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.

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.

References in periodicals archive ?
Sakr, "Analytical formulae to calculate the solid angle subtended at an arbitrarily positioned point source by an elliptical radiation detector," Nuclear Instruments and Methods in Physics Research Section A, vol.
From the observer point of vue, the geometric etendue of the HUD image can be assessed summarily as the product of the solid angle associated with the accessible Field Of View (FOV) by the transverse dimensions of the Eye Motion Box (EMB).
The correctness of the method of calculating the solid angle was confirmed experimentally by changing the distance of the target--detector.
and Forouhideh, F.: 2011, Solid angles and the impact of receiver-array geometry on microseismic moment-tensor inversion.
Electrons orbit the proton about 200 times further out than the muon and so the solid angle of the proton at the electron is much smaller.
As part of Autodesk, Solid Angle's development team will continue to drive the evolution of Arnold working in close collaboration with its user community.
The approximate value of the solid angle is obtained from the collocation of equation (4.3) over [T.sup.0.sub.n] for c([t.sup.0]) = 1/2.
Average (SD) (min~max) Number of patients 100 (M:F = 58:42) Age (year) 38.9 (12.8) (16~79) Best-corrected visual acuity 20/30 (20/30) (20/100 to 30/20) Visual field area (nsu) ([dagger]) 13.3 (24.0) (0.2~100.0) PROS area ([double dagger]) 4.1 (4.3) (0.0~18.0) ([mm.sup.2]) PROS horizontal length ([micro]m) 2202.2 (1341.6) (102~5363) PROS vertical length ([micro]m) 1767.2 (1105.3) (90~4942) Central subfoveal thickness 248.2 (40.2) (135~383) ([??]) ([micro]m) ILM-ELM thickness ([parallel]) 133.2 (34.9) (45.5~284.0) ([micro]m) ELM-RPE thickness ([??]) 65.4 (15.4) (27.0~96.0) ([micro]m) Subfoveal choroid thickness 265.5 (67.8) (89.5~422.5) ([micro]m) ([dagger]) Normalized solid angle unit.
By integrating sensor modules directly into the EXpress and EXtreme SEM platforms, the system is able to provide more than four times the solid angle using the same sensor size.
The LCS system examines the absolute lumen distribution of a luminaire in three primary solid angles, Uplight, Forward Light and Back Light.
Experienced resemblance in outline shape is the experience of sameness of the solid angle subtended by the contours on the pictorial surface and the solid angle subtended by the actual depicted objects.