Theory of point-spread function artifacts due to structured mid-spatial frequency surface errors

Optical design and tolerancing of aspheric or free-form surfaces require attention to surface form, structured surface errors, and nonstructured errors. We describe structured surface error profiles and effects on the image point-spread function using harmonic (Fourier) decomposition. Surface errors over the beam footprint map onto the pupil, where multiple structured surface frequencies mix to create sum and difference diffraction orders in the image plane at each field point. Difference frequencies widen the central lobe of the point-spread function and summation frequencies create ghost images.