# Robust Full-Screen Wavelength Calibration Algorithm
## 5 Conclusions  
In this paper, the structure and some basic principles of a scanning, double-layer, secondary diffraction, linear-array CCD spectrometer are introduced. Then, a robust, full-screen, calibration algorithm is proposed. The parameters of the calibration formula were obtained by LMA and Huber regression algorithm. Focusinng on the theory and applications of the scanning, double-layer, secondary diffraction, linear-array CCD spectrometer, we verified that the wavelengths can be calibrated by the robust spectral calibration algorithm. Compared with other methods, we found that the robust spectral calibration algorithm has the following advantages. First, we can correct the error caused by the sine mechanism and improve the calibration accuracy of the center pixels. We also found a way to convert the non-central pixels' feedback values to the central pixels' feedback values. Finally, we can calibrate the wavelength of the central pixels and the non-central pixels with high accuracy, instead of only focusing on calibrating the wavelength of the central pixels, as in other calibration algorithms. In other words, when the wave peak is not at the central pixels, we can accurately calibrate its wavelength, or, when there are multiple wave peaks in a screen, we can calibrate the wavelengths of these peaks at the same time. During the experiment, we tested the calibration accuracy of the algorithm for the wavelength outside the fitting points and showed that it has a good calibration accuracy, while polynomial fitting can not guarantee the calibration accuracy of points outside the fitting point. Finally, the fitted formula is relatively convenient and can be used to calibrate the wavelength at any pixel. In future work, we plan to introduce the automatic step-size algorithm into the non-central pixels' function fitting method. We are also interested in quickly calibrating the spectrometer's wavelength after the vibration test. As the area-array CCD also has non-central pixel positions, similar studies will be conducted on the area-array CCD to verify the validity of the model. To verify the influence of light quality on the model, we will also test our model on stable lasers characterized by a narrow line width. Conceptualization, B.J. and C.Z. ; methodology, B.J. ; software, B.J. and N.Z. ; validation, B.J., L.W. and J.C.; formal analysis, L.Y. and B.J. ; investigation, J.C.; resources, H.L. and J.C.; data curation, B.J. and J.C.; writing--original draft preparation, B.J. and C.Z. ; writing--review and editing, B.J., C.Z. and H.B. ; visualization, B.J. ; supervision, C.Z. and H.L. ; project administration, C.Z. and H.L. ; funding acquisition, C.Z. All authors have read and agreed to the published version of the manuscript. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Spectrometer Number**} & \multirow{2}{*}{**Standard Value/nm \(\lambda_{s}\)**} & \multirow{2}{*}{**Mean Value/nm \(\overline{\lambda_{n}}\)**} & \multicolumn{2}{c}{**Accuracy/nm \(\overline{\lambda_{n}}\)**} \\  & & & \(\Delta\lambda_{n}=\overline{\lambda_{n}}-\lambda_{s}\) & \((\Delta\leq\pm\)**0.05 nm)** \\ \hline \multirow{6}{*}{01} & 253.65 & 253.63 & \(-\)0.02 & 0.003 \\  & 365.02 & 365.04 & 0.02 & \(\pm\)0.002 \\  & 404.65 & 404.66 & 0.01 & \(-\)0.003 \\  & 546.07 & 546.08 & 0.01 & \(-\)0.004 \\  & 579.07 & 579.04 & \(-\)0.03 & \(\pm\)0.002 \\ \hline \multirow{6}{*}{02} & 253.65 & 253.62 & \(-\)0.03 & \(-\)0.004 \\  & 365.02 & 365.03 & 0.01 & \(-\)0.004 \\  & 404.65 & 404.67 & 0.02 & \(-\)0.002 \\  & 546.07 & 546.05 & \(-\)0.02 & \(-\)0.003 \\  & 579.07 & 579.02 & \(-\)0.05 & 0.003 \\ \hline \multirow{6}{*}{03} & 253.65 & 253.61 & \(-\)0.04 & \(-\)0.003 \\  & 365.02 & 365.04 & 0.02 & 0.002 \\ \cline{1-1}  & 404.65 & 404.63 & \(-\)0.02 & \(\pm\)0.003 \\ \cline{1-1}  & 546.07 & 546.11 & 0.04 & \(-\)0.002 \\ \cline{1-1}  & 579.07 & 579.05 & \(-\)0.02 & \(-\)0.003 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Test results of the calibration algorithm on three spectrometers.