Correction of thermal airflow induced measurement errors in the digital fringe projection system using background-oriented Schlieren technique

Abstract Digital fringe projection (DFP) has been extensively applied in high-precision 3D morphology measurements of advanced electronic packaging. However, under thermal reliability testing, the refractive index variations caused by thermal airflow distort captured fringe images, leading to significant measurement errors. To overcome this challenge, this paper proposes a correction method that integrates the background-oriented Schlieren (BOS) technique with Hamiltonian ray tracing. By reconstructing the 3D refractive index field through multi-angle BOS and applying Hamiltonian optics, light path deviations are accurately estimated and compensated. The corrected images are then used for phase unwrapping and accurate 3D reconstruction. Experimental validations on standard gauge blocks, zirconia ceramics, and BGA chips demonstrate that the proposed method significantly enhances measurement accuracy and repeatability. The phase unwrapping success rate increases from 94.21% to 98.85%, and the artifacts caused by thermal disturbances are largely eliminated. Moreover, statistical analysis of the BGA chip confirms significant reductions in radius and spacing errors of solder balls. This BOS-assisted correction method offers a reliable and low-cost solution for 3D measurements under thermal disturbances, enhancing the performance and robustness of DFP systems in electronic packaging inspection.