# Multiple-Diffraction Subtractive Double Monochromator with High Resolution and Low Stray Light
## 3 Methods
### Stray-Light Analysis  
Stray-light suppression is an important characteristic of the type of diffraction mount discussed herein. Multiple diffractions provide a higher spectral resolution but produce more stray light than a single diffraction. Two multiple-diffraction monochromators with symmetrical layouts were found to be effective in reducing the amount of stray light. Next, we analyzed the stray light from the mount. To demonstrate, we provided an example of an MSDM, in which the focal length of the lens was 173 mm, and the groove density of the grating was 1050 grooves/mm. The central wavelength was set to 1550 nm, and the incidence angle \(\alpha_{1}\) was 75\({}^{\circ}\). The entrance slit S\({}_{1}\) and the resolution slit S\({}_{2}\) had the same width of 25 um, while the exit slit S\({}_{3}\) had a width of 200 um. We assumed that \(\lambda_{0}\) was 1550 nm and that one neighboring wavelength was \(\lambda_{0}+\delta\lambda\). The unit of \(\delta\lambda\) was pm. The slit image of S\({}_{1}\) at \(\lambda_{0}\) was located at the centers of S\({}_{2}\) and S\({}_{3}\). For \(\lambda_{0}+\delta\lambda\), the displacement of the slit image due to \(\delta\lambda\) is denoted by \(x\) (um). The \(x-\delta\lambda\) graph at S\({}_{2}\) and S\({}_{3}\) was plotted accordingly, as shown in Figure 6. According to Equation (6), the linear dispersion rate was calculated to be 1.375 um/pm. Therefore, a point on S\({}_{1}\) corresponds to an image at S\({}_{2}\) as a straight line with a slope of 1/1.375 pm/um. Considering that the width of S\({}_{1}\) is 25 um, the overall image of S\({}_{1}\) at S\({}_{2}\) forms a parallelogram with a base width of 25 um and a side slope of 1/1.375 pm/um. Similarly, since the dispersion direction of the SM is opposite to that of the FM, the image of S\({}_{2}\) at S\({}_{3}\) also forms a parallelogram with a base width of 25 um and a side slope of 1/1.375 pm/um. Figure 5: Analysis of wavelength scanning process: (**a**) wavelength scanning implemented via grating rotation. M, mirror; G, grating. Red arrow indicates rotation of G. (**b**) Functional relationship of wavelength selection. Figure 6a shows the \(x-\delta\lambda\) graph for S\({}_{2}\). The shadows in the A\({}^{\prime}\) B\({}^{\prime}\) C\({}^{\prime}\) D, region represent the signal light that can pass through S\({}_{2}\) in the FM, whereas the gray shadows represent the stray light that can pass through S\({}_{2}\) in the FM. In typical monochromators, the stray-light intensity is approximately \(10^{-5}\) times the signal light intensity. For instance, if the signal light has a power of 0 dBm, the stray-light power would be \(-50\) dBm. The upper graph in Figure 6b shows the ideal optical power distribution at S\({}_{2}\), and the lower graph shows the optical power distribution after convolution of the normalized Gaussian function, which is closer to the actual situation. Gaussian convolution was adopted to simulate the instrument broadening effect caused by the inherent limitations of the system, including optical diffraction, detector resolution, and mechanical instability. The Gaussian kernel mathematically represents the composite point-spread function of the measurement system, the characteristic width of which is calibrated to match the actual instrument response. This physical-model-based convolution process effectively bridges the gap between theoretical predictions and experimental observations. The optical power distribution obtained by Gaussian convolution shows that the stray light results in a relatively low OSNR (approximately 20 dB), which significantly influences the sensitivity of the instrument. Figure 6c shows the \(x-\delta\lambda\) graph for S\({}_{3}\). The ABCD region represents the signal light passing through the subtractive double-monochromator mount. The regions DCGH and EFBA represent the first-order stray light, which is generated by the scattering effects in the FM and anomalously passes through S\({}_{2}\).