Two-step phase shifting profilometry based on Lissajous ellipse fitting technique

Phase shifting profilometry (PSP) is an effective technique to reconstruct the three-dimensional shape of object. In general, PSP needs three or more fringe patterns with phase-shifting accurately known to extract the phase distribution of objects. Therefore, the scene and the test objects should remain stationary during capturing the fringe patterns. However, the phase shifts may be unknown in an actual PSP measurement system, especially when measuring the moving object, that is, the phase-shift error may be introduced during the obtaining of the phase-shifting fringe patterns of moving object. In the dynamic measurement scenario, the use of fewer fringe patterns can realize the faster measurement speed and suppress the phase shift error introduced by the moving object. In this paper, a two-step PSP algorithm is proposed based on Lissajous ellipse fitting (LEF). The proposed method uses only two fringe patterns to extract the phase distribution of the object and can suppress the phase shift error caused by the moving object. However, in a practical PSP system, the spatiotemporally varying background intensity and modulation also significantly affect the phase accuracy extracted by LEF, and thus three error-suppressing methods are proposed to reduce the phase error caused by the non-uniform background intensity and modulation. In order to verify the effectiveness of the three error-suppressing methods, we analyze and compare their performances of error suppression under different background intensities and modulations. The advantages of three error-suppressing methods can be summarized as follows. 1) The mean and modulation correction technique has greater advantage than the other two when the background intensity and modulation vary with time.


Abstract
Phase shifting profilometry (PSP) is an effective technique to reconstruct the three-dimensional shape of object.In general, PSP needs three or more fringe patterns with phase-shifting accurately known to extract the phase distribution of objects.Therefore, the scene and the test objects should remain stationary during capturing the fringe patterns.However, the phase shifts may be unknown in an actual PSP measurement system, especially when measuring the moving object, that is, the phase-shift error may be introduced during the obtaining of the phase-shifting fringe patterns of moving object.In the dynamic measurement scenario, the use of fewer fringe patterns can realize the faster measurement speed and suppress the phase shift error introduced by the moving object.In this paper, a two-step PSP algorithm is proposed based on Lissajous ellipse fitting (LEF).The proposed method uses only two fringe patterns to extract the phase distribution of the object and can suppress the phase shift error caused by the moving object.
However, in a practical PSP system, the spatiotemporally varying background intensity and modulation also significantly affect the phase accuracy extracted by LEF, and thus three error-suppressing methods are proposed to reduce the phase error caused by the non-uniform background intensity and modulation.In order to verify the effectiveness of the three error-suppressing methods, we analyze and compare their performances of error suppression under different background intensities and modulations.The advantages of three errorsuppressing methods can be summarized as follows.1) The mean and modulation correction technique has greater advantage than the other two when the background intensity and modulation vary with time.2) When the background intensity and modulation are relevant to pixel position and the number of fringe patterns, the empirical mode decomposition normalization can more effectively suppress the influence of the non-uniform background intensity and modulation.
In experiment, a two-step phase-shifting dynamic measurement based on LEF is conducted.Compared with the traditional PSP which needs at least three fringe patterns, the two-step PSP algorithm successfully extracts the phase with only two fringe patterns and suppresses the phase shift error caused by the motion of the object.Compared with Fourier transform profilometry (FTP), the two-step PSP algorithm can obtain very accurate phase distribution and retain many phase details.

12 图 2 Fig. 2 .
Fig. 2. Simulation results of LEF method under the uniform background intensity and modulation: (a) The fringe pattern; (b) the phase distribution; (c) the phase error.

Fig. 7 .Fig. 8 .
Fig. 7. Phase error results of 2-step PSP based on the normalized LEF under different conditions.

图 9 Fig. 9 .图Fig. 10 . 5 图
Fig. 9. Measurement results of ten-step phase shifting method: (a) Test object; (b) fringe pattern of the test object; (c) the reference phase distribution based on ten-step phase-shifting method; (d) the enlarged phase details in red rectangular of Fig. (c).

5 图
Fig. 12. Experimental results of moving objects: (a) The extracted phase by three-step phase shifting method; (b) the phase obtained from two-step PSP based on Gaussian filter normalization; (c) the phase estimated from two-step PSP based on EMD normalization; (d) the phase estimated from two-step PSP based on the mean value and modulation.