of the freeform surfaces will always increase the development cycle and funding of the imaging systems, to meet this non-rotationally symmetric field mapping, we will try to introduce a little tilt and eccentricity on the field lens of the afocal telescope or the certain lens of the imager to avoid the application of freeform surfaces. Finally, the differences between the theoretical image wanders and the actual image wanders for different FOVs will be researched when the system has the manufacturing errors, the assembly errors, the position errors and the control errors of the FSM.  
Conceptualization, Q.F. and X.Z.; methodology, Q.F.; software, Q.F.; validation, J.Z. and G.S.; writing--original draft preparation, Q.F.; writing--review and editing, Q.F., S.Z. and M.L. All authors have read and agreed to the published version of the manuscript.  
This work was supported by National Natural Science Foundation of China [grant number 61505201].  
The authors would like to thank the anonymous reviewers for their useful comments and critical remarks which helped to improve this paper.  
The authors declare no conflict of interest. We have purchased the genuine software license of Zemax and stated the company name in our article. The funders had no role in the design of the study.