A method for wave-optics propagation of mid-spatial frequencies in astigmatic optics

Mid-spatial-frequency (MSF) surface errors can affect optical performance in complex ways. Accurately predicting their impact often requires full wave-optics simulations, which are computationally expensive and difficult to incorporate into optical and specification workflows. To address this challenge, this work presents the Grating Mode Series Expansion (GMSE), a coherent wave propagation method for astigmatic systems. MSF perturbations from successive surfaces are decomposed into grating modes and propagated using local optical-path approximations about nominal rays. Each mode has a closed-form solution: a displaced, phase-modulated copy of the nominal propagated field. The theory extends the paraxial limit of existing asymptotic wave solutions for MSFs and connects with classical roughness-scattering theory. Examples clarify the underlying wave effects, their implications for optical degradation, and the limitations of deflection models.