Abstract
Accurate optical three-dimensional (3D) shape measurement through aircraft observation windows is hindered by refractive distortions and the limitations of conventional calibration. We present a binocular imaging model and a corresponding in situ calibration method to address these issues. The model utilizes backway ray tracing and Snell’s law to map the light path through a planar-curved window, quantifying refraction-induced deviations. The calibration method formulates an optimization function constrained by the known spacing between adjacent calibration board features and the planarity of the board, enabling the estimation of model parameters without requiring a priori knowledge of the board’s spatial position. Only a single-frame image of a freely moved calibration board is required in this method, which is a highly desired feature in online and in situ calibration. A series of experiments is carried out, and the effectiveness of the proposed methods is quantitatively discussed. Results demonstrate that the proposed method achieves a relative error of 0.58% in the measurement of a curve surface through a complex observation window, showing a notable improvement in accuracy over the conventional method. The measurement result of the proposed method closely approaches those achieved without the observation window, indicating that the proposed imaging model accurately reconstructs the true light propagation process through complex structures and the proposed calibration method precisely identifies the model parameters.