Random Errors in Digital Image Correlation Due to Matched or Overmatched Shape Functions

The random errors of subset-based digital image correlation due to the use of matched or overmatched shape functions are investigated. Governing formulations that can quantitatively predict these random errors are derived. Theoretical results reveal that all these random errors are in linear proportion to the noise level of the speckle images and inverse proportion to the sum of square of subset intensity gradients of the interrogated subsets. However, for matched or overmatched cases, zero-order and first-order shape functions give rise to the same magnitude of random errors, while the random errors induced by second-order shape functions are approximately twice that resulted from the regularly used first-order shape functions. The correctness of the derived theoretical formulations is verified using numerical tests, and also shows good accordance with previously reported experimental results.