Angle spread function degradation by surface roughness in imaging optics

摘要

A formula is derived for the total width of the angle spread function in an imaging optical system, the performance of which is degraded by surface roughness. The derivation is done in the framework of the scalar theory of diffraction, but it does not rely on the small roughness approximation. The contribution of scattering from surface roughness to the total width of the angle spread function is found to depend only on the variance of the roughness slope. It is also shown that the common rule of obtaining the total width of the angle spread function as a square sum of the pure scattering component and the pure specular component is actually incorrect and does not fully account for the contribution of the specular component.