Abstract: Optimization of a projection system is performed to obtain a starting configuration that is at a local minimum of the merit function or simply a previously known minimum system is used as the starting configuration. A zero-thickness meniscus lens is inserted at a surface in the local minimum starting configuration with N surfaces to construct a saddle point with Morse Index=1 having N+2 surfaces. The saddle point is perturbed and optimization is performed on both sides of the saddle, and the distances at the two surfaces that have been introduced are increased, to generate two new configurations, m1 and m2, that are new minima in the merit function. Each resulting configuration is output, e.g., as a table of parameters specifying the projection system or as a computer file for use in making an actual projection system.

Abstract: Optimization of a projection system is performed to obtain a starting configuration that is at a local minimum of the merit function or simply a previously known minimum system is used as the starting configuration. A zero-thickness meniscus lens is inserted at a surface in the local minimum starting configuration with N surfaces to construct a saddle point with Morse Index=1 having N+2 surfaces. The saddle point is perturbed and optimization is performed on both sides of the saddle, and the distances at the two surfaces that have been introduced are increased, to generate two new configurations, m1 and m2, that are new minima in the merit function. Each resulting configuration is output, e.g., as a table of parameters specifying the projection system or as a computer file for use in making an actual projection system.

Abstract: A classification system for systems of n mirrors, whereby systems of mirrors are classified by a number C, is defined as follows: C = ∑ i = 1 n ⁢ a i · 2 ( n - i ) ⁢ ( M &LeftBracketingBar; M &RightBracketingBar; ) where: ai=1 if the angle of incidence of the chief ray at mirror i is negative, ai=0 if the angle of incidence of the chief ray at mirror i is positive, M is the magnification of the projection system, and index i numbers the mirrors of the system in series.