Phase-preserving fringe super-resolution for three-dimensional measurement of complex printed circuit board surfaces

Objective: This study addresses fringe-based three-dimensional measurement of local structures on complex reflective printed circuit boards. Uniform image interpolation may distort sinusoidal fringes. Curved fringes may also cause a mismatch between the interpolation direction and local iso-phase lines. Low-modulation regions may further amplify phase errors.Methods: A measurement-oriented phase-preserving fringe super-resolution resampling method is proposed. The super-resolution operation is performed in the gray-image domain. Phase-domain quantities are used as physical constraints. First, a normalized carrier intensity index is used to decouple fringe ridges, valleys, and transition regions. Ridge-valley distance and local modulation are then combined to construct a joint weight. Next, a two-dimensional fringe-alignment displacement field is estimated from multi-frequency phase-shifting data. The field is refined by local correlation and two-dimensional total-variation regularization. The original fringe images are then mapped into an aligned domain for directional interpolation. Finally, a flat/steep-region adaptive fusion strategy is constructed using the displacement-field gradient and local phase variation rate.Results: In the 3 mm, 6 mm, and 9 mm gauge-block experiments, the proposed method reduced the mean absolute error from 0.0290 mm to 0.0208 mm. It also reduced the root mean square error from 0.0428 mm to 0.0295 mm. In the high-reflective PCB pin region and the crystal oscillator package region, the proposed method improved phase continuity and three-dimensional reconstruction stability. In the pin region, compared with image-domain bicubic interpolation, the proposed method reduced the mean absolute error from 0.1753 mm to 0.0254 mm, corresponding to a reduction of about 85.5%. The error standard deviation was reduced to 0.0126 mm.Conclusion:The proposed method improves phase consistency after fringe resampling, increases point-cloud sampling density, and reduces local reconstruction errors in the selected PCB regions. This super-resolution process should be interpreted as sampling-grid densification and interpolation-induced phase-error reduction, rather than as exceeding the true lateral resolution limited by the optical system. The current conclusions are limited to the tested PCB local ROIs and imaging conditions.