Abstract For subset-based digital image correlation, the random error of second-order shape function roughly doubles that of first-order shape function, termed doubled random error phenomenon. In this work, we suggest that the fundamental cause of this phenomenon is the uniformity and isotropy of speckle pattern. Specially, we prove that the ratio of random error of second-order shape function to that of first-order shape function, from a view of statistic, is expected to be 7 / 2 ( ≈ 1.87), which is quite close to the empirical value 2. Numerical experiments demonstrate the correctness of propose theoretical analysis.

中文翻译：

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散斑图案的均匀性和各向同性导致数字图像相关中的双随机误差现象

摘要 对于基于子集的数字图像相关，二阶形状函数的随机误差大约是一阶形状函数的两倍，称为双倍随机误差现象。在这项工作中，我们认为这种现象的根本原因是散斑图案的均匀性和各向同性。特别地，我们证明了二阶形状函数的随机误差与一阶形状函数的随机误差之比，从统计的角度来看，预计为 7 / 2 (≈ 1.87)，非常接近经验值2。数值实验证明了提出的理论分析的正确性。