Gaussian optics (original) (raw)

Author: the photonics expert (RP)

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

Category: general optics

• optics
  • geometrical optics
  • wave optics
  • Fourier optics
  • quantum optics
  • Gaussian optics
  • technical optics
  • aspheric optics
  • adaptive optics
  • diffractive optics
  • integrated optics
  • fiber optics
  • flat optics
  • micro-optics
  • freeform optics
  • laser optics
  • nonlinear optics
  • ultrafast optics
  • infrared optics
  • ultraviolet optics
  • (more topics)

Related: geometrical opticsparaxial approximationimage planescardinal pointsprincipal points and principal planesABCD matrix

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DOI: 10.61835/9ow Cite the article: BibTex BibLaTex plain textHTML Link to this page! LinkedIn

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What is Gaussian Optics?

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:

• Light can be described with geometrical light rays (geometrical optics); wave effects can be ignored.
• The investigated systems are rotationally symmetric around an optical axis. (A simple generalization can lead to different behavior in two transverse dimensions, for example for treating cylindrical lenses.)
• All relevant light rays have only relatively small angles relative to the optical axis. Various equations treat only first-order terms, e.g. identifying the sine or the tangent of an angle (in radians) with the angle itself. The paraxial approximation is used throughout.

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:

• Any light ray can be described with two coordinates for a certain ($z$) position along the optical axis: for example, a transverse coordinate ($y$) and an angle ($u$). (Sometimes, one uses reduced coordinates ($\omega = n u$) and ($\tau = z / n$), where some relations are simpler.)
• For a wide range of optical components such as lenses, prisms and mirrors, one can describe the effect on the two coordinates with a 2 × 2 matrix (ABCD matrix) because the relations between inputs and outputs are linear.
• Likewise, any combination of such optical elements (and air spaces between them) can be described with such a matrix, which is obtained by multiplication of the matrices corresponding to the different elements and air spaces.
• One can also describe the optical function of an element or a combination of elements by specifying so-called cardinal points. Those can be calculated from the mentioned matrix, and vice versa. A complete optical system can thus be treated as a kind of black box, which is characterized by only a few Gaussian parameters.

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 do not appear in the realm of Gaussian optics; they belong to wave optics.

Frequently Asked Questions

This FAQ section was generated with AI based on the article content and has been reviewed by the article’s author (RP).

What is Gaussian optics?

Gaussian optics is a framework for describing optical phenomena based on geometrical optics (ray optics) and the paraxial approximation. It allows for a simplified mathematical description of light propagation through optical systems.

What are the core assumptions of Gaussian optics?

The main assumptions are that light travels in rays, the optical system is rotationally symmetric around an optical axis, and all light rays have small angles with respect to this axis (the paraxial approximation).

How does Gaussian optics describe optical systems mathematically?

It describes a light ray with its position and angle and represents the effect of optical components like lenses and mirrors with 2 × 2 matrices (ABCD matrix). An entire system can be described by multiplying the matrices of its components.

What are the limitations of Gaussian optics?

Gaussian optics neglects geometrical nonlinearities, so it cannot describe phenomena like optical aberrations. The treatment of such effects requires more sophisticated mathematical methods beyond this first-order approximation.

Are Gaussian beams part of Gaussian optics?

No, Gaussian beams are a concept from wave optics, not Gaussian optics, which is based on geometrical optics. However, the mathematical formalism of Gaussian optics, like ABCD matrices, can be used to describe the propagation of Gaussian beams.

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