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the
are
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their
ics
principles
article
test,
the
basic
phys-
relevant
radiologic
by which
characteristic
processes.
and
.
radiation,
This
article
ics
of imaging
and
nuclear
struc-
ture.
.
Understand
lung
by
Be
x-ray
phy
.
quality
x rays.
familiar
with
spectra
for
interact
are
produced
are
Bremsstrahlung
with
radiation.
called
x rays
The
the
produce
matter
and
unique
two
bremsstrahlung
and
a continuous
x-ray
familiar
with
equipment
affect
the
(or
both)
atomic
number
of
the
anode
material,
tube
potential,
filtra-
waveform.
on
x-ray
typical
production
with
mental
physics
sented
within
of this
x rays.
principles
this
first
the
articles
the
characteristic
PHYSICS
will
review
article
the
fundamental
is to review
mechanisms
x-ray
of x-ray
and
the
physics.
funda-
the material
The
production,
second
specifically
characteristics
preobjecthe
of an x-ray
that affect the quantity
user of x-ray-producing
phys-
various
for understanding
on basic
processes,
trum.
The various
equipment
parameters
an x-ray beam
are discussed
so that the
the ramifications
of his or her choices.
U FUNDAMENTAL
that
of this
the foundation
remaining
is to describe
and
of six
first
objective
that form
and
article
is the
The
spec-
or quality
(or both)
devices
can understand
of
PRINCIPLES
radiogra-
mammography
various
eters
dcc-
create
and
Be
are
mechanisms
energetic
can
the
voltage
bremsstrahlung
which
basic
which
trons
x rays
electrons
electromagnetic
INTRODUCTION
tive
charac-
bremsstrah-
processes,
the two
.
the
and
by
and
particles,
and energy.
teristic
energetic
into
includ-
fundamental
atomic
tion,
to
physics,
electromagnetic
force
highly
energy
mechanisms
is affected
Understand
when
kinetic
whereas
characteristic
x rays are produced
at specific
narrow
bands
of energies.
Many technical
parameters
of the x-ray production
equipment
affect the magnitude
and shape
of the x-ray spectrum.
The quantity
of x rays produced
varies
proportionally
to the tube potential
squared,
tube current,
exposure time, and atomic
number
of the anode
material
and is inversely
proportional
to the distance
squared.
X-ray quantity
is also affected
by the voltage
waveform
(generator
type)
and tube filtration.
The shape
of the x-ray spectrum
u’ill:
.
ing
PhD
spectrum,
reading
and
rays
convert
questionnaire
pp
H. McCollough,
I of
Physician’s
Recognition
the
Cynthia
1. 0 credit
in Category
the
Productio&
.
Physical
how
To
describe
param-
some
quantity
of an
or
Quantities
and
of which
bitrary.
are
Thus,
and
measure
the
listed
Units
physical
in Table
by international
worhd,
1.
scientists
The definition
agreement,
standards
HVL
layer,
use
various
of physical
have
been
physical
quantities,
quantities
cannot
developed
that
be arprecisely
x-
ray beam.
Abbreviations:
Index
terms:
RadloGraphics
‘From
55905.
sion
,
amu
Physics
1997;
=
atomic
mass
requested
April
=
half.value
SI
=
Syst#{232}me International
17:967-984
the Department
of Diagnostic
From
the AAPM/RSNA
Physics
RSNA,
unit,
Radiography
#{149}
3 and
received
Radiology,
Tutorial
April
Mayo
at the
2 1 ; accepted
Clinic
and
1996 RSNA
April
24.
Mayo Foundation,
scientific
assembly.
Address
reprint
200 First
Received
requests
St. SW, Rochester.
MN
February
13. 1997:
revito the
author.
1997
967
Table 1
Physical
Quantities
and
Quantity
Units
SI Units
(mks)5
Engineering
CGS
Units
Temperature
#{176}K
#{176}F
centimeter
gram
second
dyne
erg
watt
dyne/centimeter2
#{176}C
Charge
coulomb
coulomb
coulomb
Current
Potential
Resistance
Magnetic
Frequency
ampere
volt
ampere
volt
ampere
volt
Distance
Mass
Force
Energy
Power
Pressure
5mks
t CGS
foot
slug
second
pound
(hb)
foot . pound
foot . pound
meter
kilogram
second
newton
joule
watt
pascal
Time
field
.
minute’
2
ohm
ohm
ohm
tesla
hertz
gauss
hertz
gauss
hertz
meter-kilogram-second.
