Uniformity and isotropy of speckle pattern cause the doubled random error phenomenon in digital image correlation

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.