Page 40 - Modern Optical Engineering The Design of Optical Systems

Gaussian Optics: The Cardinal Points 23

∗
to the optical axis are brought to a common focus on the axis. If the
rays entering the system and those emerging from the system are
extended until they intersect, the points of intersection will define a
surface, usually referred to as the principal plane. In a well-corrected
optical system the principal surfaces are spheres, centered on the
object and image. In the paraxial region where the distances from the
axis are infinitesimal, the surfaces can be treated as if they were planes,
hence the name, principal “planes.” The intersection of this surface
with the axis is the principal point. The “second” focal point and the
“second” principal point are those defined by rays approaching the
system from the left. The “first” points are those defined by rays from
the right.
The effective focal length (efl) of a system is the distance from the
principal point to the focal point. The back focal length (bfl), or back
focus, is the distance from the vertex of the last surface of the system to
the second focal point. The front focal length (ffl) is the distance from
the front surface to the first focal point. These are illustrated in Fig. 2.1.
The nodal points are two axial points such that a ray directed
toward the first nodal point appears (after passing through the system)
to emerge from the second nodal point parallel to its original direction.
The nodal points of an optical system are illustrated in Fig. 2.2 for an
ordinary thick lens element. When an optical system is bounded on
both sides by air (as is true in the great majority of applications), the
nodal points coincide with the principal points.
Unless otherwise indicated, we will assume that our optical systems
are axially symmetrical and are bounded by air. Equations 2.11
through 2.15 cover the case where the surrounding medium is not air.

Figure 2.1 The location of the focal points and principal points of a generalized
optical system.

∗ The optical axis is a line through the centers of curvature of the surfaces which make
up the optical system. It is the common axis of rotation for an axially symmetrical optical
system. Note that in real life, systems of more than two surfaces do not have a unique
axis, because three or more real points are rarely exactly aligned on a straight line.