=
=
centimeter-gram-second.
Table
Rules
2
of
Exponents
Rule
a”
a
a
=
=
.
defme
the quantity
quantity
is measured.
as distance,
several
a
.
.
a
.
a
. ..
Example
(multiply
n times)
1/an
=
atm a
(am)
am
atm
‘
and the units
For many
units
in which
quantities,
of measure
exist.
a
such
the majority
of countries,
with the notable
exception
of the United States.
The magnitude
of many physical
quantities
can often be difficult
to express
without
the aid
of exponential
notation,
which offers a shorthand method
of writing
very large and very
numbers.
A base
a raised
to the exponent
n signifies
that a is to be multiplied
by itself
n
times.
Negative
exponents
indicate
fractional
values.
When
numbers
with the same base
small
value
U
Imaging
are multiplied,
& Therapeutic
the exponents
Technology
add.
106
10 . 10 . 10
10-6=
1/106
10 . 10 = 106
(10)
=
1O
.
10
.
10
.
10
=
1 ,000,000
(6 zeros)
Table 3
Scientif
ic Prefixes
The
International
System
of Units (Syst#{232}me International
[SI] units)
is the preferred
unit system
for
scientific
purposes
and has been adopted
by
968
Unitst
How-
Prefix
Kilo
Milhi
Mega
Micro
Giga
Nano
ever,
already
ply.
Exponential
Abbreviation
k
m
M
10
10
106
?-i
106
G
n
10
10
if an exponent
has
Several
Notation
is applied
an exponent,
examples
the
are
to a number
exponents
provided
that
multi-
in Table
2.
For further
convenience,
prefixes
can be applied as a shortcut
to signify the order of magnitude. For example,
it is more
convenient
to
speak
in terms
of kilograms
(7 kg) than grams
(7 x 10 g). Several
common
prefixes
are listed
in Table 3.
Volume
17
Number
4
Table
4
Fundamental
Particles
Particle
Proton
Neutron
Electron
Positron
Alpha
Symbol
(beta
(beta
minus)
plus)
particle
5e = the charge
of one
t amu
=
1/12 the mass
Charge
Mass
(amu)t
p
n
e
e
+1(e)
0
-1(e)
+ 1(e)
1.008
1.009
0.0005
0.0005
Ct
+2(e)
4.003
electron
=
1.6 x 10
of a carbon-12
at om
C.
1 .6 x
=
102
Energy
(MeY)
938
940
0.511
0.5 1 1
3,727
kg.
\=.wavelength
1.
Figure
Diagram
illustrates
the
electric
field and magnetic
field cornponents
of electromagnetic
radiation.
The electric
field and magnetic
fields
vary sinusoidally
at a 90#{176}
angle to one
another
and perpendicularly
to the
direction
of wave propagation.
(Redrawn
from Bushberg
et ah, 1994, and
reprinted
with permission.)
. Fundamental
Particles
In radiologic
physics,
several
sidered
fundamental,
particles
including
the
(eg, kilogram),
it is more
convenient
to discuss
mass
in terms of the atomic
mass
unit
(amu). An amu is defmed
as one-tweLfth
of the
mass
of a carbon-12
atom
(amu
= 1 .6 x 102
kg). Similarly,
the charge of these particles
is
very small with respect
to the SI unit coulomb
(C), and thus the letter
e is used to stand
for the
charge on one electron
(e = 1 .6 x 10’
C). The
are conproton,
their
neu-
tron, electron,
and positron.
Although
it is convenient
to consider
these particles
fundamental,
nuclear
and high-energy
physics
have shown
that
they
are
damental
actually
objects
for the purpose
ics, we
can
tal. Protons
blocks
composed
such
of discussing
consider
nucleus.
lively
charged
less
Electrons
quantities
served
are
similar
verted
in mass;
a system
is positively
charged
and
(ie, it has no charge).
