Consider the following simple model of projection conventional x-ray
imaging, which models the patient as a homogeneous slab of thickness
L, with linear attenuation coefficient µb. Embedded in the slab is a
target object of dimensions w×w×d and with attenuation coefficient µt.
The fluence of scattered radiation at the image receptor plane is
constant with position. The ray paths are assumed parallel. (i.e. SID
= 1).


(a). Determine an expression for the radiation contrast CR between the
target and background regions, using 	C = |A1 ? A2|
				            A
as the definition of contrast in some signal A.


(b). Show that CR = CR no scatter(1 ? F) where

F = scatter fraction = s p + s , [s = scatter, p = primary]

(c). Show that the expression for CR simplifies for low-contrast
targets (i.e. 
µd << 1) to
the following expression CR  |
µd| × (1 ? F).