Afocal Optical Systems
Based on geometrical optics, an afocal optical system is defined as a system which outputs parallel light rays in cases with parallel input rays. Concerning the ABCD matrix of the system, this implies than the matrix component <$C$> is zero. Further, we have <$A \cdot D = 1$>, assuming that the refractive index is the same on the input and output side. Such a system has no focal length, no focal points, no nodal points and no principal planes.
Other optical systems, not being afocal, are called focal or sometimes non-afocal.
The simplest example is a system with no focusing elements, but only free space, or space filled with a homogeneous optical medium. Here, we have <$A = D = 1$> in addition to <$C$> = 0.
The probably most prominent example is that of a telescope in its most basic configuration – a combination of two focal components (e.g. lenses). Such a telescope can be used for viewing distant objects, sending approximately parallel rays to the instrument, and the then also parallel output rays are sent to the observing eye (accommodated to infinite distances), where they are finally focused to the retina. Figure 1 shows two common realizations of refractive telescopes. Other realizations are based on curved mirrors or on prisms, e.g. in the form of anamorphic prism pairs.
Such an afocal telescope can not only be used as an optical addendum to the eye, but also in combination with a photo camera or an infrared viewer, for example. It then provides some amount of magnification, and at the same time there is a reduction of the field of view.
The term telescopic systems is often used for afocal systems, as the telescope is the classical example.
The magnification of a telescope equals the matrix component <$D$>. The image on the retina of the viewing eye, which is generated by an object at a large distance, is enlarged by that factor.
Beam expanders are also afocal systems. Considered in the context of wave optics, such a beam expander converts a collimated input laser beam into a collimated output beam with increased beam radius. By turning it around, one can also have the beam radius decreased. In some cases, such a beam expander is used within a laser resonator, for example in order to obtain a larger mode radius in the laser crystal.
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