Modelling and calibration of depth-dependent distortion for large depth visual measurement cameras

Lens distortion parameters vary with the distance between the object point and the image plane. We propose an analytical model of depth-dependent distortion for large depth-of-field digital cameras used for high accuracy photogrammetry. Compared with the magnification-dependent model, the proposed one does not need focusing operation during calibration, thus eliminates focusing errors and guarantees the stability of camera interior parameters. Compared with the widely used constant distortion parameter model, the proposed model reduces the maximum distortion variation from 8.0 μm to 0.9 μm at 20 mm radial distance when the depth changes from 2.46 m to 4.51 m for the 35 mm lens, and from 23.0 μm to 3.6 μm when the depth changes from 2.07 m to 4.17 m for the 50 mm lens. Additionally, when applied to photogrammetry bundle adjustment, the proposed model reduces length measurement standard deviation from 0.055 mm to 0.028 mm in a measurement volume of 7.0 m × 3.5 m × 2.5m compared with the constant parameter model.