Determination of the standard deviation of height on a rough surface using interference microscopy

When a rough surface is viewed in an interference microscope with tilt fringes introduced, the effect of the roughness is to reduce the average visibility of the tilt fringes. The relationship between the standard deviation of surface height and the average visibility of the tilt fringes is derived, and experimental results are presented of measurements made on ground glass surfaces using a Linnik interference microscope.