Wave plates are polarizing devices with specific birefringence and play a vital role in optical systems. The optical axis azimuth angle and phase retardation are two key parameters of the wave plate, directly determining the performance of the optical system. Therefore, it is of great significance to rapidly and precisely measure the optical axis azimuth angle and phase retardation. Researchers worldwide have proposed numerous single-point measurement methods for wave plates, but full-field measurement of wave plates has not been achieved. In this study, we develop a full-field measurement method and system for wave plates based on polarization-sensitive digital speckle pattern interferometry (PS-DSPI). We obtain the speckle interferogram by beam-expanding illumination of the wave plate to be measured. We position the optical axis azimuth angle by analyzing the speckle interferogram of polarization states. We measure the phase retardation through spatial carrier phase extraction and image processing techniques. We analyze the error of full-field phase retardation. Laser beam expansion causes the light to enter the wave plate at an oblique incidence, which is an important error source. The method proposed in this study is significant for the full-field and rapid measurement of wave plate performance and extends the application range of digital speckle pattern interferometry (DSPI) in polarization.

The measured setup of PS-DSPI system is shown in Fig. 1. The emitted light first is divided into object light and reference light by the beam splitter (BS). The object light passes through a half-wave plate (HWP), which is used as a polarization direction rotator. The polarization-adjustable light passes through the beam expander and illuminates the quarter-wave plate (QWP) to be measured. A polarization-maintaining metal plate is placed behind the QWP, and its scattered light is imaged on the target surface of the charge coupled device (CCD) through the imaging lens and the aperture. The reference light is coupled to a polarization-maintaining fiber (PMF) through a fiber coupler for transmission into the optical path and interferes with the object light to form a speckle interferogram in the form of an intensity recorded by a CCD camera, which is transmitted to a computer (PC) for calculation. A stepper motor is used to drive the HWP rotation to rotate the polarization direction of the incident light with a single step of 1.0° and a rotation scanning angle range of 0°?180°. We obtain the speckle interferogram by beam-expanding illumination of the wave plate to be measured. The processes of applying the PS-DSPI system to position the optical axis azimuth angle of the wave plate and solve the birefringent phase retardation are shown in Fig. 2. We control the polarization scanning angle to rotate from 0° to 180° by the HWP. We collect 180 speckle interferograms. We use the speckle interferograms acquired by the PS-DSPI system to position the optical axis azimuth angle of the wave plate. Interferograms with different polarization angles have diverse light intensities. We define the polarization angle at the maximum light intensity value as the fast axis (o light), and the minimum as the slow axis (e light). We apply the spatial carrier phase extraction technique to calculate the birefringence phase retardation of the wave plate along the optical axis (fast axis) and its orthogonal direction (slow axis). Finally, we obtain the full-field phase retardation of the wave plate by phase filtering and phase unwrapping.

The wave plate to be measured in the experiment is a standard nine-order QWP. In Fig. 4, the maximum light intensity value is at 150°, so the polarization scanning angle at 150° is determined as the fast axis azimuth angle of the wave plate. Since the interferograms recorded by the CCD camera are the imaging information of the scattered light, the light passes through the wave plate to be measured twice (incident and reflected). We select two interferograms with a 45° difference in the polarization angles as the fast and slow axes. The minimum light intensity value at 105° is the slow axis azimuth angle. We can calculate the phase retardation of the wave plate by subtracting the slow axis azimuth angle (105°) from the fast axis azimuth angle (150°). The results are shown in Figs. 9 and 10. The phase retardation tends to decrease from the center of the expanded beam to the edge, with a maximum value of 1.495 rad and a minimum value of 1.384 rad. Laser beam expansion leads to an oblique incidence of light into the wave plate to be measured. The incident angle is not a particular value but within a certain range. We establish a theoretical model of the phase retardation and birefringence caused by the oblique incident beam on the wave plate. We apply the oblique incidence error model to correct the measurement results of the wave plate. The actual incident angle range is 24.5°?29.1°. Based on the phase measurement results of 1.495 rad to 1.384 rad, we fit the phase measurement results using the least-squares method, as shown in Fig. 15. The corrected curve is indicated by the green dashed line in Fig.15. The maximum phase value is 1.605 rad. According to the size of the wave plate and the beam expansion distance, the corrected oblique incidence angle range is ±0.96°. Therefore, after error correction, the full field phase retardation range of the wave plate is 1.588?1.605 rad. The comparison before and after correction is shown in Fig. 16.

In this study, based on the current demand for accurate full-field measurement of wave plates, we propose a full-field birefringence measurement method for wave plates based on PS-DSPI. We theoretically analyze and experimentally verify the phase retardation characteristics of the birefringent element in the PS-DSPI system. We analyze the oblique incidence of light due to laser beam expansion in the system. We test the method through a standard QWP. We measure two important optical parameters, the optical axis azimuth angle of the wave plate and the full-field birefringence phase retardation. We analyze the error of the phase retardation caused by the oblique incidence of light. The experimental results demonstrate that, using this method, the accuracy of determining the azimuth angle of the wave plate’s full-field optical axis is 1.0°, and the theoretical resolution of phase retardation measurement reaches 0.012 rad. After compensation for the oblique incidence model, the full-field measurement results for the tested QWP (marked 1.571 rad) range from 1.588 to 1.605 rad. The basis of the work in this article meets the requirements of fast, high-precision, and full-field measurement.