Fig. 1. Illustration of the intensity diffusion. (a) Designed pattern. (b) Designed pattern without the central area. (c) The image of (a). (d) The image of (b). (e) Cross sections of the patterns in (a) and (b). (f) Cross sections of the images in (c) and (d).

Fig. 2. Fringe distortions induced by intensity diffusion, gamma distortion, high-order harmonics, and image saturation.

Fig. 3. Illustration of the TPU methods based on additional fringe patterns.

Fig. 4. Illustration of the parameters in IDM.

Fig. 5. Flow chart of the proposed method. (a) Procedures of establishing IDM. (b) Process of IDCA.

Fig. 6. Cross sections of the fringes distorted by the intensity diffusion and the corresponding results corrected by IDCA. (a) Fringe with 40% of maximum illumination intensity. (b) Fringe with 50% of maximum illumination intensity. (c) Fringe with 60% of maximum illumination intensity. (d) Fringe with a fringe frequency of 32. (e) Fringe with a fringe frequency of 64. (f) Fringe with a fringe frequency of 128.

Fig. 7. 3D reconstruction results of the standard plane in the four cases. (a) Normal image of the standard plane. (b) 3D reconstruction result in the case of IDCA[−,−]. (c) 3D reconstruction result in the case of IDCA[−,+]. (d) 3D reconstruction result in the case of IDCA[+,−]. (e) 3D reconstruction result in the case of IDCA[+,+]. (f) Cross sections of the reconstructed planes. (f) The local enlargement of the cross sections.

Fig. 8. 3D reconstruction results of the standard sphere in the four cases. (a) Normal image of the standard sphere. (b) 3D reconstruction result in the case of IDCA[−,−]. (c) 3D reconstruction result in the case of IDCA[−,+]. (d) 3D reconstruction result in the case of IDCA[+,−]. (e) 3D reconstruction result in the case of IDCA[+,+]. (f) Cross sections of the reconstructed 3D profile. (f) The local enlargement of the cross sections.

Fig. 9. 3D measurement accuracy for the plane and sphere with different illumination intensities and fringe frequencies. (a) Reciprocals of RMSE with the increasing illumination intensity. (b) Gradient of 1/RMSE with the increasing illumination intensity. (c) Reciprocal of RMSE with the increasing fringe frequency. (d) Gradient of 1/RMSE with the increasing fringe frequency.

Fig. 10. Fringe images in the scenes with high contrast.

Fig. 11. Unwrapped phase maps of the panda and zebra models. (a)–(d) Unwrapped phase maps of the panda model in the four cases. (e)–(h) Unwrapped phase maps of the zebra model in the four cases.

Fig. 12. 3D reconstruction results of the steel plate. (a) Normal image of the steel plate. (b) Cross sections of the fringes in the high-reflectivity areas. (c) Image of the steel plate with fringes. (d) 3D reconstruction result in the case of IDCA[−,−]. (e) 3D reconstruction result in the case of IDCA[−,+]. (f) 3D reconstruction result in the case of IDCA[+,−]. (g) 3D reconstruction result in the case of IDCA[+,+].

Table 1. Accuracies of the 3D Measurement Results in Four Combinations

Table 2. Accuracy Improvement with Different Fringe Frequencies

Table 3. Number of Iterations in the IDCA and the Corresponding RMSEs