This document discusses the attenuation of x-rays as they pass through matter. It defines key terms like quantity, quality, intensity, attenuation, linear attenuation coefficient, half value layer, and mass attenuation coefficient. It describes how the energy of x-rays, the density and atomic number of the absorbing material, and whether radiation is monoenergetic or polyenergetic affect attenuation. Higher energy x-rays or absorbers with lower density/atomic number experience less attenuation. Attenuation follows an exponential curve on semi-log graphs. Photoelectric interactions dominate at low energies while Compton scattering increases at higher energies. These principles underlie the contrast seen in x-ray images.

1. .
ATTENUATION
OF X- RAYS
MUHAMMED ASLAM BS
BSC MIT

2.  The two characteristics of an X ray beam are:
1. QUANTITY.
2. QUALITY.
QUANTITY is “The number of photons in the
beam”.
QUALITY is “The energies of the photons in the
beam”.

3.  INTESTITY of a beam is product of number and
energy of the photons.
 Intensity of an x ray beam depends on both
quality and quantity.

4. ATTENUATION :
 “ The reduction in the intensity of an X
ray beam as it traverses matter by either
the absorption or deflection of photons
from the beam”.
 It is a measure of a change in X ray
intensity, and hence it depends on both
quantity and quality.

5. MONOCHROMATIC RADIATION :
1cm
WATER
PHANTOM
1000
photons
410
photons
Detector
800 640 512
-20%

6. MONOCHROMATIC RADIATION :
 Intensity of the beam is decreased to 800 photons by the
first cm of water – an attenuation of 20% ( 200 photons).
 The second centimeter of water reduces the intensity to 640
photons – 20% lesser (160 photons).
 With each succeeding cm of water , 20 % of the remaining
photons are removed from the beam to 512 photons i.e 128
photons.

7. MONOCHROMATIC RADIATION :
 The quality of the radiation does not change as it
passes through an absorber.
50% ↓ in number of photons
=
50% ↓ in intensity.

8. After the beam has passed through many
cms of water, only few photons remain
Although each cm continues
to remove 20% of photons, the
total numbers are small. So
the end of the curve is flat
Initial portion of the curve is steep
because more photons are removed
from the beam by first few cms of
absorber.

9. When the number of photons
remaining in the beam
decreases by the same
percentage with each block of
absorber, it is called
exponential attenuation.
Exponential attenuation
plots a straight line on semi
log graph paper.

11. ATTENUATION COEFFCIENTS :
 “An attenuation coefficient is a measure of the
quantity of radiation attenuated by a given
thickness of an absorber”
 Coefficient determined by the units used to
measure the thickness of the absorber.

12. LINEAR ATTENUATION COEFFICIENT :
 “Quantitative measurement of attenuation per
centimeter of absorber”
 The most important coefficient for diagnostic
radiology.
 Symbol is μ.
 Unit is “per centimeter” or cm -1.

13.  The linear attenuation coefficient is for monochromatic
radiation.
 Specific both for the energy of the X ray beam and the type
of the absorber.
 Water, fat, bone and air all have different linear
attenuation coefficients.
 Size of the coefficient changes as energy of the X ray beam
changes
 When the energy of the radiation is increased , the number
of X rays that are attenuated decreases and so does the
linear attenuation coefficient

14. HALF VALUE LAYER :
 HVL = 0.693/ μ
 Half value layer : “ It is the absorber thickness
required to reduce the intensity of the original
beam by one half ”.

15. HALF VALUE LAYER :
Common method of expressing
quality of an X ray beam.
 A beam with high half value layer is
more penetrating.

16.  With linear attenuation coefficients , we can
calculate the percentage of transmitted
photons for a whole variety of photon
energies and for any thickness of tissue.

