Backscattering Estimation of a Tilted Spherical Cap for Different Kinds of Optical Scattering

In many optical engineering applications, a spherical cap shaped optical element is widely used such as concave or convex mirrors in reflective optics. Such an element can also tilt around the vertex which corresponds to an off-axis optical design. The optical backscattering of such an optical element sometimes could be important. For example, in the space-based gravitational wave detection, the backscattering of such an element could be superimposed with the local oscillator and limits the sensitivity of the spacecraft. The scattered contributions depend on the scattering property of the mirror surfaces and the geometrical arrangement including the radius of curvature, the tilt and the interval between the scattering source and detector plane. Based on random estimation method, this paper starts from the radiometry, combines these variables and calculates the theoretical amount of back scattered light for both diffuse and superpolished surfaces. The results are compared with analytical and ray tracing solution. The conclusions can be used to further improve the optical design of the telescope or extended to other cases where the backscattered light should be controlled.