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Gaussian optics is a technique in geometrical optics that describes the behaviour of light rays in optical systems by using the paraxial approximation, in which only rays which make small angles with the optical axis of the system are considered. [1] In this approximation, trigonometric functions can be expressed as linear functions of the angles.
The Gaussian function has a 1/e 2 diameter (2w as used in the text) about 1.7 times the FWHM.. At a position z along the beam (measured from the focus), the spot size parameter w is given by a hyperbolic relation: [1] = + (), where [1] = is called the Rayleigh range as further discussed below, and is the refractive index of the medium.
Alvan G. Clark, the son of the founder of the eponymous American optical company, designed a photographic lens using a symmetric arrangement of two Gauss lenses and patented it in 1888; [4] Paul Rudolph introduced the Zeiss Planar as an improved Double-Gauss using cemented doublets in the place of the inner negative meniscus elements, [2]: 121 ...
Consequently, Gaussian functions are also associated with the vacuum state in quantum field theory. Gaussian beams are used in optical systems, microwave systems and lasers. In scale space representation, Gaussian functions are used as smoothing kernels for generating multi-scale representations in computer vision and image processing.
In optics, surface vertices are the points where each optical surface crosses the optical axis. They are important primarily because they are physically measurable parameters for the optical element positions, and so the positions of the cardinal points of the optical system must be known with respect to the surface vertices to describe the system.
Development of the Double Gauss. The earliest double Gauss lens, patented by Alvan Graham Clark in 1888, consists of two symmetrically-arranged Gauss lenses.Each Gauss lens is a two-element achromatic lens with a positive meniscus lens on the object side and a negative meniscus lens on the image side.
Gaussian beam width () as a function of the axial distance .: beam waist; : confocal parameter; : Rayleigh length; : total angular spread In optics and especially laser science, the Rayleigh length or Rayleigh range, , is the distance along the propagation direction of a beam from the waist to the place where the area of the cross section is doubled. [1]
In optical aberration theory, it is common to describe an imaging system as diffraction-limited if the Airy disk radius is larger than the RMS spotsize determined from geometric ray tracing (see Optical lens design). The Gaussian profile approximation provides an alternative means of comparison: using the approximation above shows that the ...