Scattering model for micro-defects on cavity mirrors in cavity ring-down spectroscopy instruments
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摘要:
针对腔衰荡光谱仪器（CRDS）中的腔镜微缺陷会导致测量精度下降的问题，本文建立了基于Bobbert Vlieger BRDF 理论的腔镜微缺陷散射模型，分析了微缺陷在不同光源波长、入射角度、缺陷量级、缺陷类型、缺陷密度、基底膜层的散射光特性。腔镜微缺陷散射模型研究表明：微米至亚微米（100 μm~0.1 μm）量级缺陷会降低衰荡吸收精度。针对该量级微缺陷的检测，构建了腔镜微缺陷散射和微缺陷暗场检测的分析模型。CRDS腔镜微缺陷散射光模型的建立与分析，是实现腔镜微缺陷高精度检测和CRDS测量精度恢复的关键技术。
Abstract:Microdefects in cavity mirrors utilized in cavity ring-down spectroscopy (CRDS) instruments adversely affect measurement accuracy. Aiming at this problem, this paper establishes a scattering model for micro-defect on cavity mirrors based on the Bobbert and Vlieger Bidirectional Reflectance Distribution Function (BRDF) theory to analyze the characteristics of scattered light of microdefects under varying wavelengths, incident angles, defect sizes, defect types, defect densities, and substrate coatings. Studying on the cavity mirror microdefect scattering model shows that defects in the micrometer to submicron range (100 μm to 0.1 μm) affect the ring-down absorption accuracy. For the detection of micro-defects at this scale, analytical models for both cavity mirror micro-defect scattering and micro-defect dark-field detection is established. Establishing and analyzing the scattering light model for micro-defects in CRDS (Cavity Ring-Down Spectroscopy) cavity mirrors is critical to realizing the high-precision detection of microdefects on CRDS mirror and recovering CRDS measurement accuracy.
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图 1 CRDS中腔镜缺陷对阈值建立和衰荡吸收的影响
Figure 1. The impact of cavity mirror defects on threshold setting and ring-down absorption in CRDS
图 2 明场缺陷检测与暗场缺陷检测原理示意图
Figure 2. Schematic diagram of the principles for bright-field defect detection and dark-field defect detection
图 3 腔镜缺陷BRDF散射模型及参数
Figure 3. BRDF scattering model and parameters of cavity mirror defects
图 4 不同入射角度下的散射场空间分布。(a)和(b)为0.1 μm PSL颗粒在75°斜入射和正入射下的空间分布，(c)和(d)为1 μm PSL颗粒在75°斜入射和正入射下的空间分布
Figure 4. Spatial distribution of scattering field at different incidence angles. (a)-(b) Spatial distribution of 0.1 μm PSL particles under 75° oblique incidence and normal incidence; (c)-(d) spatial distribution of 1 μm PSL particles under 75° oblique incidence and normal incidence
图 6 由紫外至红外各典型波长75°斜入射下散射光的空间分布。(a) 266 nm；(b) 355 nm；(c) 490 nm；(d) 633 nm；(e) 808 nm；(f)
1064 nmFigure 6. Spatial distribution of scattered light at various typical wavelengths from UV to IR. (a) 266 nm; (b) 355 nm; (c) 490 nm; (d) 633 nm; (e) 808 nm; (f)
1064 nm
图 8 不同粒径颗粒75°斜入射下散射光的空间分布。(a) 3 μm；(b) 1 μm；(c) 0.5 μm；(d) 0.1 μm
Figure 8. Spatial distribution of scattered light for different particle sizes under 75° oblique incidence. (a) 3 μm; (b) 1 μm; (c) 0.5 μm; (d) 0.1 μm
图 9 不同粒径75°斜入射下散射光的散射平面分布。(a) 3 μm；(b) 1 μm；(c) 0.5 μm；(d) 0.1 μm
Figure 9. Scattering planer distribution of scattered light from particles with different sizes under 75° oblique incidence. (a) 3 μm; (b) 1 μm; (c) 0.5 μm; (d) 0.1 μm
图 11 不同颗粒密度斜入射时散射光的空间分布。 (a) 10/μm2；(b) 1/μm2；(c) 0.1/μm2；(d) 0.01/μm2
Figure 11. Spatial distribution of scattered light for different particle densities under oblique incidence. (a) 10/μm2; (b) 1/μm2; (c) 0.1/μm2; (d) 0.01/μm2
图 13 不同材质颗粒斜入射时散射光的空间分布。(a) PSL；(b) Au；(c) Cu
Figure 13. Spatial distribution of scattered light for different material particles under oblique incidence. (a) PSL; (b) Au; (c) Cu
图 5 在正入射及斜入射时，微缺陷各散射角的能量分布。蓝色绿色实线和红色虚线分别为75°斜入射和正入射时反射面内不同散射角下半径分别为3 μm、1 μm、0.5 μm、0.1 μm PSL颗粒BRDF
Figure 5. The energy distributions of microdefects at each scattering angle under normal and oblique incidences. The lines show the BRDF of PSL particles with radii of 3 μm, 1 μm, 0.5 μm, and 0.1 μm at different scattering angles within the reflective surface. Blue and green solid lines are the BRDF under 75° oblique incidence, and red dashed lines are the BRDF under normal incidence
图 7 各典型光源波长下75°斜入射时反射面内的BRDF
Figure 7. BRDF of the reflective surface at various typical wavelengths under 75° oblique incidence
图 10 不同粒径大小PSL斜入射时反射面内的BRDF
Figure 10. BRDF of the reflective surface for different sizes of PSL particles under oblique incidence
图 12 反射面内不同颗粒密度斜入射时的BRDF
Figure 12. BRDF of particles with different densities in the reflective surface under oblique incidence
图 14 不同材质颗粒斜入射时反射面内颗粒散射场的BRDF
Figure 14. BRDF of the reflective surface for different material particles under oblique incidence
图 15 基底不同膜层斜入射时反射面内的BRDF
Figure 15. BRDF of the reflective surface for different high-reflective coatings on substrates under oblique incidence
表 1 线偏振光(p光)正入射时，不同缺陷量级腔镜的散射光强度
Table 1. Scattered light intensity of cavity mirrors with different defect orders under normal incidence of linearly polarized light (p polarization)
Particle
radius/μmScattered light
intensity/ppms-polarization/
ppmp-polarization/
ppm0.01 7.939×10−11 2.3368 ×10−127.9242 ×10−110.05 1.2351 ×10−61.9405 ×10−81.2087 ×10−60.1 3.4466 ×10−51.9143 ×10−63.0221 ×10−50.5 2.9963 ×10−38.1627 ×10−42.3632 ×10−31 1.5833 ×10−22.6241 ×10−31.4189 ×10−2
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