Using defocus-induced circle of confusion features for dust particle size measurement on mirrors

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.