China
Africa
Explore chapters and articles related to this topic
Basics of Radiation Interactions in Matter
Published in Michael Ljungberg, Handbook of Nuclear Medicine and Molecular Imaging for Physicists, 2022
The two-dimensional angle is defined by a part of the perimeter of the unit circle and is measured in units of radians, where a full length around the circle equals an angle of 2π radians. A solid angle (often denoted by Ω) is defined as a unit of area, A, on a unit sphere surrounding the midpoint of the sphere divided by r2 (Figure 3.2). The unit of the solid angle is termed a steradian. The solid angle can then be calculated using the equation Ω=A/r2. For a unit sphere, the largest solid angle Ω is 4π.
Radiometric and Photometric Measurements
Published in Lazo M. Manojlović, Fiber-Optic-Based Sensing Systems, 2022
Before starting introducing radiometric quantities, there are some important geometrical parameters that must be first introduced. One of these parameters is surely the solid angle. A solid angle can be understood as the two dimensional equivalent of a linear angle or as the two-dimensional angle in three-dimensional space. This angle is the measure of the size of the object that appears to an observer looking at it from a certain point. The solid angle can be equivalently defined as the projection of an area onto a sphere surface divided by the square of the radius of the sphere, as is presented in Figure 2.1: Ω=Sr2, where S is the projected area onto the sphere surface and r is the radius of the sphere. The maximal value of the solid angle is equal to 4π sr (steradians).
Light Sources
Published in Toru Yoshizawa, Handbook of Optical Metrology, 2015
Most of the theoretical models build on the supposition of a point light source that emits in all directions, we have to define first the term “solid angle,” which is measured in steradians (sr). According to NIST SP811, the steradian is defined as follows: “One steradian (sr) is the solid angle that, having its vertex in the center of a sphere, cuts off an area on the surface of the sphere equal to that of a square with sides of length equal to the radius of the sphere.” The solid angle is thus the ratio of the spherical area to the square of the radius. The spherical area is a projection of the object of interest onto a unit sphere, and the solid angle is the surface area of that projection. If we divide the surface area of a sphere by the square of its radius, we find that there are 4π sr of solid angle in a sphere. One hemisphere has 2π sr. The solid angle, as illustrated in Figure 1.2, is defined by the area the cone cuts out from a sphere of radius R = 1 (Figure 1.2). For small solid angles, the spherical section can be approximated with a flat section, and the solid angle is dΩ(α)=π(Rsinα)2R2=πsin2α
Categorization of inorganic crystal structures by Delaunay tetrahedralization
Published in Science and Technology of Advanced Materials: Methods, 2022
Things become much more complicated with the Delaunay polyhedron is not a tetrahedron. There are multiple, equally reasonable ways to split such a Delaunay non-tetrahedron into tetrahedra, and we want to avoid dealing with this degeneracy issue. The aforementioned algorithm is demonstrated when the Delaunay polyhedron is a cube (Figure 2), which appears in the simple cubic and related structures such as rocksalt, but is valid for all possible polyhedron shapes. The same atom (vertex) is denoted with various symbols depending on the role of the atom in the analysis. There are eight vertices, A and Q1 to Q7, and six facets, F1 to F6, in Figure 2(a). Facet F1 is shown in Figure 2(b). There are three angles of the form (orange arcs), and the largest angle, , is the bond angle of A for this facet. There are three vertices, S1 to S3, that are connected by a ridge of the Delaunay polyhedron to A (Figure 2(c)). These vertices are projected to the unit sphere (projected vertices are S’1 to S’3) centered at A, and the area of the spherical triangle with vertices S’1 to S’3 (spherical excess) is π/2. Therefore, the solid angle of A is π/2 sr, or 1/8 of the solid angle of a sphere (4π sr).
Discomfort Glare from Several Sources: A Formula for Outdoor Lighting
Published in LEUKOS, 2021
Joffrey Girard, Céline Villa, Roland Brémond
We have considered a constant solid angle equal to sr. But as the LED strip was stuck on a vertical screen, the solid angle actually decreased slightly as the eccentricity of the stimuli increased (for instance, stimulus at was seen with a solid angle sr). Also, the three test sessions were carried out in strict order (single, two and three sources). We needed the results of the first session (one-LED) in order to tune the two other sessions, but we could have counterbalanced the 2-LEDs and 3-LEDs session. A posteriori, no effect of inter-distance was found neither for 2-LED nor for 3-LED stimuli and both sets of data lead to the same value of . This suggests that no learning or fatigue effect occurred in the experiment.
Efficient Design Method of Segmented Lenses for Lighting Applications with Prescribed Intensity and Low Peak Luminance
Published in LEUKOS, 2019
Karel Desnijder, Ward Deketelaere, Wouter Ryckaert, Peter Hanselaer, Youri Meuret
This is still a 2F design problem because it only requires the design of a cross section of the segmented lens, which is then rotated around the optical axis. To get a 2D description of the problem, the illuminance is considered in an infinitesimal circle segment with opening angle , as illustrated in Fig. 8. The light flux incident on an infinitesimal area must be equal to the light flux emitted in the solid angle that encompasses this area. The relation between the illuminance on a flat surface and the target intensity in an angular section is described by