Using defocus-induced circle of confusion features for dust particle size measurement on mirrors
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摘要:
光学表面颗粒污染检测是保障空间望远镜成像性能的重要措施。传统颗粒污染检测常使用暗场散射显微镜拍摄颗粒图像，再对图像中颗粒外轮廓作外接圆计算颗粒尺寸。该方法要求拍摄过程严格对焦，对不规则形状的颗粒尺寸检测结果误差较大。为了提高检测镜面上微小颗粒尺寸的精度，消除对焦不准和颗粒形状差异带来的误差。本文提出利用离焦诱导的弥散圆检测颗粒尺寸的方法。利用颗粒尺寸与颗粒散射能量的对应关系，通过离焦将颗粒的暗场散射图像变成弥散圆。最后分析颗粒离焦弥散圆特征来测量颗粒的真实尺寸。该方法可以规避颗粒形状以及系统对焦程度对检测结果的干扰。实验结果表明：利用离焦弥散圆检测颗粒尺寸的方法在不同离焦量下都有较高的检测精度，相较于传统的使用暗场散射显微镜的方法，对于不规则形状颗粒尺寸的检测误差从平均58%降低到10.3%。验证了离焦弥散圆检测颗粒尺寸方法的可行性，并可以有效提高检测不规则颗粒尺寸的精度。
Abstract:Optical surface particulate contamination detection is critical to maintaining the imaging performance of space telescopes. Conventional approaches typically employ dark-field scattering microscopy to capture particle images, where particle size is estimated from the circumcircle of the particle’s contour. However, this method requires precise focusing during image acquisition and is prone to large errors when dealing with irregularly shaped particles. To address these limitations, this paper introduces a novel sizing method based on defocus-induced blur circles. By exploiting the relationship between particle size and its scattered light energy, the defocused dark-field scattering image of a particle is transformed into a blur circle, whose properties can be analyzed to determine the actual particle size. Unlike conventional contour-based measurements, the blur-circle approach is inherently less sensitive to particle shape irregularities and system defocus. Experimental validation demonstrates that the proposed method achieves high sizing accuracy across varying defocus distances. Compared with traditional dark-field scattering microscopy, the average measurement error for irregularly shaped particles is significantly reduced—from 58% to 10.3%. These results confirm both the feasibility and effectiveness of the blur circle method in improving measurement precision for irregular particulate contaminants.
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Key words:
- particle detection /
- dark-field scattering /
- point spread function /
- Mie scattering
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图 3 对焦下的颗粒散射（左）离焦下的散射（右）
Figure 3. Particle Scattering in Focus (Left); Defocused Scattering (Right)
图 6 不同标准微球颗粒弥散圆DN总值与离焦量关系
Figure 6. The relationship between the total DN value of the dispersion circle and the defocus amount for different standard microsphere particles.
图 7 标准颗粒（5 µm/10 µm）DN总值比与曝光值关系
Figure 7. Relationship Between DN-Total Ratio (5-µm/10-µm) and Exposure Time for Calibrated Particles
图 8 不同曝光值对尺寸检测结果的影响
Figure 8. The effect of different exposure values on size detection results.
图 9 标准微球与不规则颗粒尺寸检测结果
Figure 9. Size detection results of standard microspheres versus irregular particles.
表 1 不同颗粒在不同离焦量下的DN总值差异
Table 1. Differences in total DN values of different particles across various defocus amounts.
颗粒尺寸 最大相对偏差 变异系数 1 μm 4.6% 1.93% 5 μm 2.9% 1.31% 10 μm 2.5% 0.98% 15 μm 2.4% 0.97% 
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表 2 圆形与不规则颗粒检测结果
Table 2. Round and Irregular Particles Detection Results
圆形颗粒 不规则颗粒 轮廓像素 732 430 外接圆像素 793 2156 相对误差 4.2% 401.4%
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表 3 离焦检测与外接圆算法的误差水平
Table 3. Defocus Detection and Circumcircle Algorithm Error Level
弥散圆方法误差 外接圆方法误差 1 8% 54% 2 0.5% 79% 3 10% 40% 4 20% 54% 5 13% 67% 平均误差水平 10.3% 58%
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