In designing and subsequently producing a optical system, it is necessary to get tolerance analysis for a stability assesment of optical system quality. A new tolerance theory, which defines tolerable degree of manufacturing error, is developed on the basis of optical aberration fuction. Small tolerance results in large change of aberration and optical quality, so that small tolerance indicates the design parameter which requires particular attentions in fabrication of the optical system. Tolerance theory is applied to the four-mirror optical system for sub-micron lithography, already developed in this laboratory for a prolonged time. Seidel third order aberrations are expressed by Gaussian brackets, which have 8 design parameters. Tolerances of each of the Seidel third order aberration are derived under the condition of the design parameters having the error in ±5%. Curvatures of first reflective plane and fourth reflective plane have small tolerance. Also changes of aberrations are simulated under the condition of the design parameters having the error in ±5%. Petzval field curvature has the largest change in the Seidel third order aberrations. The tolerance theory developed in this work can be incorporated during computer optical design work.
