Calibration and rectification of bi-telecentric lenses in Scheimpflug condition

Abstract

In the lens-based imaging model, the Scheimpflug principle is expressed as the object plane, the image plane, and the lens plane intersect in a line. With this principle, the focused object plane in the lens's object side can be tilted by placing a tilted sensor at the image side of the lens; thereby, multi-cameras can be focused on the same object space with an overlapping field of view and depth of field. For Scheimpflug cameras, additional tilt angles between the camera sensor and the optical axis are introduced, which has been well studied in pinhole cameras' calibration methods. Telecentric lens, as a commonly used lens type, has constant magnification in the axial direction and has a wide range of applications in close-range photogrammetry. To calibrate and rectify the telecentric lenses in Scheimpflug conditions, we derived a concise imaging model by expressing the sensor tilt angles and the lens magnification into a simplified intrinsic matrix. Based on the derived imaging model, an integrated calibration algorithm without solving the tilt angles and a stereo-rectification method for stereo matching are developed. The effectiveness and accuracy of the proposed methods are verified by experiments, including the comparison with the traditional telecentric model and pinhole model. Combined with the experimental results, we analyzed the potential impact of the extrinsic rotation matrix's ambiguity, verified whether the lens distortion affects the re-projection error, and discussed how the calibration posture influences the calibration accuracy.