Reconstruction of shape using gradient measuring optical systems

This paper deals with the problem of reconstructing a surface topography for a special type of surface sensor that measures the surface slope instead of the height. As an example, a scattered light sensor with an incoherent light source is considered. In contrast to many other applications, the scattered light sensor is used to measure form deviation in the nanometer range of mirror like surfaces. The concept is as simple as possible: A linear detector positioned in the focal plane of the lens measures the angle distribution of the back scattered light. The center of mass of the angle distribution is proportional to the gradient of the surface. The reconstruction of the shape is done by integration.