Research on the hyperspectral detection of greenhouse gas using Fabry-Perot interferometric system
doi: 10.37188/CO.EN-2025-0009
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摘要:
为了能够精确监测甲烷点源排放情况，本文研究了将法布里-珀罗（F-P）干涉仪用作空间成像光谱仪的分光元件，以实现高空间分辨率与高光谱分辨率的兼顾。围绕F-P腔的理论与物理模型构建展开研究，旨在实现高光谱分辨率，以满足甲烷排放点源监测的技术需求。首先，基于多光束干涉理论，构建了理想条件下的F-P腔干涉初始理论模型。在此基础上，考虑有限通光孔径效应，建立了相应的几何模型，并推导出有限通光孔径条件下的F-P腔理论模型。此外，通过引入表面缺陷分布函数，进一步构建了包含微观随机不均匀性缺陷和曲率缺陷的F-P腔理论模型，从而形成更完整的理论框架。在物理模型构建方面，根据初始理论模型，对F-P腔进行初步设计，使其匹配甲烷吸收光谱的监测需求。基于有限通光孔径F-P腔的理论模型，结合透射光强函数曲线及其斜率曲线，精确确定F-P腔的通光孔径尺寸。在此基础上，结合镜体背面楔角，对F-P腔物理模型进行了进一步优化。接着，以实现目标频谱特性和技术要求为导向，深入分析F-P腔两平行平板间隙间距的允许变动范围，从而确定了F-P腔间隙距离的公差范围。根据表面缺陷条件，设计F-P腔反射表面的表面粗糙度、面形精度及平行度。最终，优化后的F-P腔光谱分辨率达到0.29 nm，满足甲烷排放点源监测的技术要求。本研究通过构建更完整的F-P腔理论模型，并优化其物理设计，实现了高光谱分辨率和高空间分辨率的兼顾，为F-P干涉仪在空间成像光谱仪中的应用奠定了理论基础，同时为高精度光谱探测技术的发展提供了重要支撑。
Abstract:To accurately monitor methane emissions from point sources, this paper explores the use of a Fabry-Perot (F-P) interferometer as the spectroscopic element of a spatial imaging spectrometer, aiming to achieve both high spatial and high spectral resolution. The study focuses on constructing both theoretical and physical models of the F-P cavity to meet the technical requirements of methane point-source monitoring. First, an initial theoretical model of F-P cavity interference under ideal conditions is developed based on multi-beam interference theory. Building upon this, a corresponding geometric model is established by considering the effect of finite throughput aperture, from which a theoretical model under finite aperture conditions is derived. In addition, a more comprehensive theoretical framework is constructed by incorporating surface defect distribution functions to account for microscopic random inhomogeneities and curvature defects. In the physical model development, the F-P cavity is initially designed based on the ideal theoretical model to match the spectral characteristics of methane absorption. Using the finite-aperture theoretical model, the transmission intensity curve and its slope are analyzed, and the aperture size is precisely determined bases on the physical meaning of the slope. Subsequently, the physical model is further optimized by adjusting the wedge angle at the rear surface of the mirror. To meet specific spectral and technical targets, the allowable variation in the gap spacing between the two parallel mirrors is thoroughly analyzed, thereby defining the tolerance range for the cavity gap. Surface roughness, figure accuracy, and parallelism of the reflective surfaces are then specified according to surface defect considerations. Ultimately, the optimized F-P cavity achieves a spectral resolution of 0.29 nm, meeting the technical requirements for methane point-source monitoring. By constructing a comprehensive theoretical model and optimizing the physical design, this study enables the realization of both high spectral and spatial resolution, provides a theoretical foundation for applying F-P interferometers in spatial imaging spectrometry, and supports the advancement of high-precision spectral detection technologies.
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Figure 1. Optical system of the space imaging spectrometer with F-P interferometric cavity. The red frame is the telescope group, the blue frame is the imaging mirror group; Ⅰ: filter, Ⅱ: F-P interference cavity, Ⅲ: focal plane
Figure 3. (a) Transmitted radiation of a F-P cavity; (b) Reflected radiation of a F-P cavity
Figure 4. (a) Interference pattern of reflected light and (b)Interference pattern of transmitted light (light source: sodium lamp)
Figure 6. Two sets of interfering circles in the F-P cavity. m+i (i = 0, 1, 2) are the interference order.
Figure 12. (a) Transition intensity of methane in the SWIR band; (b) Transition intensity of methane in the
1630 -1675nm range.
Figure 14. Absorption spectrum of methane. Blue: Methane absorption spectrum from HITRAN (
1630 −1675 nm,); Red: F-P cavity transmission peaks.
Figure 19. Maximum transmission, contrast and FWHH as a function of the effective cavity size k
Figure 20. Slope of peak transmission Yk(0), contrast Ck and FWHH as functions of effective cavity size k
Figure 21. Curves of incident angle, wavelength and interference order for a gap spacing of
89000 nm
Figure 22. Effect of microscopic random inhomogeneity defects on FWHH, peak transmission and contrast
Figure 25. Angular dispersion of the F-P cavity across the entire target spectral range
Table 1. Methane monitoring satellites and some of their parametric indicators
Satellite Sensor Swath width/km Spatial Resolution/km Spectral Resolution /nm Spectral Methods Sentinel-5P TROPOMI 2600 7 0.23 PG dispersion with reflection grating GOSAT TANSO-FTS 790 10.5 0.07 Michelson interferometer FY-3D GAS 1200 10 0.3 Michelson interferometer GF-5 GMI 865 10.3 0.074 Spatial heterodyne spectroscopy MethaneSAT PILSM 200 0.1×0.4 0.25 Diffraction grating GHGSat-D WAF-P 12 0.05 0.3 F-P Interferometer GHGSat-CX 0.03 GF-5 AHSI 60 0.03 10 Convex grating Offner spectrometer ZY-1-02D AHSI 60 0.03 20 Convex grating Offner spectrometer PRISMA HYC 30 0.03 12 Prism EnMAP HSI 30 0.03 10 Curved prism 
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Table 2. Performance parameters of F-P cavity for varying number of reflections
Maximum
transmission
Yk(0)Number of
reflections
kAperture size
2a/mmWidth of profile
FWHH/nm0.88 615 15.5 0.1044 0.87 568 14.3 0.1053 0.86 527 13.3 0.1063 0.85 492 12.4 0.1072 0.84 461 11.6 0.1081 0.83 434 11.0 0.1091 0.82 410 10.4 0.1105 0.81 389 9.8 0.1115 0.80 369 9.6 0.1124 0.79 352 9.3 0.1134 0.78 336 8.9 0.1148 0.77 321 8.5 0.1157 0.76 308 8.1 0.1171
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Table 3. Performance parameters of F-P cavity under chosen aperture size
Yk(0) k 2a/mm (2a+6.8/2)/mm FWHH/nm 0.806 380 9.6 13 0.1115
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Table 4. Relationship among incident angle, wavelength and interference order for different gap spacings
89000 90000 91000 
92000 93000 94000 
95000 96000 97000 
98000 99000 100000
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Table 5. Parameters of the F-P cavity for each gap spacing
Gap spacing/nm 91000 92000 93000 94000 95000 96000 97000 Ideal FWHH/nm 0.0965 0.0954 0.0944 0.0934 0.0924 0.0915 0.0905 number of reflections k 384 380 375 371 368 364 360 Actual FWHH/nm 0.1121 0.1115 0.1090 0.1085 0.1079 0.1074 0.1069
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