Surface roughness measurement by speckle contrast under the illumination of light with arbitrary spectral profile

Quantification of surface roughness greater than a micron is desirable for many industrial and biomedical applications. Polychromatic speckle contrast has been shown theoretically to be able to detect such roughness range using an appropriate light source with a Gaussian spectral shape. In this paper, we extend the theory to arbitrary spectral profile by formulating speckle contrast as a function of spectral profile, surface roughness, and the geometry of speckle formation. Under a far-field set-up, the formulation can be simplified and a calibration curve for contrast and roughness can be calculated. We demonstrated the technique using a blue diode laser with a set of 20 metal surface roughness standards in the range 1–73 μm, and found that the method worked well with both Gaussian and non-Gaussian surfaces.