Surface-height measurement noise in interference microscopy

The pursuit of low noise in interference microscopy for topography measurement is relevant to many surface types, ranging from super-polished optical surfaces to weakly-reflecting or scattering textures that require enhanced signal sensitivity. Noise is a random error source that may be quantified using a repeatability test. Here we propose a noise density normalized to the square root of the number of data points per unit time, to evaluate performance independent of measurement speed and areal filtering. Consistent with standardized vocabulary, we also distinguish between measurement noise, which is specific to a part and environmental conditions, and instrument noise, which is an apparatus specification corresponding to measurement noise under the best possible conditions. To illustrate these ideas, we present results from a commercial phase-shifting interference microscope showing an RMS measurement noise of 0.03 nm for a 1-second data acquisition of 1 million surface topography image points, after application of a 3x3-pixel median filter. The results follow the expected inverse square root dependence on the data acquisition time.