This manuscript provides a new framework for calibration of optical instruments, in particular mobile 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 centers; and (iii) iteratively improving the calibration solution through a free-network self-calibrating bundle adjustment. It was observed that the proposed target matching effectively matched circular targets in 270 mobile phone images, taken from a calibration laboratory, with robustness to Type II errors. The proposed eccentricity adjustment, which requires only camera projective matrices from two views, behaved synonymous to available closed-form solutions, which require several additional object space target information a priori. Finally, specifically for the case of the mobile devices, the calibration parameters obtained using our framework was found superior compared to in-situ calibration for estimating the 3D reconstructed radius of a mechanical pipe (approximately 45% improvement on average).