Magnification geometric

A major advantage of radioscopy is the flexible inspection perspective that allows an optimum adjustment of beam direction and geometrical magnification to the inspection task at hand it also permits in-motion testing. 

The advantages of this approach for part 3 of the standard lie in the fact that no specifications on geometrical magnifications need to be made since these parameters implicitly result from the demanded IQI detectability. Furthermore, the standard is open to additional applications. All that is needed is to the definition of the respective equipment class and a specification on the respective IQI sensitivities. 

Additional limiting factor is the unsharpness resulted fi om the X-ray source size, [6] The unsharpness (Ug), in terms of the source size (f)and geometrical magnification (M), is given... 

High geometrical magnifications are attainable using a microfocus X-ray source. The capacity and speed of the computing system limits at present the size of the examined objeet volumes. 

To consider the geometrical magnification of the pipe image on film or IP in the tangential exposure technique according to the set-up shown in fig. 4 a correction of the measured wall thickness (w ) must be performed. The true wall thickness (w) depends in a rather complicated way on the film-focus-distance (f), the radius of the pipe (r) and the radius of the insulation (R) as shown in equation 2 ... 

Fig.4 Geometrical magnification effect inherent to the tangential exposure technique...

Equations 1 and 2 shows that the distance b between the radiation source and the object has big influence on the X-ray image [8]. Therefore you have to find a compromise between a small geometrical unsharpness and a sufficient high magnification to archive an optimal... 

A rough estimation of the magnification M can be obtained from a heuristic geometrical argument to yield... 

To determine the mean primary particle size and particle size distribution, the diameters of 3000-5000 particles are measured on electron micrographs of known magnification. Spherical shape is anticipated for calculations. However, since the primary particles generally build up larger aggregates, the results may be somewhat uncertain. The specific electron microscopic surface area can be calculated from the primary particle size distribution. This value refers only to the outer (geometrical) surface of the particles. For porous carbon blacks the electron microscopic surface area is lower than the specific surface area according to BET (see below). 

Figure 4.31 Data for the characterization of an electrostatic lens, (a) Positions of the focal and principal planes (left-hand and right-hand sides are indicated by the subscripts Y and r respectively) and their distances (optical sign conventions are disregarded, i.e., the distances are described only by their lengths). (b) Geometrical construction applied to image the arrow ye by means of characteristic asymptotic trajectories, (c) Geometrical construction for an asymptotic ray with a pencil angle a,e. The shaded areas are needed for the derivation of the linear and angular magnification factors of the lens. For details see main text.

A distinction must be made between the macro etch pits with geometrical contours (8,9,6), which are observed even at low magnifications and the micro etch pits which have no distinct geometrical shape. The former probably reveal only a fraction of the dislocations, whereas the latter give a better measure of the total number of dislocations (13,12,30). 

Figure 8 shows some of the mlcrostructural relationships that are observed at different magnifications in an oxide film on silicon. This example is merely a more detailed extension of the fundamental geometric features shown in Figure 4 as they apply to an oxide film. 

Fractals - Geometrical objects that are self-similar under a change of scale i.e., they appear similar at all levels of magnification. They can be considered to have fractional dimensionality. Examples occur in diverse fields such as geography (rivers and shorelines), biology (trees), and solid state physics (amorphous materials). 

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