Optical axes of catadioptric systems including visual, Purkinje and other nonvisual systems of a heterocentric astigmatic eye

For a dioptric system with elements which may be heterocentric and astigmatic an optical axis has been defined to be a straight line along which a ray both enters and emerges from the system. Previous work shows that the dioptric system may or may not have an optical axis and that, if it does have one, then that optical axis may or may not be unique. Formulae were derived for the locations of any optical axes. The purpose of this paper is to extend those results to allow for reflecting surfaces in the system in addition to refracting elements. Thus the paper locates any optical axes in catadioptric systems (including dioptric systems as a special case). The reflecting surfaces may be astigmatic and decentred or tilted. The theory is illustrated by means of numerical examples. The locations of the optical axes are calculated for seven optical systems associated with a particular heterocentric astigmatic model eye. The optical systems are the visual system, the four Purkinje systems and two other nonvisual systems of the eye. The Purkinje systems each have an infinity of optical axes whereas the other nonvisual systems, and the visual system, each have a unique optical axis. (S Afr Optom 2010 69(3) 152-160)