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摘要:
残余应力是光学元件的一个重要性能参数，对光学元件的制造和使用意义重大。光学元件残余应力的无损检测方法可粗略概括为两大类：一类是基于应变的测量方法，包括X射线衍射法、Stoney曲率法和显微拉曼光谱法，这些方法基于晶体和弹性力学分析方法，发展成熟、应用广泛；另一类是基于应力双折射效应的测量方法，包括数字光弹法、光弹调制器法和偏振光腔衰荡法，都是对残余应力导致的双折射相位差的测量，具有更直接的光学关联性、测量精度高的特点。本文归纳了光学元件残余应力测量的几种常见方法的测量原理、测量精度和应用场景，对比了它们的性能并分析了它们之间的关联性，以期建立起光学元件残余应力无损检测的宏观印象。
Abstract:Residual stress is an important performance indicator of optics, which is of great significance to the fabrications and applications of optical components. Residual stress measurement methods of optics can be summed up into two categories: methods based on the strain measurement and on the stress induced birefringence measurement, respectively. The strain based methods, which are built upon crystal dynamics and elastic mechanics, including X-ray diffraction (XRD), Stoney curvature method, and micro-Raman spectroscopic method, are well developed and widely used. Methods based on the measurements of birefringence phase retardation induced by residual stress, including digital photoelasticity method, photoelasticitic modulator (PEM) method and polarization-dependent cavity ring-down method, show a higher precision. The principles, measurement precisions and application scenarios of these residual stress measurement methods are summarized in this overview. Comparisons between the performances of these methods are performed and correlations between them are analyzed in detail.
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Key words:
- optics /
- residual stress /
- birefringence /
- strain
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Overview: Residual stress is an important performance indicator of optics, which is of great significance to the fabrications and applications of optical components. Residual stress measurement methods of optics can be summed up into two categories: methods based on strain measurement and on stress induced birefringence measurement, respectively.
The strain based methods, which are built upon crystal dynamics and elastic mechanics, including X-ray diffraction (XRD), Stoney curvature method, and micro-Raman spectroscopic method, are well developed and widely used. XRD method is the standard residual stress measurement for crystal materials, which is based on the Bragg diffraction of X-rays caused by crystalline lattice. By comparing the lattice distance of stressed and stress-free materials, the residual stress can be precisely determined. The uncertainty of XRD is about ±10 MPa. Stoney curvature method is commonly used for evaluating residual stress in optical thin films. The difference of thermal expansion coefficients between coatings and substrate results in a substrate curvature change after deposition. The measurement precision of Stoney curvature method is about several tens of MPa and is greatly influenced by film/substrate thickness ratio and overall stress uniformity. Micro-Raman spectroscopic method is based on a liner relationship between Raman shift and residual stress of Raman-sensitive materials. The determination of residual stress requires corresponding stress-free reference materials. The measurement precision of Raman spectroscopic method can reach ±10 MPa when the temperature is stabilized.
Methods based on residual stress induced birefringence phase retardation, including digital photoelasticity method, photoelasticitic modulator (PEM) method and polarization-dependent cavity ring-down (CRD) method, show a higher measurement precision. Digital photoelasticity method which combining polariscope and CCD image processing, is convenient for stress birefringence mapping. Analyzing of isoclinic fringe and isochromatic fringe is key to high precision measurement of birefringence phase difference. The measurement precision of ±0.03 MPa is reached. PEM method is based on periodic modulation of incident polarization in polariscope. Double detection channels and differential data processing scheme improve the measurement precision to ±0.2 kPa. Polarization-dependent CRD method is newly adopted to the measurement of residual stress birefringence of fused silica substrates. Intracavity birefringence caused s- and p- polarization of ring-down decays to oscillate with frequency linearly related to the birefringence phase difference. Polarization-dependent CRD method reaches a measurement precision of ±0.03 kPa, the highest precision for residual stress measurement of optical materials reported to date.
The principles, measurement precisions and application scenarios of these residual stress measurement methods are summarized in this overview. Comparisons between the performances of these methods are performed and correlations between them are analyzed in details.
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图 4 数字光弹法原理图和测量示例图。
Figure 4. Principle of digital photoelasticity and measuring example.
表 1 几种光学元件残余应力无损测量方法对比
Table 1. Comparisons of non-destructive residual stress measurement methods of optics
测量方法 适用元件 参考样品 测量 测量精度 横向分辨率 穿透深度 XRD 单晶、多晶、微晶材料元件 需要无应力样品参考 正应力，切应力 ±10 MPa < 10 μm < 30 μm Stoney曲率法 薄膜元件 不需要参考 等双轴正应力 ±10% —— —— 拉曼光谱法 拉曼活性光学材料 需要无应力样品参考 双轴正应力 ±10 MPa < 1 μm 不限 数字光弹法 透明光学材料(透射测量) 不需要参考 主应力差，切应力 ±0.03 MPa < 12 μm 不限 光弹调制器法 透明光学材料(透射测量) 不需要参考 主应力差 ±0.2 kPa < 1 mm 不限 偏振光腔衰荡法 透明光学材料(透射测量) 不需要参考 主应力差 ±0.03 kPa < 1 mm 不限 
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