Imaging with four spherical mirrors

Abstract

We investigate unobstructed, plane-symmetric imaging systems of four spherical mirrors. Fifteen parameters are necessary to specify the configuration of such a system. Constraints are determined that ensure that any resultant system possesses a given set of first-order properties. These constraints remove four parameters as available degrees of freedom. To illustrate the efficacy of this design approach, we present two example studies: one for a class of systems with the object at infinity and another for finite-conjugate projection systems. For each study a global optimizer is used as the primary search tool. Example systems from these studies are presented.

SLIDERS: the next generation of automated optical design tools has arrived

“…Some of the first routines to be demonstrated with SLIDERS were based on papers about one and two spherical mirror systems [5,6]. Studies of three and four spherical mirror systems followed [7,8], and these works were then added. Each of these spherical mirror systems assumes only plane symmetry, and all are based on the Hamiltonian methods as developed by Stone and Forbes [9,10].…”

“…Each of these spherical mirror systems assumes only plane symmetry, and all are based on the Hamiltonian methods as developed by Stone and Forbes [9,10]. References [5][6][7][8] all discuss systems at finite conjugates, and those with the object at infinity. Two and three mirror afocal systems are considered in [11], and multi-reflection systems are discussed in [12].…”

Nonanamorphic imaging with three conic mirrors

“…These systems were chosen for comparison purposes for similar studies on spherical mirror systems presented in Refs. [6][7]. Four representative systems are illustrated in Figure 3, and their construction parameters listed in Table 1 .…”

“…[6] and [7]. Five representative systems are also illustrated in Figure 3, and their construction parameters listed in Table 2.…”

Anamorphic imaging with three mirrors: a survey

“…Over the next decade, several applications applying these methods to the design of unobstructed reflective systems have been reported. The studies have included systems with two conic mirrors [3], and spherical mirror systems with two, three and four mirrors [4][5][6][7]. More recently in 2002, nonanamorphic systems composed of three conic mirrors were reported [8].…”