Solid Angle

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solid angle

[′säl·əd ′aŋ·gəl]
(mathematics)
A surface formed by all rays joining a point to a closed curve.
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 It might be outdated or ideologically biased.

Solid Angle

 

a surface formed by rays having a common origin and passing through a closed curve (Figure 1). Sometimes, particularly in Soviet usage, the term “solid angle” is applied to the portion of space bounded by such a surface. Trihedral and polyhedral angles are special cases of solid angles.

Figure 1

A measure of the solid angle subtended at a given point by a surface S is provided by the ratio AIR2. Here, A is the area of the portion of a sphere, with center at the given point, that is cut by a conical surface with vertex at the point and with the perimeter of S as a directrix, and R is the radius of the sphere. Clearly, the measure of a solid angle is an abstract number. For example, the measure of a solid angle that encloses an octant, that is, oneeighth of space, is the number 4π R2/8 R2 = π/2 (Figure 2).

Figure 2

The unit of measure of a solid angle is called the steradian. It is equal to the solid angle subtended at the center of a sphere of unit radius by a portion of the sphere’s surface that is of unit area. The total solid angle about a point is equal to 4π steradians.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
The preliminary BUG rating system proposed by the committee included four of the LCS solid angles that contribute to sky-glow: Front Very High (FVH) which captures light emitted in front of the luminaire between 80[degrees] and 90[degrees] above nadir, Back Very High (BVH) which captures light emitted behind the luminaire between 80[degrees] and 90[degrees], Uplight Low (UL) which captures light emitted across all horizontal angles between 90[degrees] and 100[degrees] above nadir, and Uplight High (UH) which captures the light emitted from 100[degrees] above nadir to zenith.
Per TM-15-07, "[LCS] does not provide quantitative lumen limits within each solid angle." It does, however, establish the framework in which those types of quantitative limits can be determined.
Aside from the problem noted initially, that most Canadians have not visited the scenes depicted in the paintings they enjoy perceptually as depicting those particular scenes, the depicted rocks and trees have shapes that subtend quite different solid angles from those subtended by actual trees and rocks, shapes that we would describe as highly indeterminate.