In digital photoelasticity, the stress field contains isoclinic information of the main stress direction angle and isochromatic information of the main stress difference, both of which are indispensable in stress calculation, so it is very important to obtain isoclinic and isochromatic information quickly and accurately. The ten-step phase shift method is the most widely used one, as it solves the problem of isoclinic and isochromatic line coupling in the six-step phase shift method for monochromatic light. Although the ten-step phase shift method has higher measurement accuracy, its efficiency is lower due to the acquisition of four white light incident images. Some researchers have improved the image acquisition devices, such as expensive polarization sensors, to increase efficiency. This paper proposes a minimal phase shift scheme that satisfies the requirements of calculating an isoclinic line in a planar polarized light field and an isochromatic line in a circularly polarized light field, so as to balance measurement accuracy and efficiency.

In photoelasticity experiments, the planar polarized light field with white light incidence has more advantages than the circularly polarized light field with monochromatic light incidence, and the isoclinic line calculated based on the former field effectively avoids the problem of coupling with isochromatic line. Therefore, in this paper, under the planar polarized light field with white light incidence, the isoclinic line is calculated by reducing photoelastic images from 4 to 3, which effectively avoids the problem of isoclinic and isochromatic line coupling and quarter wave plate mismatch errors. For the problem of low efficiency of the ten-step phase shift method caused by acquiring massive images, this paper reduces photoelastic images from 6 to 3, so as to calculate isochromatic line under the circularly polarized light field with monochromatic light incidence, which solves the problem of low efficiency due to image acquisition. In the next simulation experiment, this paper calculates the isoclinic and isochromatic lines under different noise levels to evaluate their anti-noise performance. In addition, the paper calculates isoclinic and isochromatic lines under different azimuth errors to evaluate the anti-jamming capability of phase shift errors. Furthermore, the effectiveness of the proposed method is verified by a radially compressed polycarbonate disc.

Firstly, in view of the problem of isoclinic and isochromatic line coupling caused by monochromatic light in the traditional six-step phase shift method and the low data acquisition efficiency in the ten-step phase shift method, a six-step hybrid phase shift method is designed, which changes the 6+4 measurement method in the ten-step phase shift method to 3+3 measurement method. The feasibility of this method is verified by real experimental data. In addition, compared with the traditional six-step phase shift method, the six-step hybrid phase shift method effectively avoids the problems of isoclinic and isochromatic line coupling and quarter wave plate mismatch errors (Fig. 4); compared with the ten-step phase shift method, the method has an average deviation of isoclinic line of about 0.01 rad and an average deviation of isochromatic line of about 0.09 rad (Table 8). Furthermore, the proposed method reduces image quantity and improves the acquisition efficiency by 40% while ensuring measurement accuracy (Fig. 5-Fig. 8). Secondly, in order to verify the noise immunity and phase shift error immunity of the six-step hybrid phase shift method, the deviations of isoclinic and isochromatic lines calculated under different noise levels are generally comparable to those of the ten-step phase shift method (Table 5), and the deviations of isoclinic line calculated under different azimuth errors are consistent with those of the ten-step phase shift method, which indicates that this method has the same immunity to phase shift error interference as the ten-step phase shift method (Table 6). The deviations of the isochromatic line calculated under different azimuth errors are approximately twice as large as those of the ten-step phase shift method (Table 7). The reason for this is that the ten-step phase shift method uses six images to calculate the isochromatic line, while the proposed method only requires three images, but it loses some effective information to a certain extent, so the resistance to phase error interference of the proposed method is relatively weak compared with that of the ten-step phase shift method.

This paper analyzes the disadvantages of the six-step and ten-step phase shift methods and proposes an optimized six-step hybrid phase shift method. The paper uses three photoelastic images of a planar polarized light field with white light incidence and three photoelastic images of a circularly polarized light field with monochromatic light incidence to calculate isoclinic and isochromatic lines separately and balance the efficiency and accuracy of the six-step and ten-step phase shift methods. Through the simulation experiment of the radially compressed disc, it is verified that the proposed method has excellent anti-noise and anti-interference abilities for phase shift errors. The experimental results of the radially compressed polycarbonate discs show that compared with the traditional six-step phase shift method, the proposed method avoids the problem of isoclinic and isochromatic coupling. Furthermore, the features of the isoclinic and isochromatic images calculated by the proposed method are consistent with those calculated by the ten-step phase shift method. The average deviation of the isoclinic line is 0.01 rad, and the average deviation of the isochromatic line is 0.09 rad. The proposed method reduces the number of images, and the acquisition efficiency is improved by 40%. The effectiveness of this method is verified by repeated experiments under the conditions of changing load and disc diameter.