Tolerancing the impact of mid-spatial frequency surface errors of lenses on distortion and image homogeneity

The polishing of high-precision surfaces of optical elements like spheres, aspheres and mirrors requires small polishing tools to achieve rms-surface errors below 2 nm. This can lead to typical mid-spatial frequency surface errors that cannot be considered by standard tolerancing tools anymore but might have a major impact on image performance criteria like wavefront error, distortion or image homogeneity. In this paper we will discuss an analytical approach to describe the effect of mid-spatial frequency surface errors on distortion and image homogeneity. Furthermore we have realized a Zemax user-defined surface allowing us to formulate rings and spokes of different frequencies and amplitudes and therefore giving us a tool to do the tolerancing of mid-spatial frequency errors in Zemax directly. We will present the results especially the dependency on the position of the surface in the optical system as well as the ratio of beam diameter to surface error size.