```Radiation Quality
Chapter 4
X-ray Intensity
• Intensity: the amount of energy present per unit
time per unit area perpendicular to the beam
direction at the location of interest.
 The number of photons reaching the detector per
second is a measure of beam intensity (photons/cm2).
 Exposure Rate: (mR/hr); dose rate: (cGy/min)
• Intensity of photon beam at the tumor
 Depends primarily on the original strength of the
beam.
 Reduced by beam divergence and attenuation.
Beam Divergence
proportional to the square of the distance
from the source.
• Inverse square law: intensity is inversely
proportional to the square of the distance
from the source.
I1 / I2 = D22 / D12
Or
I2 = I1(D1/D2)2
Beam attenuation
• Attenuation: the removal of energy from the beam.
• X-rays interact with charged particles through the
electromagnetic fields associated with the electric and
magnetic fields of electrons and nuclei.
 When a beam passes through matter, energy is removed from
the beam.
• Photons will either…
 Interact with the filter/attenuator
 Be absorbed by the material
 They deposit all their energy in the filter
 Direction changed or scattered
 Unaffected by the filter
Transmission
• Transmission: the ratio of beam intensity
I to IO.
• As the filter thickness increases, the
intensity of the attenuated beam drops.
• Transmission = I/ IO
IO: initial intensity at the detector before
filtration
I: the final beam intensity after filtration
Transmission
• Photon source with single energyattenuation of the beam:
I = IOe-μx
• x = thickness of the filter
• μ = linear attenuation coefficient, (length-1)
• e = base of natural logarithm (2.718)
• Each millimeter of thickness added to the
filter reduces the beam by a constant
percent
Transmission Example
• Attenuation coefficient (μ) = 0.2 mm-1
• Thickness (x) = 3mm
• IO = 2000 photons
I = IOe-μx
I = 2000 * e(-0.2 *3)
I = 2000 * 0.549
I = 1098 photons
Linear Attenuation Coefficient
• Linear attenuation coefficient (μ ): a
function of the filter material and the
energy of the photon beam.
Represents a probability per unit thickness
that any one photon will be attenuated.
• Half-Value Layer determined by μ
Monoenergetic / Homogenous
• Monoenergetic/homogenous: all photons in
the beam have the same energy
 μ: remains unchanged for all filter thicknesses or
number of photons removed (number of photons
change)
 Higher μ  higher probability of interaction  smaller
HVL
• More easily reduced in intensity
• An exponential function produces a straight line
on semi-log graph paper.
Polyenergetic / Heterogenous
photon energies (bremsstrahlung).
 μ: each energy has a different value.
• On semi-log graph paper, the slope changes as
filter is added due to beam hardening.
• Beam Hardening: the effective energy of the
beam increases as it passes through the filter.
 Only occurs in a polyenergetic/heterogeneous beam.
Half-Value Layer
• Half-value layer (HVL): the thickness required
for a particular material to cut the beam’s
intensity in half.
 HVL = 0.693/ μ
 Used to describe the beam’s penetrability
 Convenient to characterize different bremsstrahlung
beams using their attenuation characteristics.
• Materials used to specify beams HVL changes
with energy range
 Diagnostic/superficial: mm Al
 Orthovoltage: mm Cu
 MeV: mmPb
Homogeneity Coefficient
• Homogeneity Coefficient:
HC = 1st HVL/2nd HVL
• As HC  1: the more alike individual
beam energy are.
• 1st HVL = 2nd HVL = 3rd HVL…
monoenergetic beam
Equivalent Energy
• Equivalent Energy: represents the
average energy of the beam
The energy of the monoenergetic beam that
would have an HVL equal to the first HVL of
the bremmsstrahlung beam in question.
Attenuation Coefficients
• Linear attenuation coefficient (μ): gives the
probability that a given photon will be attenuated
in a unit thickness of a particular attenuator.
– Photon energy & material dependant
• Mass attenuation coefficient (μ/ρ): probability
of interaction per unit mass length when
μ/ρ << 1, (cm2/g)
– Decreasing the density of the material will cause
much less attenuation.
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