Influence of object motion on roughness measurements using spectral speckle correlation

Spectral speckle correlation (SSC) enables fast, non-contact surface-roughness metrology, but object motion usually degrades its accuracy. We aim to enable measurements on moving objects and present a unified model that separates the total correlation into a wavelength-dependent term, from which the surface roughness is derived, and a kinematic term that quantifies motion blur, which affects the speckle contrast. The kinematic contribution yields a closed-form variance expression, similar to that in laser speckle contrast imaging (LSCI). The model was validated using a galvanized steel sheet with a roughness of 1.23 µm S_a, translated at up to 20 mm s^-1 (approximately five speckles per exposure). Measured correlations agree with theory to within 1.06 % on average and 4.4 % at worst. Further improvements can reduce the error to 2.5 % for blur values smaller than 4 speckles per exposure. Scaling laws derived from the model indicate that the use of lasers with a power output of 125 mW and an illumination spot diameter of 5 mm can enable SSC at velocities up to 16 m s^-1, which is comparable to typical industrial band feeding rates. The results establish SSC as a viable, high-throughput alternative to conventional profilometry for continuous in-line roughness monitoring of fast-moving surfaces.