The
are negatively
and posirespectively,
massive
and
phys-
fundamen-
are the building
particles,
considerably
trons.
particles
They
however,
the proton
the neutron
is neutral
electron
and positron
fun-
Nevertheless,
radiologic
these
and neutrons
of the
of smaller
as quarks.
than
positrons
and
protons
are
tons
of a helium
and
these
two
fundamental
Because
small
July-August
neutrons.
compared
1997
atom
and
Several
particles
the mass
with
must
be
for elsewhere
conserved.
in the
. Electromagnetic
Electromagnetic
neu-
referred
contains
and
energy
are con-
Interactions
occur
in which charged
particles
cease to exist, but
the charge must be conserved
and accounted
to as beta minus or beta plus particles,
depending on the charge.
An alpha particle,
which
has
two units of positive
charge,
is actually
the
nucleus
mass,
interaction.
are
and
also
of charge,
nature.
Mass and energy can be coninto one another,
but the total energy of
in
two
properties
is visible
pro-
are given
in Table
particles
is so
standard
units
possesses
Radiation
an example
the
properties
of which
of a
wave. It is a transverse
wave because
the electric and magnetic
field components
of light
move transversely
(perpendicular)
to the direction
of the wave propagation
(Fig 1). This
of
of these
light,
radiation,
4.
of mass
McCollough
U
RadioGraphics
U
969
Wavelength
(nanometers)
1015
I
Frequency
10’
1012
I
I
-#{149}l-_
I
I
I
I
10’
I
I
1
10’
I
I
I
10-3 l_
I
I
I
10
I
I
60
1012
lOS
1O’
I-
(hertz)
4
10”
0
Ultra
,
Rao
Television
Radar
4
MRI
0
4
Infra
red
C
Rad
C
Gamma
C
rays
X-rays
C
C
-
he
Visible
Th_
4
C
Cosmic
I
Energy
I
10-12
I
I
I
I
I
I
10.#{149}
I
I
1
1
1
1
103
10S
1
1
I
I
I
10’
I
I
rays
III
10’
10’
(electron volts)
Figure
2.
Schematic
of the electromagnetic
large range
of wavelengths
and frequencies.
MRJ = magnetic
resonance
imaging.
(Redrawn
from
differs
tion
sound
of the
wave
waves,
in which
travels
parallel
the
to the
oscillation
needs
no
to conduct
Sound
waves
their
have
conduction
and
or transport
a physical
will
not
it.
medium
travel
for
in a vac-
uum.
Generically,
the
velocity
of a wave is
wave times
(i’)
(f)
equal to the frequency
wavelength
(A):
of the
its
(1)
v=fX.
Frequency
is defined
as the number
of times
wave travels
from its maximum
to minimum and back to its maximum
value within
the
second.
The
tance
the
propagation
to-maximum
quantity
tities
970
U
wavelength
is defined
solving
ensure
that
match
and
from
other
1
dis-
physical
an equation),
the
units
cancel.
of meters
In this
units
tial
to express
the
the
frequency
in hertz
& Therapeutic
per
quan-
it is essential
of measure
the
Imaging
as the
wave travels
along the direction
of
during
one maximum-to-minimumcyche (Fig 1). When
any physical
is calculated
(ie,
example,
wavelength
to
appropriately
velocity
second.
has
Thus,
it is essen-
in meters
and
(1/second).
Technology
I
I
Green
A special
wave-
(a longitudinal
wave).
Ehectrocan travel in a vacuum;
it
must
I
OrWQeYeIIOW
radiation
spectrum.
Electromagnetic
Visible
light occupies
only a small
from Bushberg
et al, 1994, and
form propagation
magnetic
radiation
medium
I
Red
is that
property
length.
Because
quency
and
Thus,
a longer
Violet
radiation
encompasses
a
portion
of this entire
spectrum.
reprinted
with permission.)
of electromagnetic
radiac is
the speed
of light in a vacto 3 x 10 m/sec.
All electrotravels
at this speed
in a
of its frequency
or wave-
its velocity
used to represent
uum and is equal
magnetic
radiation
vacuum,
regardless
1
Blue
the
is fixed.
velocity
wavelength
are
wavelength
The
letter
is fixed,
the
inversely
implies
fre-
related.
a lower
fre-
wavelength
units for visible
light and x rays are the angstrom
(A) and nanometer
(nm),
which
equal
10#{176}m and 10
m,
respectively.
