The Solid Angle—General Definition

To illustrate the concept of solid angle, consider a point isotropic source at a certain distance from a detector as shown in Fig. 8.3. Since the particles are emitted by the source with equal probability in every direction, only some of the particles have a chance to enter the detector. That portion is equal to the fractional solid angle subtended by the detector at the location of the source. In the general case of an extended source, the solid angle fl is defined by 

The mathematical expression for a is derived as follows (Fig. 8.4). A plane source of area emitting Sq particles/(m s), isotropically, is located a distance d away from a detector with an aperture equal to A. Applying the definition given by Eq. 8.2 for the two differential areas dA and dAj and integrating, one obtains  

Equation 8.4 is valid for any shape of source and detector. In practice, one deals with plane sources and detectors having regular shapes, examples of which are given in the following sections. 

As stated earlier, II is equal to the fractional solid angle (0 fl 1). In radiation measurements, it is called either solid angle or geometry factor. In this text it will be called the solid angle. 

3 The Solid Angle for a Point Isotropic Source and a Detector with a Circular Aperture 

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