  In this paper, a method for solving the initial structure of an off-axis
multi-mirror system applied to extreme ultraviolet (EUV) lithography using a
paraxial ray-tracing algorithm based on Seidel aberration theory is proposed.
By tracing the characteristic rays in the reflection system, the height and
paraxial angle on each surface can be obtained, then through the relationship
between the Seidel aberration coefficient and these parameters, the initial
structure with good aberration performance can be solved. We can obtain
different initial structures by adding different initial condition constraints.
In this paper, we have solved two different initial structures by assigning
different optical powers as different initial structures, and on this basis, we
have optimized two off-axis six-mirror systems with numerical aperture (NA) of
0.25. Their wavefront aberration RMS value is about 0.04 wavelength, and the
absolute distortion is less than 1.2nm, with good imaging quality. We believe
that this method can greatly improve the design efficiency and optimization
effect of complex multi-mirror systems.