Electromagnetic
radiation
encompasses
a
wide spectrum
of wavelengths
and frequencies.
In Figure
2, electromagnetic
waves
are described
for a wide variety
of wavelengths,
frequencies,
and energies.
Long-wavelength
(lowfrequency)
waves
carry radiant
heat from its
quency.
Typical
source.
As the
quency
increases),
wavelength
decreases
the
waves
radio,
television,
and
region
of the
electromagnetic
radar
(and
are used
signals.
fre-
to carry
It is in this
spectrum
that
the
waves
used to induce
and receive
magnetic
resonance
imaging
signals
are found.
The visible light region
of the electromagnetic
spectrum is narrow,
with
wavelengths
on the order
of 400-750
nm. As the wavelength
decreases
further,
the energy
of the wave increases
to a
point
at which
it can remove
electrons
from an
atom,
and the photons
are known
as ionizing
Volume
17
Number
4
Table
5
Fundamental
Forces
Relative
Force
Description
Strong
Electromagnetic
Short-range
Attraction
magnetic
Weak
Gravitational
Interacts
Attraction
attraction
or repulsion
field
rays
originate
gamma
outside
rays
the
originate
between
nucleons
of charges
and magnetic
ray of the same
They are
their origin.
X
nucleus,
inside
the
whereas
responsible
for beta
Force
the
their
miiar
ally
four
fundamental
forces
in nature
and
relative
strengths.
Although
the most faof these
is gravitational
force,
it is actuweak
compared
with
the
other
three
forces.
The strong
force interacts
at small distances
on the order
of 10
m and is responsible for holding
nuclei
together.
The electromagnetic
force
is what causes
charged
particles
to be attracted
or repelled
by one another,
depending
on the polarity
of the charge.
It also is
responsible
for
the
weak force is perhaps
the four fundamental
classified
force.
as a subset
The
weak
action
of magnets.
The
the least understood
forces
and is sometimes
of the
interaction
of
electromagnetic
is involved
an electric
or
in
subpartiche
transformations
such
as beta
decay.
To understand
basic radiologic
physics,
it is
important
to be familiar
with the basic properties of electricity
and magnetism.
Electrical
charge
can exist as a monopole;
that is, a posilively charged
object
or a negatively
charged
object
can exist independenthy.
This is not the
case for magnetic
materials,
which
exist in the
form of a dipole
and must have both a north
and a south
pole. A north
magnetic
object
or a
south
magnetic
object
cannot
exist indepen-
decay
Electricity
l0’
l00
and
magnetism
are interrelated
that
one
opposite
magnetic
charges
attract
nucleus.
The motion
of an object
depends
on its properties and the environment
in which
it exists.
The
termforce
is used
to describe
the property
of
the environment
that acts on an object.
Table
5
lists
with
and have the similar
property
(or like magnetic
poles)
repel
tric
.
1
dipoles
102
at a subparticle
level,
between
masses
radiation.
An x ray and a gamma
energy
are, in fact, indistinguishable.
named
differently
only to denote
Strength
each
(or
other.
charge
opposite
Furthermore,
creates
protons,
are
deflected
poles)
a moving
a magnetic
ing magnetic
field induces
Moving
charged
particles,
like charges
another
and
field,
and
eleca mov-
an electric
current.
such as electrons
and
by magnetic
fields.
How-
ever, stationary
charged
particles,
or uncharged
particles,
such as neutrons
and photons,
are not
affected
by magnetic
fields.
.
Energy
The energy
within
a system
must be conserved:
It can neither
be created
nor destroyed;
it can
only
change
ergy
are known
forms.
of motion)
stored
and
by an
tion). A ball
energy
equal
ject times its
ergy of a ball
is equal
times
common
energy
potential
object
energy
forms
of en-
(the energy
(the energy
in a particular
configura-
rolling
across
the floor has a kinetic
to one-half
of the mass of the obvelocity
squared.
The potential
enraised
above
the floor on a ladder
to the
the
Two
as kinetic
mass
of the
gravitational
ergy is not an
of energy
for
the energy
of
the example
the top of the
tential
energy
floor. Energy
placed
on top
absolute
balh
times
its height
constant.
