散斑质量评价的关键在于构建能够描述散斑特征参数与数字图像相关方法测量误差关系的模型。现今缺少描述散斑图案与其功率谱之间关系的理论分析模型。基于此,从随机过程分析角度出发,先构建了二值化散斑的自相关函数与散斑占空比、散斑半径、灰度值等参数的关系。依据Wiener-Khintchine定理得出了二值化散斑功率谱的理论解析形式。利用数值实验的方式对理论分析结果进行了验证。结果表明:理论推导的结果在功率谱主瓣以及其附近的几个旁瓣上与数值实验结果较吻合,功率谱主瓣极值与实验结果契合程度高。该模型可以应用于后续的散斑误差分析工作。

The key in the quality evaluation of the speckle is to construct model which can describe the relation between speckle pattern feature parameters and measurement error of digital image correlation method. Till date, no theoretical analysis model describing the relation between the speckle pattern and its power spectrum has been reported. To address this issue and considering the perspective of stochastic process analysis, the relations between the auto-correlation function of the binary speckle and parameters of speckle duty, speckle radius, and gray value are investigated herein. Furthermore, the theoretical analytical form of the binary speckle power spectrum is obtained according to the Wiener-Khintchine theorem. Finally, the theoretical analysis results are verified by numerical experiments. It is observed that the theoretically derived results are consistent with the numerical experiment results on the main lobe of the power spectrum and on several side-lobes nearby. Considering the power spectrum, the maximum value of the main spectrum is consistent with the experimental results. This model can be applied to subsequent speckle error analysis studies.