Depending on the value of the view angle (angle between the central X-ray beam and the object plane) two models are discussed. First, it is assumed that the central X-ray beam is perpendicular to the object plane. Second, an arbitrary view angle model is analyzed.
Let us first consider a case when the X-ray falls perpendicular to the object plane (i.e., the central X-ray beam is at the zenith position with respect to the patient). A point P x, y (Fig. 12) is projected onto the input phosphor surface at Pa x, y . The original distance d0 is magnified to dx and then lengthened to da (arc between S and Pa) by the input phosphor spherical surface. Since in this approach no other distortions are considered, a linear magnification is assumed.
Magnification along the central beam is dx £2 g d0 £1
where d0 is the distance from the object to the central point in the input phosphor, dx is the magnified distance of d0, and £1 and £2 are a distances from the focal spot FS to the object plane and input phosphor screen, respectively. From the geometry of Fig. 12, d, £ £2
From Eq. (10) and by the use of Eq. (11), the magnified distance dx is
With substitution of the relationship between the chord d,, arc 0, and radius R of the sphere, d, 2R sin 0/2
If we substitute Eq. (14) in Eq. (9), the relationship between the original distance d0 and its projection onto the input phosphor surface da is given by d0
52 2R tg2 da/2R
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