Adaptive resolution in speckle displacement measurement using optimized grid-based phase correlation and statistical refinement

Speckle metrology is a powerful optical sensing tool for non-destructive testing (NDT) and advanced surface characterization, enabling ultra-precise measurements of surface deformations and displacements. These capabilities are critical for material analysis and surface assessment in sensing-driven applications. However, traditional correlation methods often struggle to balance resolution and robustness, particularly when simultaneously measuring both small- and large-scale deformations in noisy, high-frequency data environments. In this paper, we present an adaptive resolution approach for speckle displacement measurement that combines grid-based phase correlation with statistical refinement for enhanced accuracy and resolution. Unlike traditional phase correlation techniques that rely on global correlation, our method introduces a flexible grid-based framework with localized correlation and dynamic overlap adjustments. To improve measurement performance, we developed an optimization technique that uses the median absolute deviation of residuals between reference and deformed images, enabling the algorithm to automatically adapt grid sizes based on local deformation characteristics. This allows it to handle both small- and large-scale deformations simultaneously and effectively. The approach resulted in a relative error reduction of up to 14 % compared to the best of the results obtained using a manually fixed grid size. The proposed sensing methodology is validated through a series of numerical simulations and experimental studies, including controlled deformations with a micrometer translation stage and random speckle displacements on water-sprayed surfaces. Results demonstrate that our method can accurately detect both known and unknown deformations with high accuracy and precision, outperforming traditional techniques in terms of adaptability and robustness, particularly for surface deformation analysis.