Impact of cryogenic mirror deformation on asymmetric spatial heterodyne interferometers and its correction
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摘要:
针对星载长波红外多普勒非对称空间外差干涉仪在低温真空环境下热致面型形变引起的干涉条纹畸变及风速反演误差问题，开展了像差机理分析与相位补偿方法研究。首先，基于光机热集成分析，建立−113 °C均匀稳态温度载荷下包含柔性胶层的光机有限元模型，并分析光学系统的面形变化，并采用 Zernike 多项式对面形误差进行拟合与建模，揭示热致面型形变主要引入球差和像散等低阶像差，然后分析上述像差通过引入附加光程差导致干涉条纹弯曲、对比度下降及空间分布不均匀，从而降低相位提取精度并引入风速反演误差。最后，提出基于 Zernike 多项式的相位域补偿方法，对干涉相位进行校正, 抑制热致面型形变对系统性能的影响。仿真结果表明：该方法能够有效恢复干涉条纹的空间特性，风速反演误差降幅约为 62.5%，从而抑制热致面型形变对系统性能的影响。保证了系统在极端低温环境下的测风精度。
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关键词:
- 多普勒非对称空间外差干涉仪 /
- 镜面形变 /
- Zernike多项式 /
- 相位域补偿 /
- 干涉条纹
Abstract:To address the problem of interference fringe distortion and wind velocity retrieval errors caused by thermally induced surface deformation in a spaceborne long-wave infrared Doppler asymmetric spatial heterodyne interferometer operating in a low-temperature vacuum environment, a systematic study on aberration mechanisms and phase compensation methods was carried out. First, based on integrated opto-mechanical-thermal analysis, a surface deformation model of the optical system under the −113 °C operating condition was established. The surface errors were fitted and modeled using Zernike polynomials, revealing that thermally induced surface deformation primarily introduces low-order aberrations such as spherical aberration and astigmatism. Subsequently, the mechanism by which these aberrations generate additional optical path differences was analyzed. The results show that they lead to fringe bending, reduced contrast, and non-uniform spatial distribution, thereby degrading phase extraction accuracy and introducing wind velocity retrieval errors. Finally, a phase-domain compensation method based on Zernike polynomials was proposed to correct the interferometric phase and suppress the influence of thermally induced surface deformation on system performance. Simulation results demonstrate that the proposed method effectively restores the spatial characteristics of the interference fringes, reducing the wind velocity retrieval error by approximately 62.5%. This effectively mitigates the impact of thermal surface deformation and ensures wind measurement accuracy under extremely low-temperature conditions.
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图 7 −113 °C均匀稳态温度载荷下干涉仪系统变形云图
Figure 7. Deformation contour of the interferometer system under a uniform steady-state temperature load of −113 °C
图 8 −113 °C均匀稳态温度载荷下透镜表面S6a、S6b、S9a和S9b的面形变化。(a)6a;(b)6b;(c)9a;(d)9b
Figure 8. Surface deformations of lens surfaces S6a, S6b, S9a, and S9b under a uniform steady-state temperature load of −113 °C
图 10 工作温度-113.15 °C干涉条纹
Figure 10. Interference fringes at an operating temperature of −113.15 °C
图 11 工作温度-113.15 °C干涉条纹风速反演
Figure 11. Wind velocity retrieval from interference fringes at an operating temperature of −113.15 °C
表 1 有限元模型材料参数
Table 1. Material Parameters of the Finite Element Model
Materials, Density/
(g·cm−3)Elastic
Modulus/
(Gpa)Poisson's
Ratio/(u)Coefficient of thermal expansion/
(×10−6·C−1)Silicon 2.329 130 0.28 2.6 Irg202 4.6 19 0.3 20 Irg204 4.7 18 0.3 22 Znse 5.27 70 0.28 7.3 Tc4 4.44 109 0.29 8.8 4j32 8.1 150 0.29 0.5 RTV566 1.49 0.005 0.49 200 
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表 2 -113°C下各光学镜片RMS、PV变化
Table 2. RMS and PV Variations of Optical Lenses at -113 °C
表面 RMS P-V 表面 RMS P-V S1a 4.86E-05 1.68E-04 S6a 6.47E-05 2.19E-04 S1b 2.66E-05 8.75E-05 S6b 5.42E-05 1.83E-04 S2a 2.05E-05 8.35E-05 S7a 1.62E-05 5.89E-05 S2b 2.63E-06 9.97E-06 S7b 9.96E-06 3.34E-05 S3a 4.80E-05 1.02E-04 S8a 1.02E-06 3.71E-06 S3b 3.10E-05 1.09E-04 S8b 7.20E-06 3.24E-05 S4a 3.20E-05 1.22E-04 S9a 3.14E-05 9.86E-05 S4b 3.60E-05 4.10E-05 S9b 3.77E-05 1.19E-04 S5a 3.20E-05 1.66E-04 S10a 3.46E-06 1.97E-05 S5b 4.80E-05 1.08E-04 S10b 1.73E-06 6.08E-06 注：a为前表面；b为后表面。
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