Abstract
For the micro-lithography using a KrF excimer laser beam(λ=0.248${\mu}{\textrm}{m}$) a mirror system consisting of four spherical surfaces with reduction magnification 5$\times$ is designed. Initially the aplanat condition of the mirror system is considered. And for the further improved performance of the system the distortion free condition and flat field condition within Seidel 3rd order aberrations are added to the above condition. During the process of designing the computer-aided optimization technique is extensively employed. The spherical aberration, coma, field curvature and distortion of the optimized four-spherical mirror system are removed to the diffraction limit, and residual astigmatism and off-axial vignetting are not corrected enough.