Potential
number.
It is an amount
en-
one state of an object
relative
the object
at a reference
state.
of the ball on a ladder,
the ball
ladder
has a given amount
of
relative
to that of the ball on
was stored
in the ball when
it
of the ladder,
because
someone
to
In
at
pothe
was
dently.
July-August
1997
McCollough
U
RadioGraphics
U
971
had
to fight
higher
the
force
position.
(coulomb)
of gravity
Likewise,
attraction
object
to lift it to its
the
electromagnetic
of a negatively
to a positively
charged
charged
object
creates
po-
because
of the
physical
constants
ergy (joules)
ond),
where
use
in radiologic
volts)
equals
they
stroms).
are
of this
allowed
is the
to come
potential
together.
energy
An
stored
example
referred
to as voltage
is actually
the
electric
potential
between
two points.
For example,
9 V of electric
potential
exists
between
the positive
and negative
contacts
of a 9-V battery.
When
trons
are
the
contacts
allowed
to flow
the positive
contact.
through
an electric
eV (electron
is equal
tial
to the
not
lost,
of energy
charge
forms.
the
the
potential,
and
negative
to
energy
converted
of these
poten-
must
be
It cannot
be
to alternative
alternative
forms
is mass.
The relationship
between
energy
and mass was
discovered
by Einstein
and is expressed
as energy equals
mass times
the velocity
of light
squared:
E
(2)
mc2.
=
and
Electromagnetic
properties
terms
of wavelength
composed
and
of discrete
photons.
late
radiation,
of waves
and
Thus,
radiation.
frequency,
it is also
The
determined
from
to its wavelength
which
exhibits
is characterized
bundles
referred
energy
pressed
in Eq
[1],
velocity
quency
a photon
frequency
times
wavelength).
can be expressed
or wavelength:
called
to as particu-
of a single
its frequency
through
the
photon
is
(which
is related
relationship
ex-
of light
equals
=
the
term
(the
latter
is valid
kiloelectron
volts
expressions
look
only
and
different
E is expressed
amount
but
are
U
Imaging
& Therapeutic
Technology
to
two
(x
listed
and
character-
gamma
rays),
6. Fluence
in Table
area
quanti-
the
the
number
and
is expressed
it is difficult
is
of phoin
or flu-
Flux,
per unit
in number
Intensity,
of photons
area and is exjoules)
per
to measure
the
abso-
of charge
produced
gamma
the
per
radiation.
amount
unit
mass
Exposure
of ionization
of air
meters
in a specific
volume,
typically
composed
of air. When
exposure meters
are appropriately
calibrated,
exposure can be accurately
measured
with a relatively inexpensive
device.
The conventional
unit for exposure
is the roentgen
(R), but the SI
is the
coulomb
C/kg
the
per
kilogram.
units
The
is 1 R equals
x and
is not
of exposure,
gamma
x
gamma
a less
for
by charged
impossible
rays
familiar
above
to measure
particles.
2-3
known
the
radiation
energy
and
field;
absorbed
kerma
MeV
in energy.
as kerma,
amount
describe
It is
exposure
was
of kinetic
ergy released
in matter
per unit mass.
nition
of kerma
allows
it to be applied
photon
and charged
particle
radiation
Exposure
ex-
measuring
to measure
unit,
is valid
Therefore,
quantity
produced
x and
however,
radiation.
a useful
essentially
developed
equivalent
rela2.58
of air.
for
also
(C)
between
The definition
the
the
972
apply
additional
to express
a given
x and
only
in
The
several
to describe
Physically,
of
(4)
when
(ang-
of energy
lute number
of photons
per area or per unit
time in an x-ray beam.
The quantity
exposure
is
more practical
to measure
and is defmed
as the
Thus,
A in angstroms).
by wavelength
radiation
crossing
for
12.4/A
for
(kioelectron
number
per centimeter
squared.
ence rate, is the number
of photons
area per unit time and is expressed
per centimeter
squared
per second.
or fluence
energy,
is the number
times the photon
energy
per unit
pressed
in energy
units (typically
centimeter
squared.
i0-
or
E=
convenient
Energy
used
are
used
tionship
(3)
are
of which
posure
hf
(3) is en(1/sec(6.63 x
Units
of ionizing
ionization
E
is more
divided
physics,
some
unit
fre-
Thus,
the energy
in terms
of either
appropriate
Equation
expressions
units
measure
in
is actually
of energy
12.4
istics
from
the
(4)
physics:
These
tons
of
to 1 .6 x 1019
system.
