Surface error effect on reflectivity and focused spot of an EUV tubular mirror machined by ultra-precision diamond turning

Grazing-incidence tubular mirrors, which provide high reflectivity and significant demagnification of the meridian and sagittal plane through a single reflection, are important optical elements in extreme ultraviolet (EUV) focusing systems. Surface errors induced by the manufacturing process have a vital impact on optical performance. In this paper, a tubular focusing mirror is directly fabricated via ultra-precision diamond turning. According to ray tracing and Rayleigh–Rice vector perturbation theory, a surface error model is established based on the measurement data from different spatial frequency ranges. The effects of figure error and roughness on the reflectivity and the focused spot are studied in detail. The results reveal that these surface errors cause a decrease in reflectivity from 88.9% to 83.2%, along with a significant increase in the root mean square spot radius, rising from 63.9 µm to 138.3 µm. This study also provides a method to bridge the machined surface geometry to the optical functionality.