High-precision anamorphic lens calibration with 3D and 2D calibration targets

Abstract

This paper presents a high-precision camera calibration approach for anamorphic lenses. The distortion model for anamorphic lenses is substantially more sophisticated than the distortion model for spherical lenses for the adaption of cylindrical lenses in anamorphic lens attachments. Based on the anamorphic aberration theory and numerical experiments, a polynomial type distortion model is provided for anamorphic lenses, with which high-precision camera calibrations can be achieved using 3D calibration targets. 3D calibration targets are typically limited in size, unable to encompass the whole imaging field of anamorphic lenses. The calibration results using 3D calibration targets tend to be unstable with the increased number of distortion coefficients in the anamorphic distortion model. Thus, after the anamorphic lenses have been calibrated with 3D calibration targets, they are recalibrated with 2D calibration targets that may fill the anamorphic lenses’ field of view, resulting in more dependable and exact calibration results. Two anamorphic lenses are calibrated with high precision at the end the paper, which proves the effectiveness of the proposed method.

3D Metrology Using One Camera with Rotating Anamorphic Lenses

“…If we individually increase the anamorphic distance from 30 mm to 100 mm, the measuring accuracy will increase correspondingly, as shown in Figure 18 . The lens parameters ad , f x , and f y are closely related because they are determined by the anamorphic lens structure, and it is not possible to simply change one parameter independently [ 25 ]. We proposed paraxial lens designs for anamorphic lenses with zero anamorphic distance [ 26 ], but designing an anamorphic attachment with an extremely large anamorphic distance appeared to be difficult.…”

“…The front anamorphic attachment introduces many more aberrations [ 26 ]. Based on the aberration theory and numerical experiments for anamorphic lenses, we proposed a polynomial distortion model for anamorphic lenses, which allows for high-precision camera calibration [ 25 ]. As shown in Equation (2), anamorphic distortions can be divided into radial distortions ( X rad , Y rad ), third-order distortions ( X 3 , Y 3 ), and second-order distortions ( X 2 , Y 2 ).…”

“…Commonly, the 3D calibration target cannot cover the entire imaging area, which will lead to a poor calibration result for other imaging areas. Therefore, to achieve a stable calibration result for the entire imaging area, mixed calibration targets are adopted, which means 3D calibration targets and 2D calibration targets are both required [ 25 ]. The initial values of the internal parameters are calibrated using the 3D calibration target, and those parameters are refined using 2D calibration targets.…”

“…F. Blais performed an exploratory calibration of anamorphic lenses based on a pinhole imaging model [ 24 ]. In our previous work, a high-precision anamorphic lens calibration method was proposed with 3D and 2D calibration targets [ 16 , 25 ].…”