Fig. 1. Spectrum analysis of binary defocusing fringes. (a1)‒(a3) No defocusing; (b1)‒(b3) insufficient defocusing; (c1)‒(c3) appropriate defocusing; (d1)‒(d3) excessive defocusing

Fig. 2. Correlation between binary defocusing fringes and its second-order differential. (a) Insufficient defocusing; (b) appropriate defocusing; (c) excessive defocusing

Fig. 3. Phase error analysis. (a) 3D plot of phase error in the case of insufficient defocusing; (b) 3D plot of phase error in the case of excessive defocusing; (c) phase error of line 300 in Fig.3(a); (d) phase error of line 300 in Fig.3(b)

Fig. 4. Simulation results of correlation coefficient and phase error, as well as the comparison with reference [7]. (a) Correlation coefficient; (b) average phase error; (c) reference [7]

Fig. 5. Experimental setup

Fig. 6. Progressively defocused binary fringe pattern captured. (a) Twelve-step phase-shifting progressively defocused fringe patterns; (b) gray scale reduced fringe contrast

Fig. 7. Experimental results of the proposed method. (a) 3D plot of the correlation coefficients; (b) correlation coefficient of a cross-section of Fig. 7(a); (c) 3D plot of the phase errors; (d) phase error distribution of the corresponding cross-section

Fig. 8. Comparison between the proposed method and the method of reference [7]. (a) Evaluation result of defocus of experimental fringe patterns using the proposed method; (b) the corresponding results by reference [7]

Fig. 9. Four-step phase-shifting fringe patterns of group 4 projected on the object surface measured

Fig. 10. 3D plot of the phase value of the measured object obtained using group 4 fringe patterns and four-step phase-shifting algorithm

Fig. 11. Phase error and contours. (a1) Phase error of group 3; (a2) phase error of group 4; (a3) phase error of group 5; (b1) contour map of group 3; (b2) contour map of group 4; (b3) contour map of group 5