# Indicatrix

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## indicatrix

[in′dik·ə‚triks]
(optics)
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Indicatrix

in optics a vector diagram representing the dependence on direction of the characteristics of a light field (light intensity and polarization) or of the optical characteristics of the medium (indexes of refraction; reflectivity).

A particular case of the indicatrix is the scattering indicatrix, which represents the dependence of the intensity of the scattered light on the angle of scattering under the condition that the incident light is not polarized, and the optical indicatrix (in crystal optics). The optical indicatrix of an optically isotropic medium is a sphere. The indicatrix for crystals with trigonal, hexagonal, and tetragonal systems is an ellipsoid of revolution. The indicatrix for crystals with rhombic, monoclinic, and tri-clinic systems is a general ellipsoid.

The indicatrix is used when the analytical equations for the corresponding angular dependences are complex or unknown, and also for the systematization of experimental data.

References in periodicals archive ?
Let X(U) be a Lorentzian surface in anti-de Sitter space, the lightcone Gauss indicatrix is constant if and only if there exists a unique lightlike hyperplane HP(n, -1) in [R.sup.n + 1.sub.2], such that the M = X(U) is a part of [H.sup.n.sub.1] [intersection] HP(n, -1), where n = [L.sup.[+ or -]] (u).
The recorded species of Foraminifera are as follows: Alveolina indicatrix HOTTINGER, 1960.
Moreover, we give some new characterizations of the Mannheim partner curves by considering the spherical indicatrix of some Frenet vectors of the curves.
Scientists mostly from post-socialist countries describe their experiments or review the literature regarding such matters as paraxial light beams with angular momentum, quasi-ballistic light scattering on particulate media, a novel single-shot technique of micro-nano patterning in single-step through selective laser ablation, optical design techniques in developing current eye models, optical waves in a medium with a rotating optical indicatrix, and a geometrical-optics analogue of an astigmatic elliptic Gaussian beam.
To better imagine optical relationships, the model of the indicatrix has proven very useful.
(For all p [member of] P, [e.sub.p] denotes the indicatrix row-vector of state p) and two matrices [R.sub.r] and [S.sub.r] and are defined for the block (i, j) with 0 [less than or equal to] i, j [less than or equal to] r - 1 by:
It is applicable for any Finsler space  for which in any point of the main space [x.sup.1], [x.sup.2] ..., [x.sup.n] the indicatrix volume [([V.sub.ind]([x.sup.1], [x.sup.2], ..., [x.sub.n])).sub.ev] can be defined, provided the tangent space is Euclidean.
Kittler  further developed a sky luminance model for the clear sky by expressing the relative sky luminance as a product of two functions, namely, indicatrix and gradation functions.
(2) The following statement about dispersion is given: "Dispersion follows in the format r [greater than] v or r [less than] v in accordance with whether the indices are greater for red or violet light, but the notation may also refer to dispersion of the optic axis or orientation of the indicatrix." This is wrong; a statement such as "dispersion r [greater than] v, strong" refers only to the dispersion of the optic axes not the indices of refraction.
This enables one to explain that the nonlinear effects in the polarizability are linked with a "nonspherical optical indicatrix surface on microstructures distribution of the crystalline phase" .

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