Real-time measurement of surface roughness by correlation of speckle patterns

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Abstract
In a previous article we have shown that the two speckle patterns produced from the same rough surface illuminated by two coherent plane waves under two different angles of incidence are correlated. The correlation depends on the surface roughness. In this paper a method is described where the rough surface is illuminated simultaneously by the two plane waves. The ensemble-averaged coherence function, that is, the correlation function, of the scattered field is measured by using a two-waves interferometer. This affords a real-time measurement of the surface roughness in the range of large roughness (σ > λ). The theoretical calculations have been performed for a normally distributed surface. The experimental results are in good agreement with theory. We describe the optical arrangement of an instrument based on this principle.