This paper outlines a new framework for the calibration of optical instruments, in particular smartphone cameras, using highly redundant circular black-and-white target fields. New methods were introduced for (i) matching targets between images; (ii) adjusting the systematic eccentricity error of target centres; and (iii) iteratively improving the calibration solution through a free-network self-calibrating bundle adjustment. The proposed method effectively matched circular targets in 270 smartphone images, taken within a calibration laboratory, with robustness to type II errors (false negatives). The proposed eccentricity adjustment, which requires only camera projective matrices from two views, behaved comparably to available closed-form solutions, which require additional a priori object-space target information. Finally, specifically for the case of mobile devices, the calibration parameters obtained using the framework were found to be superior compared to in situ calibration for estimating the 3D reconstructed radius of a mechanical pipe (approximately 45% improvement on average).