Fig. 1. Digital speckle images generated from different speckle shapes in Table 1

Fig. 2. Algorithm for generating speckle coordinates

Fig. 3. Distribution of two speckles. (a) Gray intensity overlap curves of two Gaussian speckles at different distances; (b) occupancy of adjacent speckle pixels

Fig. 4. Speckle pattern construction process

Fig. 5. MIG analysis of speckle patterns with different speckle radii and EMSD

Fig. 6. Standard deviation of interpolation errors. (a) Bicubic interpolation; (b) bicubic B-spline interpolation

Fig. 7. Properties of Gaussian speckle patterns. Images with (a) proposed speckle coordinates, (b) random speckle coordinates, and (c) proposed speckle coordinates with fixed speckle center intensity at 255, respectively; (d)‒(f) intensity gradient in the x-direction of Fig. 7(a)‒(c); (g)‒(i) ZNCC matrix and central column curves of the central 50 pixel×50 pixel in Fig. 7(a)‒(c) with a 21 pixel×21 pixel subset

Fig. 8. Gaussian speckle images generated by different methods

Fig. 9. Analysis results of zero-order displacement. (a) Mean bias error and (b) standard deviation with a 9 pixel×9 pixel subset; (c) mean bias error and (d) standard deviation with a 15 pixel×15 pixel subset

Fig. 10. Average numbers of feature points. (a) Subset size of 9 pixel×9 pixel; (b) subset size of 15 pixel×15 pixel

Fig. 11. Effect of noise variance on displacement. (a) Mean bias error; (b) standard deviation

Fig. 12. Characteristics of the second-order displacement fields generated by Eq. (3) and Eq. (4). (a)(d) Displacement vectors from the deformed images to the reference images; (b)(e) displacement fields in the x-direction; (c)(f) deformed images

Fig. 13. RMS of displacement residuals in the x-direction. (a) Eq. (3); (b) Eq. (4)

Fig. 14. Distributions of displacement residuals for Eq. (4). (a) 9 pixel×9 pixel subset; (b) 15 pixel×15 pixel subset

Fig. 15. Analysis of grating displacement field. (a) Grating displacement field and its corresponding Fourier spectrum in the x-direction; displacement and Fourier spectrum calculation results for sample A with subset sizes of (b) 9 pixel×9 pixel, (c) 15 pixel×15 pixel, and (d) 31 pixel×31 pixel

Fig. 16. Grating displacement field calculation results with a 9 pixel×9 pixel subset. (a) Sample B; (b) sample C; (c) sample D

Fig. 17. Rigid-body translation platform and samples

Fig. 18. SPD system and captured speckle images

Fig. 19. Measured displacement fields of sample A with a subset size of 15 pixel×15 pixel. (a) x direction; (b) y direction

Fig. 20. Distributions of fitting residuals for displacement fields in the x-direction with different subset sizes. (a) 9 pixel×9 pixel; (b) 15 pixel×15 pixel; (c) 31 pixel×31 pixel

Fig. 21. Displacement fields with a subset size of 9 pixel×9 pixel in the y-direction for different samples. (a) Sample A; (b) sample B; (c) sample C; (d) sample D