Example: Field Lens in a Telescope
We first consider a Keplerian telescope, which consists of two lenses: an objective and an ocular (eyepiece). It provides some angular magnification for viewing distant objects according to the ratio of focal lengths of objective and ocular. For a large magnification, one will thus need to use an ocular with small focal length, which will in practice limit the size of the ocular, since the f-number cannot be arbitrarily small. The problem is then that the diameter of the ocular limits the field of view. Even for moderate viewing angles, some of the rays cannot enter the ocular anymore, so that one has some vignetting, as can be seen in Figure 1.
This problem can be cured by inserting an additional lens (a field lens) in the intermediate image plane (see Figure 2). The rays for the on-axis object point are not affected by the field lens because they go through its center. For the off-axis object point, however, the rays are bent towards the ocular – all by the same amount because they all go through the same point on the field lens –, so that they can now get through the ocular. Thus, the vignetting effect is avoided. The field lens can effectively expand the field of view of the telescope.
Interestingly, the field lens (when placed in the intermediate image plane) does not modify the magnification. Also, it can be shown that the combination of field lens and ocular lens has the same focal length as the ocular lens alone.
A general problem with a field lens arises from the fact that it is placed in an image plane: its details can then appear in the generated image. For example, scratches on a lens surface or dust particles will be visible – while for other lenses (e.g. the outer surface of the objective) they may not have any noticeable effect on the image because they are far away from an image plane. In order to mitigate that problem and/or in order to place some other optical element (e.g. a reticle) in the image plane, a field lens is sometimes slightly displaced from the image plane. There, it may still perform essentially the same function, while still not having a substantial influence on the image magnification.
Another problem with field lenses can be that they reduce the eye relief, i.e., the distance of the exit pupil from the eye lens.
The field lens can be integrated into the ocular. The second lens of the ocular may then be called the eye lens.
Field Lens in an Illumination System
In the illumination system of an overhead projector, for example, one often uses a condenser lens just before the object to be imaged (e.g. a slide). While that lens does not significantly modify the diameter of the illuminated object area, it serves to bend the light rays coming from the light source such that they stay within the imaging system, and a brighter image is obtained. The condenser lens is then also called a field lens.
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