17. MASS ATTENUATION COEFFICIENT :
 “The coefficient used to quantitate the
attenuation of materials independent of their
physical state”.
For eg,
water
ice
water vapour

18. MASS ATTENUATION COEFFICIENT :
Unit (for the X ray absorber ) :gm per
square centimeter or g/cm2
This is a mass unit, hence “ mass
attenuation” coefficient.
Mass attenuation coefficient =
𝑙𝑖𝑛𝑒𝑎𝑟 𝑎𝑡𝑡𝑒𝑛𝑢𝑎𝑡𝑖𝑜𝑛
𝑑𝑒𝑛𝑠𝑖𝑡𝑦
or
μ
ρ

19. o The absorber and the coefficients
have different units
o Unit for the coefficient is reciprocal of
the unit of the absorber
Linear
attenuation
coefficient
Mass
attenuation
coefficient
Absorber Cm g/cm2
Coefficients Cm -1 Cm2/g

21. FACTORS AFFECTING ATTENUATION :
RADIATION MATTER
Energy Density
Atomic Matter
Electrons per gram

22. RADIATION AND ATTENUATION :
 Increasing the radiation energy increases the
number of transmitted photons and decreases
attenuation.
 Increasing the density, atomic number or
electrons per gram of absorber decreases the
number of transmitted photons i.e. increases
attenuation.

23. DENSITY AND ATOMIC NUMBER :
 General rule:
Elements with high atomic numbers are
denser than atoms with low atomic numbers.
 Exceptions:
ATOMIC
NUMBER
DENSITY
(gm/cm3 )
Gold 79 19.3
Lead 82 11.0

24. DENSITY AND ATOMIC NUMBER :
 No relationship between atomic number and
density when different physical states of
matter are considered.
 Eg : Water has an effective atomic number of
7.4 in ice, liquid and vapor form.

25. DENSITY AND ELECTRON PER GRAMS :
 Since density depends on volume (weight per
unit volume), there is no relationship between
density and electrons per gram.
 A gram of water has the same number of
electrons regardless of whether they are
compressed together in a 1 cm cube as liquid
or spread out over 1670 cm3 as vapor.

26. ATOMIC NUMBER AND ELECTRONS PER
GRAM
 The number of electrons per gram is really a
function of the number of the neutrons in the
atom.
 If elements didn’t have neutrons, all materials
would have 6 X 10 23 electrons per gram.

27. ELECTRONS PER GRAM FOR ELEMENTS IMP
IN DIAGNOSTIC RADIOLOGY
ELEMENTS ATOMIC
NUMBER
NO OF
ELECTRONS
PER GRAM
Hydrogen 1 6.00 X 10 23
Oxygen 8 3.01 X 10 23
Calcium 20 3.00 X 10 23
Copper 29 2.75 X 10 23
Iodine 53 2.51 X 10 23
Barium 56 2.45 X 10 23
lead 82 2.38 X 10 23

28.  Elements found in soft tissue- oxygen, carbon
and nitrogen- all have 3.00 X 10 23
electrons/gram.
 In general, elements with low atomic numbers
have more electrons per gram than those with
high atomic numbers.

29. EFFECTS OF ENERGY AND ATOMIC NUMBER :
 Energy and atomic number together
determine the percentage of each type of
basic interaction.
 Hence their effects on attenuation are
inseparable

30. PERCENTAGE OF PHOTOELECTRIC REACTIONS
RADIATION
ENERGY (keV)
WATER
(Z=7.4)
COMPACT
BONE
(Z=13.8)
SODIUM
IODIDE
(Z=49.8)
20 65% 89% 94%
60 7% 31% 95%
100 2% 9% 88%
Percentage of Compton reactions =
100 – (% of photoelectric reactions)

32. As radiation energy increases, the
percentage of photoelectric
reactions decreases
As atomic number increases,
the percentage of
photoelectric reactions
increases

33.  In extremely low energy radiation(20keV), photoelectric
attenuation predominates , regardless of atomic number of
the absorber
 As radiation energy is increased, Compton scattering
becomes more important until eventually it replaces the
photoelectric effect as the predominant interaction.
 In high atomic number absorbers, like sodium iodide, the
photoelectric effect is the predominant interaction
throughout the diagnostic energy range.

34. Linear attenuation coefficient is the sum
of the contributions from coherent
scattering, photoelectric reactions and
Compton scattering.
μ = μcoherent + μPE + μCompton
Attenuation is greater when the photoelectric effect
predominates.

35. ENERGY AND ATTENUATION :
Percent transmission through ten cm of water :

36. Photoelectric
Energy
interactions
Compton
scattering
% of
transmitted
photons
Low energy
like 20 keV
More Less Few
Increase in
energy
Decreases Increases Increases
High energy
above 100
keV
Ceases Complete Continues to
increase
COMPTON ATTENUATION IS ALL THAT IS LEFT :
increasing the beam energy will cause only a slight decrease in
attenuation and slight increase in attenuation.

