Algorithm for accurate and efficient calculation of coating-induced effects

Multilayer coatings are widely used in reflective optical systems, particularly for short-wavelength applications. Such coatings, while playing a key role in enhancing the reflectance, may cause non-negligible aberrations, which are often omitted in the typical optical design and simulation. In this study, we investigate the effects induced by the multilayer coatings and present a practical computational algorithm that correctly considers the lateral shift, the phase change, and the amplitude modulation. Several examples are included to show the effectiveness of the algorithm.