Equation
Radiologic
ties
1
is a unit
is equal
a closed
be
electric
J/sec).
In radiologic
the energy
volt
mentioned,
it can
One
times
.
elec-
because
an electron
within
but
from
Thus,
As previously
conserved
connected,
An electron
that moves
potential
of 1 V acquires
volt)
(voltage).
energy,
J (joule).
are
units.
electromagnetic
waves
(photons)
of any energy. Because
approximately
1 5 eV of energy
are required
to remove
an electron
from an
atom,
those
photons
with energy
greater
than
15 eV are called ionizing
radiation.
in a bat-
tery. Energy
is released
when
the positive
and
negative
contacts
are connected.
The quantity
commonly
of the
and
equals
h times frequency
h equals
Planck’s
constant
tentiah
energy.
Energy
must be put into the system to move
the positive
and negative
charges
apart
from
one another
and is stored
there
until
10-
application
the
The
endefi-
to both
fields.
energy
of
in contrast,
dose describes
by an object.
That is, expo-
Volume
17
Number
4
Table
6
Radlologic
Units
Quantity
Description
Fluence
Flux (fluence
Number
Fluence
rate)
of photons
per
per unit time
Conventional
unit
area
1/centimeter
1/(centimeter
(meter
Intensity
fluence)
Exposure
(energy
Number
of photons
times
area
Charge
produced
per unit
gamma
rays
Kinetic
energy
released
in
Energy
absorbed
per unit
(X)
Kerma
(K)
Dose (D)
$5
photon
energy
mass
of air from
matter
mass
per
per
unit
[ 1/meter’J
. second)
second)]
F1/
kiloelectron
volt/centimeter[joule/meter2]
roentgen
[coulomb/kilogram]t
x and
unit
.
Unit5
rad
rad
mass
[joule/kilogram
[jouhe/kihogram
or gray]
or gray]t
‘SI units are given in brackets.
t 1 roentgen
=
2.58 x 10
coulomb/kilogram.
$ 100 rad = 1 gray.
The
ergy
S
relationship
within
pute
Photon
energy
(keV)
and
(the
dose
(the
enen-
dose:
dose
Figure
3.
Graph
shows
the roentgen-to-rad
conversion factor
(ffactor)
for bone,
muscle,
and water
and photon
energies
between
10 and 1 ,000 keV.
The appropriate
f factor (rad/roentgen)
is multiplied
by exposure
(roentgen)
to yield dose (rad).
(Redrawn
from Bushberg
et al, 1994, and reprinted
with
permission.)
=
unity.
ergy
keV,
and
kerma
are
used
to describe
the
radia-
of the
x-ray
beam,
which
reflects
the
en-
ergy carried
by the x-ray
beam.
Dose
is defmed
in terms
of energy
absorbed
per unit mass. The
traditional
unit for dose is the rad (radiation
absorbed
dose),
but the SI unit for energy
per
mass
is the
given
the
joule
special
per
name
kilogram
and
gray
(Gy):
has
1 Gy
.
However,
for
dependence.
the radiation
(dose)
tion source;
dose is used to describe
the effect
of the radiation
on an object
or person.
All
three
quantities
are proportional
to the inten-
exposure
f
factor.
(5)
For photons,
the roentgen-to-rad
conversion
factor
for muscle
and water
remains
relatively
constant
from 100 to 1 ,000 keY and is near
by bone,
sity
exposure
field)
ergy absorbed
by an object)
depends
on the
properties
of the absorbing
object
(density
and
atomic
number)
as well as the energy
of the radiation.
Thus,
for a given material
and photon
energy,
a conversion
factor
is used to rehate cxposure
to dose. This conversion
factor
between
exposure
(roentgen)
and dose (rad), often
referred
to as theffactor
(rad/roentgen),
is plotted in Figure
3 for water,
muscle,
and bone for
photon
energies
between
10 and 1,000 keV,
where
the following
equation
is used to com-
P
sure
between
a radiation
thereby
of the
bone,
there
is a strong
At energies
less
is more efficiently
increasing
same
the
amount
en-
than 100
absorbed
biologic
of incoming
effect
radia-
tion (exposure).
