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摘要:
针对传统中阶梯光栅光谱仪高分辨率与微型化难以兼容的技术难题，本文提出了一种紧凑型中阶梯光栅光谱仪设计方法。该设计基于交叉Czerny-Turner型光路结构，采用透射棱镜作为交叉色散元件，通过正交色散分离不同级次光谱的同时结合反向离轴抛物面聚焦镜消除棱镜引入的像差，以实现空间布局小型化。本文对中阶梯光栅及色散棱镜参数进行设计建模，并由光程像差理论分析了聚焦光路的像差特性。仿真结果表明，抛物面-棱镜型中阶梯光栅光谱仪光谱范围为450~650 nm，数值孔径为0.05，分辨率可达0.06 nm，并且在公差范围合理情况下，系统体积仅有80 mm×44 mm×18 mm。基本能够满足便携式、高精度光谱检测的使用要求。
Abstract:Aiming at the technical challenge of reconciling high resolution with miniaturization in traditional echelle spectrometers, this paper presents a novel optical design for a compact echelle spectrometer. First, based on the crossed Czerny-Turner structure, the design adopts a transmission prism as the cross-dispersing element to separate spectra with different orders and a reverse off-axis parabolic focusing mirror is primarily used to eliminate the aberrations introduced by the prism, thereby enabling the miniaturization of the spatial layout. In this paper, we briefly describe the design methods for echelle gratings and dispersive prisms. Additionally, the aberration characteristics of the focusing optical path are analyzed using the theory of optical path aberration. The simulation results show that the parabolic-prism type echelle spectrometer has a spectral range of 450~650 nm, a numerical aperture of 0.05, and a resolution up to 0.06 nm. Moreover, under the condition of reasonable tolerance range, the system volume is only 80 mm × 44 mm × 18 mm. It can satisfy the application requirements of portable and high-precision spectral detection.
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图 1 中阶梯光栅光谱仪光路示意图
Figure 1. Schematic diagram of the optical path for an echelle spectrometer
图 2 中阶梯光栅衍射示意图。（a）光栅截面内色散；（b）准Littrow模式
Figure 2. Schematic diagram of the echelle grating diffraction. (a) Dispersion in grating cross-section; (b) quasi-Littrow configuration
图 5 过焦点平行光经离轴抛物面镜的像差原理图
Figure 5. Schematic of aberration principle for parallel light passing through the focal point via an off-axis parabolic mirror
图 8 42衍射级次下光谱仪的调制传递函数曲线
Figure 8. MTF curves of spectrometer at 42th diffraction order
图 9 第35、39、42、45、49级次下中心及边缘波长的点列图
Figure 9. Spot diagrams for central and marginal wavelengths at 35th, 39th, 42th, 45th and 49th diffraction orders
图 10 15个特征波长的像面坐标及狭缝几何图像仿真
Figure 10. Image plane coordinates of 15 characteristic wavelengths and slit geometric image simulation
表 1 光谱仪的设计参数
Table 1. Parameters of the designed spectrometer
系统参数 数值 数值孔径 0.05 入射狭缝 15 μm×50 μm 光谱范围 450 nm~650 nm 光谱级次 35th~49th 准直镜 R = 140 mm, θ = 5° 聚焦镜 R = 150 mm, θ = 16.7° 中阶梯光栅 79 gr/mm, $ {\theta }_{{\mathrm{B}}} $= 63.5°, γ = 7° 色散棱镜 Glass:H-ZF3, α =16° 
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表 2 系统公差设置明细
Table 2. Setting details of system tolerance
公差类型 参数 表面不规则度 ±0.2光圈 曲率半径 ±2光圈 元件/表面偏心 ±0.05 mm 元件/表面倾斜 ±0.05 mm 厚度 ±0.1 mm 折射率 0.001
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表 3 对光学性能影响最大的公差项
Table 3. Tolerances with greatest effect on optical performance
类型 表面 评价函数下降 表面不规则度 准直镜 4.9% 元件倾斜/X 离轴抛物镜 3.82% 表面倾斜/X 离轴抛物镜 3.81% 曲率半径 准直镜 2.59% 元件偏心/Y 准直镜 2.56%
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