Solid Angle
- Practical Electron Microscopy and Database -
- An Online Book -

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This book (Practical Electron Microscopy and Database) is a reference for TEM and SEM students, operators, engineers, technicians, managers, and researchers.
 

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Solid angle is derived from the Greek stereos, and the symbol for solid angle is Ω (Greek letter omega). The steradian (symbol: sr) is the SI unit (International System of Units) of solid angle. The solid angle can be defined in terms of an area on the surface of a sphere which is centred at the vertex of the angle. The solid angle is a dimensionless measure (like the radian) of how big an object appears to an observer (a point).

Solid angle can be simply given by,

         solid angle ---------------------------- [2671a]

Therefore, dΩ, as indicated in Figure 2671, is given by,

         solid angle ---------------------------- [2671b]

Schematic illustration of scattering of an electron by a single atom

Figure 2671. Schematic illustration of scattering of an electron by a single atom.

Everyone knows what a 90° angle looks like, and even referring to it as π/2 radians is relatively easy to understand. However, it is a different matter altogether with solid angles since it must be imagined in three-dimensional (3-D) space without an obvious reference. For instance, one steradian is equal to (180/π)2 square degrees. Table 2671 lists some typical values of solid angles of some specific shapes.

Table 2671. Typical values of solid angles of specific shapes.

Shapes
Solid angle measured at the centre (sr)
Complete sphere
Face of a cube
2π/3

If the solid angle Ω in steradians is known, then the corresponding area of the surface of any sphere can be calculated by,

         AS = R2·Ω ---------------------------- [2671c]
where,
          R -- The radius of the sphere.

 

 

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