Spectral speckle displacement in defocused and tilted imaging systems

Speckle patterns offer valuable insights into the surface characteristics or the characteristics of the light generating the speckle. One possible way to extract this information is via spectral speckle correlation (SSC). The cross-correlation between two speckle fields, generated at different wavelengths, can be used for example to determine the roughness of the illuminated surface. Taking defocused measurements of the surface or measuring on a tilted surface leads to a displacement between the speckle, which in turn affects the cross-correlation and leads to errors in the calculated roughness. In this work we present a model to determine the lateral speckle displacement for a change in wavelength in the case of subjective speckle and defocused, tilted objects. This model is therefore applicable to a wide range of applications and allows to estimate and correct for this speckle displacement. Experimental results show sub-pixel accuracy for object tilts up to ±7° and defocus distances up to ±25 mm.