In Figure
3, the scale on both
the horizontal
and vertical
axes of the plot is
logarithmic.
That is, equal distances
along the
axis represent
a tenfold
increase
in magnitude
(eg, equally
spaced
tick marks
occur
at the vahues
of
1, 10,
scales
are
pass
a large
100,
used
and
when
1,000).
the
Logarithmic
values
plotted
encom-
range.
been
=
100
rad.
July-August
1997
McCollough
U
RadioGraphics
U
973
.
Atomic
and
Objects
in the
posed
of millions
ample,
Nuclear
The
alh atoms
shell
and
Bohr
Figure
charged
an atom
and
atom.
protons,
and
called
atomic
many
ments
of neutrons).
Some
state
and
naturally
A hydrogen
number
and
mass
topes
of deuterium
tron)
and
trons),
which
Outside
els
the
around
the
exist
in one
(energy
levels).
mains
in orbit
in a specific
ther
gained
is known
farther
nor
from
so on.
the
assigned
can
The
innermost
(Fig
inhabit
a given
the
1evorbit
re-
is nei-
electron
The
4).
or-
L shell
M shell,
is
and
to each
of
the K shell beof 1 , the L shell
number
of electrons
cannot
exceed
the
maximum
value,
which
is equal to two times
the quantum
number
squared.
Thus,
only two
electrons
can inhabit
the K shelh, eight can inhabit
the
so on.
ber
L shell,
A neutral
of electrons
the
number
cheus.
Thus,
for
many
arrangement
more
inhabit
is one
in orbit
equals
bers,
18 can
atom
the
elements
electron
of electrons
M shell,
in which
about
of protons
& Therapeutic
more
the
chemically
reactive
properties.
Neutral
outermost
orbital
stable
shell
and
and
may
atoms
in
cx-
is completely
known
the
the
nucleus
within
of higher
shells
within
and
num-
the
as inert
these
in which
Technology
energy
orbital
is one
or K, shell.
an
electron
ergy-leveh
in Figure
electron
diagram
for a tungsten
atom is shown
5. Energy
must be added
to move
an
from an inner
shell to a more exterior
shell
or to remove
Thus,
an electron
lower
(more
electron
it completely
bound
in a more
bound
ermost
shells
are
shell
atom.
very
is at a
than
and
Electrons
wealdy
atom.
shell
state
exterior
en-
the
inner
energy
to the
electron
from
in an
negative)
tightly
An
are
the
innermost,
an
is more
at the
bound
out-
to the
atom and are most easily removed.
These
are
called
the valence
electrons.
An electron
that is
not bound
to an atom is said to be afree
electron. A free electron
is not under
the influence
of the nucleus
and requires
no energy
to move
it away
filled.
state
electrons
nucleus,
is at the
from
an atom.
Electrons
nu-
atomic
are
lowest
num-
This
The
leases
can
movement
from
atomic
energy
is required
from
an interior
shell
is a lower
an outer
to the
between
requires
Energy
electron
interior
move
either
energy.
bound
closer
Imaging
are
influences
charged
charged
tron
U
no.)2
Because
the negatively
attracted
to the positively
an
974
#{149}
(quantum
fulh are chemically
electron
is assigned
shelh
98
of
which
specific
as is the
The
72
atoms
filled
magnetic
neu-
energy
K shell
so on.
50
characteristics
hibit
energy
as the
orbital
shells,
with
a quantum
number
2, and
greatly
shells
electrons
of these
number
32
gases.
shell,
nucleus,
A quantum
the electron
ing assigned
that
host.
as the
18
an element.
Elements
in which
neutral
have unpaired
electrons
or incompletely
isoneu-
defmed
As long
8
2
=
(atomic
one
two
shells
enenergy
has
and
The
shells
bit
ra-
radioactive.
electrons.
nucleus
are
neutrons
and
34567
2
number
number
nuclear
proton
nucleus
by
dc-
to a lower
no
proton
both
further
which
of 1) but
(one
(one
are
inhabited
decay
has
2
and neutrons
(ti)
is orbited
by electrons
at discrete
energy
levels.
