White-light interferometry measuring an optically rough surface commonly does not resolve the lateral structure of the surface. This means that there are height differences within one resolution cell that exceed one-fourth of the wavelength of the light used. Thus the following questions arise: Which height is measured by white-light interferometry? How does the surface roughness affect the measurement uncertainty? The goal of the presented paper is to answer these questions by means of numerical simulations. Before the aforementioned questions can be answered, the distribution of the intensity of individual speckles, the influence of surface roughness, and the spectral width of the light source used are discussed.

White-light interferometry on rough surfaces is an optical method for the measurement of the geometrical form of objects. The longitudinal coordinate of the measured surface is obtained from the measured interferogram by means of an evaluation method. However, the longitudinal coordinate cannot be determined completely accurately because the interferogram is affected by noise. We calculate the lower limit of the longitudinal measurement uncertainty caused by noise by use of the Cramer-Rao inequality. Additionally, we calculate the lower limit of the longitudinal measurement uncertainty caused by shot noise only.

White-light interferometry (WLI) on rough surfaces is based on interference from individual speckles. The measurement uncertainty of WLI is limited by a random shift of these individual interference patterns. The statistical error in each measurement point depends on the brightness of the corresponding speckle: a dark speckle yields a larger error than a bright speckle. In this paper, a novel method is presented to reduce the measurement uncertainty significantly: by sequentially switching the direction of the illumination, the camera sees several independent speckle patterns in sequence. From each pattern, the brightest speckles are selected to eventually calculate an accurate height map. This height map displays no outliers, and the measured surface roughness is close to the stylus measurements.