Measurement uncertainty of phase measuring deflectometry

Abstract

Phase measuring deflectometry (PMD) is a proven optical measurement method for measuring the shapes of objects. This method is suitable for measuring the shape of an object with an optically smooth (mirror-like) surface. The measured object is used as a mirror through which the camera observes a defined geometric pattern. We derive the theoretical limit of measurement uncertainty using the Cramér–Rao inequality. It shows that the measurement uncertainty is expressed in the form of an uncertainty product. The factors of the product are the angular uncertainty and lateral resolution. The magnitude of the uncertainty product depends on the mean wavelength of the light used and the number of photons detected. The calculated measurement uncertainty is compared with the measurement uncertainty of other deflectometry methods.