Aspect ratio of elongated polychromatic far-field speckles of continuous and discrete spectral distribution with respect to surface roughness characterization

Here polychromatic speckle patterns generated either by a polychromatic light source that emits at discrete frequencies or by a light source showing a continuous narrow-band spectral distribution are studied. The purpose here is the application of polychromatic speckle-pattern analysis to an in-process surface roughness characterization. To compare the coherence properties of the different polychromatic light sources, first a modified definition of the coherence length is introduced. Furthermore, the relevant optical phenomena, namely, the speckle elongation caused by the angular dispersion and the roughness-dependent speckle decorrelation, are summarized. It is shown that light sources with a continuous spectral distribution have essential advantages in comparison with discrete wavelength sources. The theoretical results are confirmed by experimental investigations based on a digital algorithm for the evaluation of CCD images of polychromatic speckle patterns, which are recorded in the Fourier plane of a Fourier-transforming lens.