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Gaussian Optics

Definition: a framework for describing optical phenomena, which is based on geometrical optics and the paraxial approximation

German: Gauß-Optik

Category: general optics

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Gaussian optics is a framework for describing optical phenomena, which is based on geometrical optics (ray optics) and makes extensive use of the paraxial approximation. It has been developed by Johann Carl Friedrich Gauss (1777 – 1855) and is still widely used for many purposes.

The essential assumptions on which Gaussian optics is based are the following:

It is no problem that substantial angles can be involved e.g. in refraction at prisms; at those optical components, the optical axis can also be assumed to be bent. Only angles relative to the optical axis need to be small.

Under the mentioned assumptions, a substantially simplified mathematical description of optical phenomena is possible:

One can also apply the related rules in geometrical drawings.

The described framework can be applied to a wide range of optical systems – for example, to telescopes, photo cameras and microscopes. One can calculate parameters like focal lengths, the transverse, linear and longitudinal magnification, identify conjugate planes, focal planes, image planes etc. However, important phenomena like optical aberrations cannot be treated, because those involve geometrical nonlinearities which are neglected in Gaussian optics. Their treatment requires substantially more sophisticated mathematical methods. One can consider Gaussian optics to provide a simplified description, which is relatively easily calculated, and aberrations (as calculated with more sophisticated methods) are deviations from that.

Although Gaussian optics belongs to the methods of geometrical optics, various parameters have a direct correspondence to quantities in wave optics. Therefore, it is possible, for example, to describe the propagation of Gaussian beams (including wave effects like diffraction) based on parameters calculated with Gaussian optics.

Note that the well known Gaussian beams are not appearing in the realm of Gaussian optics; they belong to wave optics.

See also: geometrical optics, paraxial approximation, image planes, cardinal points, principal points and principal planes, ABCD matrix
and other articles in the category general optics

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