Flexible and accurate system calibration method in microscopic fringe projection profilometry.

The three-dimensional (3D) measurement task of complex microstructures holds paramount significance in the domains of precision manufacturing and inspection. The calibration of the 3D system heavily determines the final reconstruction accuracy. The widely adopted system calibration method is phase-height mapping (PHM) and stereo vision (SV) based. The former can be applied directly to the calculation without considering the imaging model of the system, but it relies on highly precise and expensive translation stages or standard blocks. The latter's accuracy cannot be guaranteed because it is difficult to accurately calibrate the projector. In this paper, we establish an optically coupled microscopic fringe projection profilometry system that consists of a Scheimpflug pinhole projector and a super-low distortion bi-telecentric camera. We introduce a simplified 3D system calibration approach that combines phase modulation transfer and ray propagation. Our method enables the simultaneous calibration of the system, including the calibration of the projector, camera, and the phase to a 3D coordinates relationship, using only a 2D target. The calibrated projector's external parameters are used to obtain the target's complete poses, and then the direct mapping coefficients of the phase to the 3D coordinates can be obtained through the optical geometry structure and phase labels. Comparable experiments verify the feasibility of the proposed method.

Constrained nonlinear optimization method for accurate calibration of a bi-telecentric camera in a three-dimensional microtopography system.

Telecentric cameras are widely used in the field of microscopic imaging because of their constant magnification and tiny distortion in the depth of field. Camera calibration has always been a key step in the field of computer vision. Usually, the precise parameters of the telecentric camera are obtained by nonlinear optimization; however, the randomness of the optimization algorithm without proper constraints will cause the results to be inconsistent with reality. Existing studies paid little attention to this issue; therefore, we show a reliable optimization approach for the bi-telecentric camera in a structured illumination three-dimensional microtopography measurement system. In this method, the distortion-free camera parameters are solved through a closed-form solution. Then a nonlinear optimization algorithm with constraining the world coordinates of the precise calibration target is proposed to refine the global parameters, leading to the calibration results being more accurate and authentic. The real experiments are conducted to verify the feasibility of the proposed method. The comparative experiments with the exiting approach are then carried out, manifesting that the proposed method enjoys advantages in terms of both reprojection error and operating efficiency. Additionally, the average offset of the world coordinates on the calibration target derived from the proposed method verifies its effectiveness and reasonability.

Accurate stereo vision system calibration with chromatic concentric fringe patterns.

Camera calibration is used to determine the intrinsic and extrinsic parameters of a 3D imaging system based on structured light. Traditional methods like chessboard and circular dots usually employ an intensity-based feature point detection procedure, and are susceptible to noise, image contrast, and image blur. To address these issues, we proposed an active calibration method to accurately detect the centers of chromatic concentric fringe patterns (CCFP). Specifically, we first acquired the circular phase using a phase analysis algorithm, then extracted nine phase contours from the circular phase for the corresponding subpixel center coordinates using an ellipse fitting algorithm, and precisely calculated the final center with their weighted sum. We ran a simulation and evaluated the impacts of different degrees of Gaussian blur and noise on the calibrated parameters. The simulation demonstrates that our approach is more robust to noise and blur than previous ones, and our approach yields a higher calibration accuracy. Moreover, we carried out a comparison experiment to evaluate the performance of our method. It showed that the reprojection error can be reduced by at least 10% in the out-of-focus condition (i.e., the target is beyond the working distance of the camera) and the 3D reconstruction accuracy can be improved by nearly 10%.