37.  General rule:
“the higher the energy of the radiation, the larger
the percentage of transmitted photons, regardless
of the type of basic interaction”
 Exception:
high atomic number absorbers

38. ATOMIC NUMBER :
With high atomic number
absorbers, transmission may
actually decrease with increasing
beam energy.

39.  There is an abrupt change in the likelihood of a
photoelectric reaction as the radiation energy
reaches the binding energy of an inner shell
electron.
 A photon cannot eject an electron unless it has
more energy than the electron’s binding energy.
 Thus a lower energy photon is more likely to be
transmitted than a high energy photon , provided
one has slightly less and the other slightly more
energy than the electron’s binding energy.

41. K EDGE :
 “Sudden change in transmission occurring at the
binding energy of the K shell electron”
 Below the K edge : a fairly large percentage of
photons is transmitted.
 Above the K edge : transmission drops to nearly
zero.

42. PERCENT TRANSMISSION OF MONOCHROMATIC RADIATION
THROUGH 1 MM LEAD :
ENERGY
(keV)
TRANSMISSION
(%)
50 0.016
60 0.40
80 6.8
88 12.0
-K edge for lead-
88 0.026
100 0.14
150 0.96

43. MASS ATTENUATION COEFFICIENTS FOR
LEAD & TIN :

44.  Tin attenuates more radiation per unit weight than lead.
Thus a lighter tin apron gives the same protection as a
standard lead apron.
 Barium and iodine , the commonly used contrast agents
have ideal K shell binding energies.
 These binding energies are almost the same as the mean
energy of most diagnostic X ray beams.
 So many interactions occur at the K shell level.
 Attenuation is more intense than it would be for a higher
atomic number element.

46. APPLICATIONS OF K EDGE :
 When maximum X ray absorption is desired, the
K edge of the absorber should be closely matched
to the energy of the X ray beam.
 Selenium ( K edge : 12.7 keV) used as absorber in
mammography. Excellent absorber of 30 to 35 kVp.
 Tungsten ( K edge : 59.5 keV) used as absorber in
chest radiography with a field emission unit

47. DENSITY AND ATTENUATION :
 Tissue density is one of the most important
factors in X ray attenuation.
 Difference in tissue densities is the reason we see
an X ray image.
 Density determines :
 the no of electrons present in a given thickness and
hence
 the tissue’s stopping power
Density ∝ attenuation

48. EFFECT OF ELECTRONS PER GRAM :
 The number of Compton reactions depends on number of
electrons in a given thickness.
 Absorbers with more electrons are more impervious to
radiation.
 Electrons per gram X Density = electrons per cubic
centimeter.

49. N0 = number of electrons per
gram
N= Avogadro’s number
Z= atomic number
A= atomic weight

50. When comparing two elements, relative number of
electrons per gram is
𝑍
𝐴
or
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑠
𝑤𝑒𝑖𝑔𝑕𝑡 𝑜𝑓 𝑡𝑕𝑒 𝑎𝑡𝑜𝑚
AVOGADRO’S NUMBER : is the number of atoms or
molecules of a substance per unit mole. It remains
same for all atoms.
As atomic weight varies, different atoms have
different electrons per gram.

51.  Hydrogen has no neutrons, and it has twice as
many electrons per gram as any other element.
 Oxygen has one neutron per electron and half as
many electrons per gram as hydrogen.
 Higher atomic number elements have about 20%
fewer electrons per gram than the low atomic
number elements.

52. COMPARISON OF PHYSICAL CHARACTERISTICS OF
WATER, FAT, AIR AND BONE
ATOMIC
NUMBER
DENSITY
(g/cm3)
ELECTRON
S PER
GRAM
ELECTRONS
PER CUBIC
CENTIMETE
R
Air 7.64 0.00129 3.01 X 10 23 0.0039 X 10 23
Fat 5.92 0.91 3.48 X 10 23 3.27 X 10 23
Water 7.42 1.00 3.34 X 10 23 3.34 X 10 23
Bone 13.8 1.85 3.0 X 10 23 5.55 X 10 23

