Suppose you have a 20-cm-thick slab of material. You measure the fraction t(E) of x-rays that get…

Suppose you have a 20-cm-thick slab of material. You measure
the fraction t(E) of x-rays that get through this material (on average) over
the energy band 50150 keV, and discover that it is well modeled by the
relation

(a) Find an expression for the linear attenuation
coefficient of this material as a function of x-ray energy E.

Suppose a 5-cm cube of a second material replaced a 5-cm
cube of original material from the center of

Suppose you have a 20-cm-thick slab of material. You measure
the fraction t(E) of x-rays that get through this material (on average) over
the energy band 50150 keV, and discover that it is well modeled by the
relation

(a) Find an expression for the linear attenuation
coefficient of this material as a function of x-ray energy E.

Suppose a 5-cm cube of a second material replaced a 5-cm
cube of original material from the center of the slab and suppose this second
material has linear attenuation coefficient of 0.15 cm_2 at 75
keV.

(b) What is the intrinsic contrast of this new material
relative to the slab at 75 keV? (Intrinsic contrast is defined by the linear
attenuation coefficients alone, as if you could image them directly.)

(c) What is the contrast of this new material if imaged
through a standard radiographic system at 75 keV? (Ignore photon noise,
detector efficiency, beam divergence, scatter, and magnification effects.)

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