Vertical Fringe Patterns Research Articles

Model-free method for intrinsic camera parameters calibration and lens distortion correction

Although various camera calibration methods have been proposed, most of these methods cannot deliver accurate determination of the intrinsic camera parameters, because of the coupling errors existing between intrinsic and extrinsic camera parameters and the use of explicit distortion models. Here, we propose a model-free method for accurate camera calibration, which utilizes phase-shifted fringe patterns shown on a liquid crystal display (LCD) screen for estimating the intrinsic parameters of a camera and correcting lens distortion. Horizontal and vertical fringe patterns are consecutively displayed on the LCD screen, which is placed at two positions parallel to the camera sensor plane. These fringe patterns are captured by the camera from the front viewpoint for calculating the absolute phase maps. Then, the images with lens distortion can be transformed to the distortion-free images using an inverse mapping operation. Subsequently, the principal point coordinates are calculated according to the geometric imaging relationship between the positions of the two LCD screens. Finally, the focal length can be estimated using the similarity of triangles formed by the obtained principal point coordinates and the obtained phase maps at the two positions. Both simulated and real experiments are performed to verify the validity of the proposed method. The results demonstrate that this method not only successfully eliminates coupling errors but also perfectly corrects lens distortion.

High-accuracy projector calibration method for fringe projection profilometry considering perspective transformation.

Camera and projector are the key components of structured light three-dimensional (3-D) measurements, and Digital Light Processing (DLP) projector has been widely used for projecting digital structured light patterns for the measurement. The light projecting of projectors can be modeled as the inverse procedures of camera imaging, and its high-accuracy calibration is still a remaining challenge. Therefore, this paper proposes a novel projector calibration method to improve the calibration accuracy of DLP projector. By fixing the position of the camera and calibration board, this method essentially eliminates the perspective transformation error and effectively avoids the distortion of the extracted marker points. The proposed projector calibration procedures are given as follows: Firstly, the optical axis of the camera is adjusted parallel to the normal of the hollow ring calibration board, and a texture image is captured by the camera; Secondly, the horizontal and vertical fringe patterns with nine different positions and directions are projected onto the calibration board, and nine sets of projected images are taken; Finally, a one-to-one correspondence between the camera and the projector is established, and the projector is accurately calibrated using the phase equivalence. The experimental results show that the proposed projector calibration method is feasible and easy to operate, which can essentially eliminate the perspective transformation error and ensure the competitive accuracy.

High Sensitivity Fringe Projection Profilometry Combining Optimal Fringe Frequency and Optimal Fringe Direction

Phase sensitivity plays a vital role in accurately retrieving three-dimensional (3D) shape of diffused objects in fringe projection profilometry (FPP). With regard to traditional means that simply project horizontal or vertical fringe patterns, the fringe frequency and direction may not be the best choice to acquire optimal sensitivity to depth variations. To overcome this problem, this paper proposes a novel method to obtain 3D shape with high accuracy by combining the optimal fringe frequency and the optimal fringe direction (OFF + OFD). Firstly, in order to reduce phase error caused by periodic inconsistency of the traditional fringe projection methods, period of the projected fringe is corrected by using the high-accuracy planar homography. Secondly, the optimal fringe direction is calculated by projecting sets of corrected horizontal and vertical fringe patterns onto a depth-known standard block with the optimal fringe frequency. Finally, the validation is conducted by projecting the optimized fringe patterns onto the measured objects to reconstruct 3D shape. The simulations and actual experiments demonstrate that the proposed optimization method is feasible and effective in increasing phase sensitivity and measurement accuracy.

Optimal fringe angle selection for digital fringe projection technique

Existing digital fringe projection (DFP) systems mainly use either horizontal or vertical fringe patterns for three-dimensional shape measurement. This paper reveals that these two fringe directions are usually not optimal where the phase change is the largest to a given depth variation. We propose a novel and efficient method to determine the optimal fringe angle by projecting a set of horizontal and vertical fringe patterns onto a step-height object and by further analyzing two resultant phase maps. Experiments demonstrate the existence of the optimal angle and the success of the proposed optimal angle determination method.