Per-Pixel Calibration Based on Multi-View 3D Reconstruction Errors Beyond the Depth of Field

In 3D microscopic imaging, the extremely shallow depth of field presents a challenge for accurate 3D reconstruction in cases of significant defocus. Traditional calibration methods rely on the spatial extraction of feature points to establish spatial 3D information as the optimization objective. However, these methods suffer from reduced extraction accuracy under defocus conditions, which causes degradation of calibration performance. To extend calibration volume without compromising accuracy in defocused scenarios, we propose a per-pixel calibration based on multi-view 3D reconstruction errors. It utilizes 3D reconstruction errors among different binocular setups as an optimization objective. We first analyze multi-view 3D reconstruction error distributions under the poor-accuracy optical model by employing a multi-view microscopic 3D measurement system using telecentric lenses. Subsequently, the 3D proportion model is proposed for implementing our error-based per-pixel calibration, derived as a spatial linear expression directly correlated with the 3D reconstruction error distribution. The experimental results confirm the robust convergence of our method with multiple binocular setups. Near the focus volume, the multi-view 3D reconstruction error remains approximately $8~\mu $ m (less than 0.5 camera pixel pitch), with absolute accuracy maintained within 0.5% of the measurement range. Beyond tenfold depth of field, the multi-view 3D reconstruction error increases to around $30~\mu $ m (still less than 2 camera pixel pitches), while absolute accuracy remains within 1% of the measurement range. These high-precision measurement results validate the feasibility and accuracy of our proposed calibration.