Fig. 1. Basic measurement principle of the proposed method

Fig. 2. Computer simulated brightness at different points. (a) Imaging point coinciding with the projection point; (b) imaging point is right in the middle of the two projection points; (c) other points

Fig. 3. Computer fitted standard deviation. (a) Imaging point coinciding with the projection point; (b) imaging point is right in the middle of the two projection points; (c) other points

Fig. 4. Experimental flow chart

Fig. 5. Brightness curve and standard deviation curve of a point. (a) Brightness distribution of a point; (b) standard deviation curve of a point

Fig. 6. Fitted curve for quadratic fitting after median filtering. (a) Quadratic fitting after median filtering; (b) regional zoom

Fig. 7. Fitted curve for Gaussian fitting after median filtering. (a) Gaussian fitting after median filtering; (b) regional zoom

Fig. 8. Fitted curve of the quadratic fitting. (a) Quadratic fitting; (b) regional zoom

Fig. 9. Fitted curve of the Gaussian fitting. (a) Gaussian fitting; (b) regional zoom

Fig. 10. Fitting curve between distance and maximum serial number

Fig. 11. Measurement results on steps. (a) Step model; (b) modulation maximum serial number in the first line; (c) modulation maximum serial number in the first column; (d) calculation result; (e) the 200th line of Fig.11 (d); (f) fitting curve between distance and maximum serial number

Fig. 12. Plane measurement results. (a) Measured plane; (b) depth measurement result; (c) measurement result in the 200th line; (d) three-dimensional structure

Fig. 13. Comparison of the proposed method with modulation measuring profilometry. (a) Distribution of point brightness of the proposed method; (b) distribution of point brightness of modulation measuring profilometry (step N=3); (c) distribution of point brightness of modulation measuring profilometry (step N=6); (d) standard deviation curve of the proposed method; (e) modulation curve of modulation measuring profilometry (step N=3); (f) modulation curve of modulation measuring profilometry (step N=6); (g) measurement result of the proposed method; (h) measurement result of the modulation measuring profilometry (step N=3); (i) measurement result of the modulation measuring profilometry (step N=6); (j) measurement result at the 200th line of the proposed method; (k) measurement result at the 200th line of the modulation measuring profilometry (step N=3); (l) measurement result at the 200th line of the modulation measuring profilometry (step N=6)

Fig. 14. Measurement results of the proposed method