# Multiple-Diffraction Subtractive Double Monochromator with High Resolution and Low Stray Light
## 1 Introduction  
Grating spectrometers disperse polychromatic light, enabling spectroscopic analyses to determine the chemical composition and other properties of various materials. These instruments are widely used in communication networks, astronomical observations, metallurgical industries, pollution control, and food safety [1, 2, 3]. In addition, spectrometers are also used to evaluate lighting quality, such as measuring the spectral power distribution of a light source [4, 5, 6]. Some applications require these devices to be highly accurate and portable. Hence, the design of grating spectrometers has been trending toward achieving high resolution and miniaturization [7]. The spectral resolution of a spectrometer can be effectively enhanced using higher diffraction orders, increasing the incidence and diffraction angles, or increasing the number of illuminated grooves in the grating. For instance, Echelle gratings with relatively high groove spacing provide higher resolving power because they are used at large angles and with high diffraction orders [8, 9]. Echelle gratings with higher groove densities andlarger ruled widths are more effective in terms of resolution. However, Echelle gratings require cross-dispersion because of order overlap, and the acquisition of a spectrum in two dimensions requires area array detectors, which can be expensive for broadband spectral detections that do not require completing the analysis in one shot [10; 11; 12; 13; 14]. Moreover, it is difficult to fabricate Echelle gratings with a high groove density and large ruled width, and the resolution power of a dispersion system inevitably depends on the volume of the optics [15; 16; 17]. Numerous new technologies have been developed for compact, high-resolution dispersion mounts [7; 18]. Some approaches focus on new dispersion elements, such as virtual imaging phased arrays (VIPAs) [19; 20], crossed gratings [21], and arrayed waveguide gratings (AWGs) [22; 23], which have shown promise for future high-resolution spectrometers; notably, these methods have enabled spectrometer miniaturization to chip-scale dimensions. However, they are expensive for current commercial uses. Other methods are concerned with the innovation of optical structures using conventional optical elements, enhancing resolution and compressing volume. Multiple diffractions can be achieved, for example, through a grating multiplexing structure [24; 25] or the double-grating approach [26; 27]. These improved mounts can successfully increase the resolution while ensuring a compact size. However, in plane-grating diffraction spectrometers, the stray-light level fundamentally constrains the instrument's spectral performance [28; 29; 30]. In recent years, comprehensive mathematical treatments and comparative analyses of stray-light and noise issues in grating spectrometers have emerged alongside well-established measurement systems and robust suppression strategies [31; 32; 33]. While multiple diffraction processes enhance spectral resolution, they inevitably elevate stray-light intensity and degrade the optical signal-to-noise ratio (OSNR), which are important for grating spectrometers to ensure accurate and sensitive spectral analysis. Hence, increasing the spectral resolution while suppressing stray light within a compact volume is a challenge in the design of high-precision grating spectrometers. To address the aforementioned issues related to spectral resolution and OSNR, we developed a multiple-diffraction subtractive double monochromator (MSDM) comprising two symmetrical multiple-diffraction monochromators in series. In the first monochromator (FM), the incident light is diffracted repeatedly on the same grating and then exits from a resolution slit, thereby achieving a high spectral resolution. The second monochromator (SM) is a duplicate of the FM; however, its optical layout is completely inverted. The SM produces the opposite dispersion effect to merge the stray light.