A design of a four mirror optical system with reduction magnification 5X for UV(KrF excimer laser) submicron lithography is presented. We have obtained initially the analytic solutions of the four spherical mirror system free from the four Seidel aberrations that are spherical aberration, coma, astigmatism and field curvature. However, the systems obtained after numerous corrections have still sizable amount of residual aberrations and the half field angle of only 1 degree is realizable, which limit the numerical aperture and image field diameter to 0.15 and 3.5mm, respectively.
To overcome these shortcommings, at first, the conic surfaces are introduced to the primary, tertiary and quaternary mirrors, and then the optimization is carried out to the system using a simple damped least squares method. These procedures give improved performances, in other words, higher order aberrations are significantly reduced and vignetting effect compared with that of the four spherical mirror system is far less. The numerical aperture is 0.25 and image field diameter increases up to 7mm. But the overall performances are still limited mainly by residual distortion and small field, so the system at this stage may be useful in a scanning lithography.
Hence, another method which is a aspherization of all mirrors with higher order(up to tenth) asphericities is proposed. As a result, we obtain a reflection system useful in a submicrion lithographic applications. The image field diameter of the resulting system is 10mm and numerical aperture is 0.25, which gives practical resolution of 0.8$\mu$m.
