## Info

s1

Fig. 2.6. Aperture stop, entrance and exit pupils

Fig. 2.6. Aperture stop, entrance and exit pupils

E the exit pupil. The aperture stop limits the beam width such that beams from all object points which pass through the field stop, of radius IIh , pass centrally through it. This implies that all the other elements in the system S are sufficiently large to allow the passage of the extreme rays r2 and r3 from the upper edge Ih of the object through the system. In other words, all the other elements in the system must have a free diameter larger than the axial beam emanating from I as it passes through them. The light beam cannot think! If no clear aperture stop is defined in a system, the light will be limited by that aperture in the system which is effectively the smallest. But, in such a case, aperture limitations at other elements may obstruct one side of oblique beams. This phenomenon is called vignetting. Sometimes an aperture stop is deliberately made large enough to allow vignetting by other elements. This may be done, for example in certain photographic systems, to remove rays from the oblique image-forming beams which would otherwise cause unacceptable aberrations.

In Fig. 2.6, the paraxial image of A traced backwards towards the front of the system, is formed at E in the object space. This is the entrance pupil. The principal ray is, by definition, that ray that passes through the centre of the aperture stop A. Again, by definition in the paraxial sense, it must also pass through the centre of E. The real principal ray, entering the system at an angle which exceeds the paraxial region, may depart slightly from this theoretical path: this is the effect of pupil aberration. The entrance pupil E is therefore the paraxial image of the aperture stop A formed by backward imagery through all optical elements in front of the aperture stop. E may be real or virtual. For an aperture stop inside a relatively compact, complex system, E is usually virtual. In such cases, although the entrance pupil must, by definition, be mathematically in the "object space", it may physically be well to the right of the aperture stop or, indeed, of the whole physical system. In Fig. 2.6 it is shown to the left, physically in the object space, for the sake of clarity. This implies that the total optical power of that part of the optical system to the left of A must be positive (i.e. like a convex lens) and sufficient to form a real image of A. Such cases are uncommon.

Similarly, the exit pupil E is the paraxial image of A formed in the forward direction of the light by all those elements which are to the right of A. Again, E may be real but is more often virtual. If one places one's eye at the image plane I of an optical system and moves it over the plane, the exit pupil is that aperture out of which the light appears to come.

The angle IhEI in Fig. 2.6 is the angle to the axis upr of the incident principal ray, angle IhE I the angle upr of the emergent principal ray. In general |upr | = |upr |. In telescope systems with telephoto characteristics (see ยง 2.2.5), there is normally a large difference between |upr| and |upr|. But in an optical system placed in one medium, the ray angles up and Up are the same because of the nodal point property of the principal planes P and P in this case. As mentioned above, in the afocal case all rays from the infinitely distant object (or image) point are parallel so that up = upr (or up = upr). This means that, in the normal telescope case in one medium and with the object at infinity, the condition up = up = upr obtains. In this case n = uprf , (2.31)

a very convenient relation.

We shall see below in Chap. 3 the role that pupil position can play in various telescope systems. An important special case remains to be dealt with: telecentric systems.

Figure 2.7 shows a telecentric aperture stop, an aperture stop A placed at the focal point F of an imaging system. A is also the entrance pupil E since there is no element to the left of it. The axial image of the object point I is formed at I , the image of the point Ih in the object field at IH. The principal ray rpr passes through the centre of the stop A (and E) and is refracted by the system parallel to the axis so that the exit pupil is at infinity.

Ih