## 4 Experiment Results
### Test of Spectrometers
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Wavelength/nm**} & \multicolumn{6}{c}{**FWHM of SRF at Different Fields/nm**} \\ \cline{2-7}  & \(-\)**1 Field** & \(-\)**0.5 Field** & **0 Field** & **+0.5 Field** & **+1 Field** & **Average** \\ \hline
312.9 & 3.92 & 3.93 & 3.93 & 3.92 & 3.93 & 3.95 \\
346.3 & 3.98 & 3.97 & 3.95 & 3.97 & 3.96 & 3.98 \\
404.6 & 4.02 & 3.98 & 3.99 & 4.00 & 4.00 & 4.01 \\
435.8 & 4.01 & 4.02 & 4.01 & 4.00 & 4.02 & 4.02 \\
467.8 & 3.99 & 3.98 & 3.98 & 3.98 & 4.00 & 4.00 \\
479.9 & 4.02 & 4.01 & 4.01 & 4.00 & 4.02 & 4.02 \\
508.5 & 4.01 & 4.02 & 4.01 & 4.00 & 4.01 & 4.01 \\
546.1 & 4.01 & 4.02 & 4.00 & 3.99 & 4.00 & 4.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Spectral resolution of B1 spectrometer with 6\(\times\) pixels binning. is shown that the spectrometer optical system has extremely small smile, and the later installation of the detector also require high alignment accuracy to minimize the spectral non-uniformity as much as possible, and the detector alignment must also enter in the final system assessment. Keystone distortion in this paper is defined as the difference in the slit images' lengths at different wavelengths. Figure 18a shows the schematic diagram of the device for testing the keystone. A broadband polychromatic point source is formed at both ends of the slit, and two dispersion lines are formed at the image plane, as shown in Figure 18b. The keystone can be calculated by the slope difference of the dispersion lines:  
\[\text{Keystone}=(k_{1}-k_{2})d_{\text{dispersion}} \tag{7}\]  
where \(k_{1}\) and \(k_{2}\) are the slope of dispersion line 1 and 2, respectively. \(d_{dispersion}\) is the dispersion width of the spectrometer, which is 5.90 \(\upmu\)m for the developed B1 spectrometer. The experiment device is shown in Figure 18c, and the dispersion lines collected by CCD are shown in Figure 18d. The test result shows that the keystone of the B1 spectrometer is 1.9% of a pixel (pixel size 15 \(\upmu\)m). In Figure 18d, the dispersion lines have a slope of about 0.3 pixels (pixel size 5.5 \(\upmu\)m), and this is caused by the incomplete alignment of the dispersion lines and the detector array during the test. That means the detector-to-grating rotation. The tested keystone calculated by Equation (7) not only excludes the effect of detector-to-grating rotation, but also ignores the slit-to-grating rotation. When we test the optical performance of spectrometer, we need to exclude the effect of the detector-to-slit and detector-to-grating rotation, but the slit-to-grating rotation could also cause spatial non-uniformity, as described in Section 4.2. Therefore, the perpendicularity of the spectral dimension and the spatial dimension needs to be measured. In the process of testing smile and keystone, as shown in Figures 17b and 18c, we only changed the light source illuminating the slit, and the relative position of CCD and spectrometer is unchanged. Thus, we can use the spectral lines and dispersion lines acquired in two experiments to calculate the angle between the spatial dimension and the spectral dimension. The average angle between the spectral lines in Figure 17c and the dispersion lines in Figure 18d is 89.98\({}^{\circ}\), indicating extremely high rotational alignment  
Figure 18: Test of keystone. (**a**) Schematic diagram of the test device, (**b**) the polychromatic point source is formed at both ends of the slit, and two dispersion lines are formed at the image plane, (**c**) the experiment device, and (**d**) dispersion lines corresponding to both ends of the slit. accuracy of the slit and grating. Such a high perpendicularity only results in a spatial alignment error of 2 \(\upmu\)m (\(d_{dispersion}\)\(\times\) tan0.02\({}^{\circ}\)) at most between the dispersion line and the detector array. Meanwhile, the MTF of the B1 spectrometer is tested by the OPTIKOS(r) lens measurement system, including a long-focus collimator, a microscope, and a computer containing processing software, as shown in Figure 19a.