## 4 Experiment Results
### Test of Spectrometers
An optical filter can be added in front of the light source of the collimator to obtain near-monochromatic parallel light. We use a Mitutoyo(r) 10\(\times\) apochromatic objective in the parallel light to form a point source at the slit of the spectrometer. The OPTIKOS(r) lens measurement system captures the spot image of the optical system under test through a microscope to obtain its point spread function (PSF), and then performs Fourier transform on PSF to obtain the MTF of the optical system. However, the near-monochromatic point source forms a slender image instead of a spot image after passing through the spectrometer and is then captured by the microscope, as shown in Figure 19b. Only the PSF in the spatial dimension can be obtained; thus, only the spatial MTF can be tested in such a configuration. The tested MTF curve is shown in Figure 19c, and the MTF value is 0.81 at 460 nm and 33.3 lp/mm, close to the diffraction limit. In spectral dimension, we generally use the SRF to show its spectral performance, which has been discussed above. In addition, stray light of the B1 spectrometer is also tested using a large diameter integrating sphere, as shown in Figure 20a. To test the stray light more accurately, we use a neutral density (ND) filter to artificially extend the dynamic range of the detector. We first increase the brightness of the integrating sphere to saturate the detector on the image plane of the spectrometer. Secondly, we place a ND filter with an optical density of 1 in front of the slit, and the detector acquires a uniform dispersion image, as shown in Figure 20b, and its average grey level is \(I^{\prime}_{mor}\). Then, we remove the ND filter and install a block in front of the slit. The average grey level at the center of the blocked portion in the image is \(I^{\prime}_{spa}\), as  
Figure 19: Test of MTF. (**a**) Schematic diagram of the test device and the experiment device, (**b**) the narrow band point light source with the center wavelength of 460 nm forms a slender image after passing through the spectrometer and is captured by the microscope, (**c**) the MTF curve. shown in Figure 20c. Next, we remove the block and place a notch filter in front of the slit. The average grey level at the center of the notched portion in the image is \(I^{\prime}_{spe}\), as shown in Figure 20d. The spatial stray light coefficient \(S^{\prime}_{spa}\) and the spectral stray light coefficient \(S^{\prime}_{spe}\) can be calculated by the following equations. \[S^{\prime}_{spa}=\frac{I^{\prime}_{spa}-I^{\prime}_{buc}}{\left(I^{\prime}_{ nor}-I^{\prime}_{buc}\right)/T_{ND}} \tag{8}\]  
\[S^{\prime}_{spe}=\frac{I^{\prime}_{spe}-I^{\prime}_{buc}}{\left(I^{\prime}_{ nor}-I^{\prime}_{buc}\right)/T_{ND}} \tag{9}\]  
where \(I^{\prime}_{buc}\) is the background grey level of the detector, and \(T_{ND}\) is the transmission of the ND filter. The test results show that the stray light coefficient is only 0.22% in spatial dimension and 0.45% in spectral dimension. However, both spatial and spectral stray light coefficients are larger than the simulated value, at 0.05% and 0.09%, respectively. We hypothesize that the main reason is that the diffraction efficiency of the grating's working order (\(-1\)st order) is lower than the design, whereas the stray light of the non-working orders is higher than the theory. Another reason is that the surface absorptivity of the machine is not as high as the theory, the measured absorptivity is about 88%; however, this value used for the simulation is 92%. The test device for the B3 spectrometer is shown in Figure 21a. A supercontinuum white light laser and an integrating sphere promote uniform illumination at the slit with tunable wavelength. A SWIR T2 SL detector is used to acquire spectral lines. Figure 21b shows the spectral lines of 1100 nm, 1700 nm, and 2300 nm. According to the centroid coordinates of spectral lines, the dispersion power of the B3 spectrometer is calculated to be 187.5 nm/mm, and the spectral sampling distance is 12 nm with 2\(\times\) pixels binning.