Transferences of heterocentric astigmatic catadioptric systems including Purkinje systems.

Purpose: To develop the linear optics of general catadioptric systems with allowance for both astigmatism and heterocentricity.
Methods: Reflecting elements partition a catadioptric system into subsystems of four distinct types: (unreversed) dioptric subsystems, anterior catoptric subsystems, reversed dioptric subsystems, and posterior catoptric systems. Differential geometry of an arbitrary astigmatic and tilted or decentered surface is used to determine the anterior and posterior catoptric transferences of a surface.
Results: The transference of a catadioptric system is obtained by multiplication of the transferences of unreversed and reversed dioptric subsystems and anterior and posterior catoptric transferences of reflecting elements. Formulae are obtained for the transferences of the visual system of an eye and of six nonvisual systems including the four Purkinje systems.
Conclusions: The transference can be calculated for a catadioptric system, and from it, one can obtain other optical properties of the system including the dioptric power and the locations of the optical axis and cardinal structures.