Diopter of Curvature c 1R

Let us consider a surface - a diopter - which separates two media of refractive indexes n and n' (Fig. 1.15), and set the origin of the z-axis at its vertex. The abscissa f = OF of the object focus F in the object space is defined as the distance from the surface vertex O to the convergence point F of rays issued from a source point at infinity in the image space.

Conversely, the abscissa f' = OF' of the image focus F' in the image space, is defined from a source point at infinity in the object space. These abscissa represent the focal lengths n' n f = ~-R, f = ---R, (1.20a) Fig. 1.15 Paraxial focii - also called Gaussian focii - and conjugate distances. Bracket ends towards z show a diopter with curvature c = 1/R > 0

from which we deduce

The quantity f R

is called the optical power of the surface or of the optical system. Also in the image space, its reciprocal f /n' is the effective focal length (efl) of the system.

The conjugate distances z = OA and z' = OA' of an axial object A and its image A' are obtained by considering a four-angle equation set in u, i, i', u', expressing the local geometrical transformation at intersection point I. The quantities u, u' are the aperture angles of a ray at the object and image points, sometimes called convergence angles. Solving this system leads to

which may be written