Flexible calibration of phase-to-height conversion in fringe projection profilometry

High-accuracy camera calibration method based on coded concentric ring center extraction

In the field of three-dimensional (3-D) metrology based on fringe projection profilometry (FPP), accurate camera calibration is an essential task and a primary requirement. In order to improve the accuracy of camera calibration, the calibration board or calibration target needs to be manufactured with high accuracy, and the marker points in calibration image require to be positioned with high accuracy. This paper presents an improved camera calibration method by simultaneously optimizing the camera parameters and target geometry. Specifically, a set of regularly distributed target markers with rich coded concentric ring pattern is first displayed on a liquid crystal display (LCD) screen. Then, the sub-pixel edges of all coded bands radial straight lines are automatically located at several positions of the LCD screen. Finally, the sub-pixel edge point set is mapped into parameter space to form a line set, and the intersection of the lines is defined as the center pixel coordinates of each target point to complete the camera calibration. The simulation and experimental results verify that the proposed camera calibration method is feasible and easy to operate, which can essentially eliminate the perspective transformation error to improve the accuracy of camera parameters and target geometry.

Key concepts for phase-to-coordinate conversion in fringe projection systems

Fringe projection systems encode the scanned object shape as a phase distribution according to the system parameters. However, to obtain the object shape in physical units of length, the demodulated phase must be converted to the coordinates of the observed points on the object surface. The design of a phase-to-coordinate conversion algorithm is straightforward when the following key concepts are considered: cameras and projectors as direction sensors, gratings as coordinate-encoding devices, absolute phase, and triangulation. In this paper, the theoretical principles of these concepts are formalized. Then, an efficient and generalized phase-to-coordinate conversion method, which supports systems with multiple cameras and projectors arranged arbitrarily, is proposed. The usefulness of this approach is illustrated by a 3D surface imaging experiment.

Accurate calibration method for a fringe projection system by projecting an adaptive fringe pattern

In fringe projection profilometry, the lens distortion of a commercial projector may introduce larger error when testing large objects and can become one of the major error sources. In this paper, a calibration method for a fringe projection system is adapted in order to remove the influence of projector lens distortion without the need to calibrate the projector. In the proposed method, the accuracy of the fringe projection system has a considerable improvement because an adaptive fringe pattern is calculated in order to compensate for all possible distortions generated by the projector.

Hybrid 3D Shape Measurement Using the MEMS Scanning Micromirror

A surface with large reflection variations represents one of the biggest challenges for optical 3D shape measurement. In this work, we propose an alternative hybrid 3D shape measurement approach, which combines the high accuracy of fringe projection profilometry (FPP) with the robustness of laser stripe scanning (LSS). To integrate these two technologies into one system, first, we developed a biaxial Microelectromechanical Systems (MEMS) scanning micromirror projection system. In this system, a shaped laser beam serves as a light source. The MEMS micromirror projects the laser beam onto the object surface. Different patterns are produced by controlling the laser source and micromirror jointly. Second, a quality wised algorithm is delivered to develop a hybrid measurement scheme. FPP is applied to obtain the main 3D information. Then, LSS helps to reconstruct the missing depth guided by the quality map. After this, the data fusion algorithm is used to merge and output complete measurement results. Finally, our experiments show significant improvement in the accuracy and robustness of measuring a surface with large reflection variations. In the experimental instance, the accuracy of the proposed method is improved by 0.0278 mm and the integrity is improved by 83.55%.

Out-of-Focus Projector Calibration Method with Distortion Correction on the Projection Plane in the Structured Light Three-Dimensional Measurement System

The three-dimensional measurement system with a binary defocusing technique is widely applied in diverse fields. The measurement accuracy is mainly determined by out-of-focus projector calibration accuracy. In this paper, a high-precision out-of-focus projector calibration method that is based on distortion correction on the projection plane and nonlinear optimization algorithm is proposed. To this end, the paper experimentally presents the principle that the projector has noticeable distortions outside its focus plane. In terms of this principle, the proposed method uses a high-order radial and tangential lens distortion representation on the projection plane to correct the calibration residuals caused by projection distortion. The final accuracy parameters of out-of-focus projector were obtained using a nonlinear optimization algorithm with good initial values, which were provided by coarsely calibrating the parameters of the out-of-focus projector on the focal and projection planes. Finally, the experimental results demonstrated that the proposed method can accuracy calibrate an out-of-focus projector, regardless of the amount of defocusing.

Calibration method for projector-camera-based telecentric fringe projection profilometry system

By combining a fringe projection setup with a telecentric lens, a fringe pattern could be projected and imaged within a small area, making it possible to measure the three-dimensional (3D) surfaces of micro-components. This paper focuses on the flexible calibration of the fringe projection profilometry (FPP) system using a telecentric lens. An analytical telecentric projector-camera calibration model is introduced, in which the rig structure parameters remain invariant for all views, and the 3D calibration target can be located on the projector image plane with sub-pixel precision. Based on the presented calibration model, a two-step calibration procedure is proposed. First, the initial parameters, e.g., the projector-camera rig, projector intrinsic matrix, and coordinates of the control points of a 3D calibration target, are estimated using the affine camera factorization calibration method. Second, a bundle adjustment algorithm with various simultaneous views is applied to refine the calibrated parameters, especially the rig structure parameters and coordinates of the control points forth 3D target. Because the control points are determined during the calibration, there is no need for an accurate 3D reference target, whose is costly and extremely difficult to fabricate, particularly for tiny objects used to calibrate the telecentric FPP system. Real experiments were performed to validate the performance of the proposed calibration method. The test results showed that the proposed approach is very accurate and reliable.

Sub-pixel projector calibration method for fringe projection profilometry

Digital projectors are used as standard parts at present in fringe projection profilometry systems to project structured-light patterns onto the object surface to be measured, and the distortion of the projector lens must be calibrated and compensated accurately to satisfy the accuracy requirement of industrial applications. A novel method is proposed to determine the projector pixel coordinates of the marker points of a calibration target accurately in terms of projective transform. With the method, the projector can be calibrated with accuracy of sub-pixel level. The method is applicable for the calibration target with a chessboard pattern or a circle pattern, and the calibration result is independent on the results of camera calibration. Experimental results are shown to demonstrate the effectiveness and validity of the proposed method.