(a) True value of the displacement gradient in x-direction (red) and random error of (blue), i. e., the standard deviation of in y-direction. Dotted vertical lines indicate the four numbered sections of the displacement field. Sections I and IV are characterized by a constant displacement value, while sections II and III have a constant second-order displacement gradient. Subset size S = 20 × 20 pixel. The dashed lines show an alternative displacement field with a constant first-order gradient of 10 × 10⁴ με in sections III and IV. (b) DSP result d_x in x-direction. The displacement field is evaluated from simulated speckle patterns.