53. POLYCHROMATIC RADIATION
 Polychromatic beams contain a whole spectrum
of photons of various energies.
 The most energetic are determined by the peak
kilovoltage (kVp) used to generate the beam.
 Mean energy = 1/3 to 1/2 of its peak energy
 Depends on filtration

54. As polychromatic radiation passes through an absorber
 the transmitted photons undergo a change in both
quantity and quality
 Number of photons decreases because some are
deflected and absorbed out of the beam
 quality of beam also changes because lower energy
photons are more readily attenuated than higher energy
photons (unlike monochromatic radiation )
 As the lower energy photons removed from the beam,
the mean energy of the remaining photons increases

55. ATTENUATION OF POLYCHROMATIC
RADIATION :
1000
Photons
40 kV
mean
650 474 365
288
Photons
57 kV
mean47 kV 52 kV 55 kV
-35% -27% -23% -21%

56. The slope becomes straight when mean energy of polychromatic
radiation approaches its peak energy.

57.  When the percentage of transmission is plotted
on semi logarithmic graph paper, it results in a
curved line
 Initial slope is steep because many low energy
photons are attenuated by the first few cm of
water
 Eventually curve becomes similar to slope for
monochromatic beam as the mean energy of the
poly chromatic radiation approaches its peak
energy

58. APPLICATIONS TO DIAGNOSTIC RADIOLOGY :
 The photons in an X ray beam enter a patient
with uniform distribution and emerge in a
specific pattern of distribution
 The transmitted photons carry the X ray image
 Their pattern carries the memory of the
attenuated photons

59. APPLICATIONS TO DIAGNOSTIC RADIOLOGY :
 Complete transmission Film becomes uniformly black
 Complete attenuation Film becomes uniformly white.
Some tissues attenuate more X rays than others
and the size of this differential determines the
amount of contrast in the X ray image.

61. SOFT TISSUE AND FAT :
 Effective atomic number of water : 7.4
 Effective atomic number of fat : 5.9
 Water
 Net electrons per unit volume of water and fat remains the
same.
 So if Compton reactions predominate, differentiation
between water and fat is difficult.
Increased density
Fewer electrons per gram

62. SOFT TISSUE AND FAT :
 Effective atomic number of water : 7.4
 Effective atomic number of fat : 5.9
 This difference in atomic number helps in
differentiating soft tissue and fat if photoelectric
reactions predominate.
 Photoelectric reactions predominate in low
energy techniques.

63. SCATTER RADIATION :
 Primary radiation carries the x ray image.
 Secondary radiation: undesirable radiation
which includes photons and electrons that might
contribute to film fog
 Compton scattering causes significant secondary
radiation.

64. SCATTER RADIATION :
 Makes up 50 to 90% of
total number of photons
emerging from the patient.
 With thick body parts like
abdomen, only 1% of the
photons in initial beam
reach the film.
 The rest are attenuated.

65. FACTORS AFFECTING SCATTER RADIATION :
1. Kilovoltage (kVp).
2. Part thickness
3. Field size

66. FIELD SIZE :
 Most important factor.
 Small X ray field ( narrow beam) irradiates only
a small volume of tissue so it generates only a
small number of scattered photons.
 Most miss the film because of a large angle of
escape

68.  As x ray field is enlarged, the scatter radiation increases
rapidly at first.
 Then gradually tapers off until it reaches a plateau or
saturation point.
 Further increase in field size does not change the quantity
of scatter radiation that reaches the film
 The total number of scattered photons in the field increase
but the number that reaches any particular point on the
film remains constant

69. PART THICKNESS :
 Just as with field size, quantity of scatter
radiation reaches a saturation point with
increasing part thickness.
 The total number of scattered photons keep
increasing as the part becomes thicker but
photons originating in the upper layers of the
patient do not have sufficient energy to reach the
film

70. KILOVOLTAGE :
 In low energy range, extremely little scatter
radiation is produced.
 As the radiation energy increases, the production
of scatter radiation increases.
 After Compton scattering becomes the
predominant interaction, scatter radiation tends
to plateau.

71. KILOVOLTAGE :
 At this stage, quantity of scatter radiation
increase with increasing beam energy.
 Energy at this plateau point depends on atomic
number of the tissue.
 Plateau is not as well defined as with field size
and part thickness.