Results and Discussions To verify the feasibility and accuracy of the proposed method, this paper establishes a monocular laser speckle projection system (Fig. 5). Firstly, the extrinsic parameters of the monocular laser speckle projection system are calibrated according to the aforementioned process. Then, the corresponding speckle points in the camera images are projected to the virtual imaging plane of the projector, and the offset error of corresponding points is calculated. The average offset errors mainly vary from 0.10 pixel to 0.18 pixel. The projection points of corresponding speckle points on the virtual imaging plane tend to be one point. The result shows that the calibration accuracy of the rotation matrix and the translation vector is high. Next, fourteen displacement experiments are further conducted in the range of 2-9 mm. The measured curve is basically consistent with the ideal curve (Fig. 7). The measurement errors of displacement are less than 0.16 mm. Furthermore, we conduct the 3D reconstruction experiment of standard spheres with known geometric parameters. The radius measurement errors of the two standard spheres are 0.0916 mm and 0.1274 mm, respectively. Their root-mean-square (RMS) errors are less than 0.1346 mm (Table 1). Finally, the ORBBEC's Astra-Pro is selected to demonstrate the depth measurement accuracy of the proposed method. Regardless of the average offset error or the depth distribution range, the plane reconstruction results of the proposed method are significantly better than those of Astra-Pro (Table 2). Simultaneously, the depth variation of the target model reconstructed by the method is smoother, and its density of point cloud is larger (Fig. 11). Hence, it can be easily concluded that the proposed method is able to calibrate the monocular laser speckle projection system effectively and achieve high-precision depth measurement.

Laser speckle projection systems have been widely used in various fields, including but not limited to three-dimensional (3D) reconstruction, industrial detection, and gesture recognition. According to the number of infrared cameras, laser speckle projection systems are generally divided into two categories: the binocular mode and the monocular mode. A binocular laser speckle projection system consists of a laser speckle projector and two infrared cameras. The feature information provided by random speckle patterns is sufficient to match images in textureless areas, which significantly improves the accuracy and stability of binocular stereo vision systems. Moreover, speckle patterns in the infrared spectrum minimize the impact of the ambient light. However, the cost of binocular laser speckle projection systems is typically high, and the calibration process is complex. Compared with their binocular counterparts, monocular laser speckle projection systems are more compact and cost-effective. Due to the lack of reference speckle patterns, monocular laser speckle projection systems generally use a precise range finder to capture speckle images at different standard distances in advance. The measurement process is complex, and the deviation of the optical axis cannot be corrected online. To solve the aforementioned problems, this paper proposes a calibration method for the extrinsic parameters of monocular laser speckle projection systems. The virtual speckle image of the projector is generated by calculating the pose relationship between the infrared camera and the laser speckle projector. Only a calibration board with corner features is required in the proposed calibration process, rather than the precise range finder. With this method, a monocular laser speckle projection system becomes equivalent to a binocular stereo vision system with speckle images.

First, a simple calibration board with corner features is designed. These features only occupy a small part of the calibration board, which leaves sufficient area for the speckle pattern. The plane equation of the calibration board in the camera coordinate system is calculated by extracting the coordinates of corner features in the image. Then, the laser speckle projector projects a random speckle pattern to the calibration board in different poses, and the infrared camera captures speckle images. Next, the digital image correlation (DIC) method is utilized to determine the corresponding speckle points in different speckle images. According to the plane equations of the calibration board, those speckle points are projected to corresponding planes, whose 3D coordinates can be obtained in the camera coordinate system. The straight lines fitted by corresponding speckle points pass through the center of the laser transmitter in the projector, which is regarded as the optical center of the projector. Therefore, the optical center and axis of the projector in the camera coordinate system are estimated by fitting corresponding lines. Finally, the pose relationship between the camera and the projector is solved and optimized. The virtual speckle image of the projector is generated by constructing the equation of planar homography. Through the aforementioned process, a monocular laser speckle projection system can be equivalent to a binocular stereo vision system with speckle images.

In this paper, a simple and efficient calibration method for the extrinsic parameters of monocular laser speckle projection systems is proposed. The 3D coordinates of the corresponding speckle points are calculated by adjusting the pose of the calibration board. Then, the relationship between the infrared camera and the laser speckle projector is solved and optimized to generate the virtual speckle image of the projector. The pose relationship of the monocular laser speckle projection system can be easily calibrated with the help of a calibration board with corner features, which improves calibration efficiency and reduces calibration costs. Generating the virtual speckle images of the projector enables the monocular laser speckle projection system to be equivalent to a binocular stereo vision system with speckle images, which significantly improves depth measurement accuracy. Simultaneously, the deviation of the optical axis can be corrected online. The experimental results show that the measurement errors of displacement and sphere radii are less than 0.16 mm and 0.13 mm, respectively. Within a certain depth range, the reconstruction results of the proposed method are significantly better than those of Astra-Pro. The proposed method can well improve the calibration efficiency and depth measurement accuracy of monocular laser speckle projection systems.