Theoretical Measurement Uncertainty of White-Light Interferometry on Rough Surfaces

A great advantage of the white-light interferometry is that it can be used for profile measurement of objects with a rough surface. A speckle pattern that arises in the image plane allows one to observe the interference; however, this pattern is also the source of the measurement uncertainty. We derive the theoretical limits of the longitudinal uncertainty by virtue of the first-order statistics of the speckle pattern. It is shown that this uncertainty depends on the surface roughness of the measured object only; it does not depend on the setup parameters.