Physics-constrained equation and dual-compensation network for monocular calibration of spatially varying focal lengths

Camera calibration is essential for vision-based measurement because it establishes the mapping between pixel coordinates and real-world geometry. Traditional methods assume constant focal length, which fails in wide field-of-view systems where spatially varying aberrations introduce systematic bias. This paper proposes a physics-constrained dual-compensation framework for monocular calibration of spatially varying focal lengths. A high-order polynomial regression enforces geometric consistency, while focal-length and coordinate compensation networks correct nonlinear residuals. The framework requires only about 10 calibration points for initialization, markedly reducing workload, and achieves stable convergence when at least 400 evaluation points are used. Experiments across tilt angles from 8.9° to 65° demonstrate achieved a measurement accuracy within tolerance above 98.6% within ±0.03 mm with mean absolute measurement deviation below 0.03 mm. Comparative results with Zhang’s method confirm consistency at moderate tilts and improved robustness under large tilts. Cross-device validation on a fisheye camera further confirms adaptability. Statistical analysis yielded average correlation coefficients of Pearson r = 0.902 and Spearman [[EQUATION]] = 0.913, validating measurement robustness and repeatability under varying conditions. An uncertainty budget following the Guide to the Expression of Uncertainty in Measurement (GUM) quantified both type A and type B components, ensuring traceability to measurement standards. This work demonstrates a practical and traceable pathway for wide-FOV vision calibration in measurement science.