Flexible Calibration of the Telecentric Vision Systems Using Only Planar Calibration Target

With the large demand for micro-vision systems with telecentric lenses in applications such as precision 3-D sensing, how to achieve fast and high-precision calibration of the vision system has become increasingly important. In this article, we propose a flexible telecentric calibration method that does not require additional <inline-formula> <tex-math notation="LaTeX">$Z$ </tex-math></inline-formula>-axis information and can perform the whole calibration task using only one planar target. First, the main challenges in the planar-target-based calibration of the telecentric vision systems are analyzed in detail, including the noise-induced nonnormalization of rotation vectors and sign ambiguity caused by an affine imaging model. For the former challenge, a solution strategy that first uses the orthogonality and modulus equality of the rotation vectors to solve the parameters and then performs vector normalization is proposed. For the latter, according to the pinhole approximation characteristics of the actual telecentric lens, a scheme to determine the signs of the rotation parameters related to the telecentric lens by using the calibration results of the pinhole model is given. The experimental results demonstrate that the proposed rotation parameter solution strategy and the sign determination scheme are both effective. In addition, the proposed method can effectively calibrate different telecentric vision systems with the reprojection errors at a subpixel level. Finally, the application of the calibrated structured micro-vision system on 3-D measurement shows that the achieved measurement accuracy can reach the micrometer level.