In the past, almost all optical design was concerned with systems having rotational symmetry, such as camera lenses, microscopes, etc. Other systems that did not have rotational symmetry (such as prismatic binoculars) could often be simulated assuming rotational symmetry, and techniques were developed which implicitly assumed that decentered and asymmetric systems (in the sense of having no axis of symmetry) were rarely required. Within the last couple of decades, this situation has entirely changed, and we are now faced with many instruments and devices that do not have an axis of symmetry.
The variety is enormous, and this chapter will not attempt to explain the design of specific decentered systems, but will instead discuss the general techniques common to many of these devices. Some of the comments below apply to systems with cylindrical or toroidal surfaces; although these systems do not have an axis of symmetry (they may have a plane of symmetry), they are not strictly decentered systems. However, we will use the term decentered to include all systems that are not rotationally symmetric.
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