When light propagates through aberrated optical systems, the resulting degradation in amplitude and phase has deleterious effects, for example, on resolution in imaging, spot sizes in focusing, and the beam quality factor of the output beam. Traditionally, this is either pre- or post-corrected by adaptive optics or phase conjugation. Here, we consider the medium as a complex channel and determine the corresponding eigenmodes which are impervious of the channel perturbation. We employ a quantum-inspired approach and apply it to the tilted lens as our example channel, a highly astigmatic system that is routinely used as a measure of orbital angular momentum. We find the eigenmodes analytically, show their robustness in a practical experiment, and outline how this approach may be extended to arbitrary astigmatic systems.