Numerical simulation tool for synthetic speckle pattern images and their intensity-based integration under variable conditions for metrology applications

Abstract

In many metrological applications speckle can be used to determine surface properties where several complex effects and parameters are of concern. However, an analytical modelling of the decorrelation of speckle patterns created e.g. by twowavelength illumination of a surface is possible only for Gaussian-distributed surface height values and in illumination regimes where the separation of the two illumination wavelengths is much smaller than the mean value of the two wavelengths. Depending on the fabrication process of the illuminated surface the statistical distribution of the surface height values can differ significantly from a Gaussian distribution. We present a numerical simulation tool for the synthetic generation of laser-speckle patterns which a non-imaging observer (e.g. a bare CCD-chip) detects in the farfield of an illuminated surface. We investigate for which illumination wavelengths separation the analytical model is valid with a centre wavelength of 650 nm and compare simulated speckle images originating from surfaces with equal-and Gaussian-distributed height values under two-wavelength illumination. We show which differences from the analytical model for the correlation of the two emerging speckle images occur and consider the implications for an experimental situation.