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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.
Optical systems can be folded using plane mirrors; the system is still considered to be rotationally symmetric if it possesses rotational symmetry when unfolded. Any point on the optical axis (in any space) is an axial point. Rotational symmetry greatly simplifies the analysis of optical systems, which otherwise must be analyzed in three ...
In geometric optics, the paraxial approximation is a small-angle approximation used in Gaussian optics and ray tracing of light through an optical system (such as a lens). [1] [2] A paraxial ray is a ray that makes a small angle (θ) to the optical axis of the system, and lies close to the axis throughout the system. [1]
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 ...
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.
A perfect optical system produces an image with the same etendue as the source. The etendue is related to the Lagrange invariant and the optical invariant, which also share the property of being constant in an ideal optical system. The radiance of an optical system is equal to the derivative of the radiant flux with respect to the etendue.
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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.