Simple estimates for the effects of mid-spatial-frequency surface errors on image quality

Mid-spatial-frequency surface errors can be introduced by various manufacturing processes. These errors bridge the gap between traditional figure and finish errors. Although the effects of mid-spatial-frequency errors on the imagery of an optical system can be modeled with a ray-based approach, simply tracing rays provides little insight. We present an alternative method that treats surface errors as perturbations to the nominal surface profile. This approach, combined with standard statistical methods, allows one to make simple back-of-the-envelope predictions of the effects of mid-spatial-frequency errors for various measures of optical performance. Two examples illustrating the effectiveness of this approach are presented.