K through
Q indicate
the orbital
dcctron shells.
(Modified
from Bushberg
et al, 1994, and
reprinted
with permission.)
is
Most
all isotopes
number
tritium
(A) and
in an elevated
atom
capacity
of nude-
isotopes,
not
Maximum
i
Figure
4.
Diagram
of the Bohr model
of the atom,
in which
a central
nucleus
composed
of protons
(p)
a nucleus
atom.
no.
electron
two
number
number
but
exist
to
Helium
the same atomic
number
(different
They
Quantum
an atomic
within
different
have
mass
elements
contains
of the
I!
of
proton.
total
mass
are atoms
that
but a different
state.
The
several
dioactive:
one
properties
have
has
neutrons)
of
according
of 2 and
so on.
and
the
defines
of the
I
a
Z)
element
contains
have
within
properties
table
number
in
of positively
number
many
Nucleus
an outer
which
Hydrogen
1 and
(protons
ergy
atomic
number.
of
and
of protons
each
cxthat
as diagrammed
periodic
an atomic
states
of neutrons,
identifies
number
atom
is composed
the
The
its atomic
ons
a nucleus
determines
graphically
has
both
number
is called
comFor
6 x 1023 copper
of the
and
The
nucleus
the
contains
nucleus
protons
charge.
actually
of atoms.
electrons,
4. The
are
millions
model
contain
of orbiting
no
world
1 g of copper
atoms.
Structure
everyday
nucleus
shell
to remove
shell.
energy
will
shells.
or re-
state,
naturally
to fill the
an dcc“fall”
vacancy
Volume
a
Because
left
17
by
Number
4
-2.5 keV
-2.5 keV
67 keV
-11 keV
64.5
keV
Auger
-11 keV
Characteristic
electron
-69.5
Vacant
K
L
teristic
energy
M
6, 7. (6) Diagram
depicts
emission
of a characteristic
x ray from a tungsten
atom.
Emission
of characx rays occurs
when
an electron
from an outer
shell moves
into an inner shell vacancy,
and the excess
is converted
into electromagnetic
radiation.
(Redrawn
from Bushberg
ci al, 1994, and reprinted
with
(7)
occurs
is transferred
to
Diagram
depicts
when
an electron
another
electron.
electron.
This
with permission.)
Zero
C
electron
Valence
the emission
of an Auger
electron
from a tungsten
atom.
from an outer
shell moves
into an inner shell vacancy,
The
excess
energy
of the transition
is decreased
by the
is known
as an Auger
a-
electron.
(Redrawn
from
ejected
electron.
the
moves
the
atom.
X rays
is released.
nucleus
fled
and
by
the
shell
x rays
can
and
0
C
0
ray
are one
form
shell.
be
off
moves
energy
in the
a characteristic
is called
electron
from
in which
fall
the
this
into
en-
the
x ray is identi-
Thus,
when
to the
ehec-
K shell,
K-
emitted.
an electron
gives
M shell
re-
is released
electrons
off x rays,
the
and
an outer
energy
give
from
et ah, 1994,
When
destination
move
Emission
of Auger
and the excess
energy
binding
energy
of the
shell,
When
trons
When
>
0,
Bushberg
to an inner
ergy
toward
form
the
nucleus
of x rays,
x ray (Fig
energy
of the
the
6).
x
This
term is used because
the
resulting
x ray is characteristic
of the atom
from
which
it
originated.
The energy
of the x ray is equal to
the difference
between
the binding
energy
of
the destination
shell and the binding
energy
of
the origination
shell. In the example
in Figure
0
C
0
0
0
Figure
5. Electron
shell energy
diagram
for a
tungsten
atom (atomic
number,
74). By convention, the potential
energy
of a free electron
(e) is
defmed
as 0. Electrons
closer
to the nucleus
have
a lower-energy
state and thus negative
potential
energy
compared
with this reference
value.
Ehectrons closest
to the nucleus
have the most negalive binding
energy.
The binding
energy
of the K
shell decreases
(ie, becomes
more negative)
as
the atomic
number
(Z) of an atom
increases.
X
rays produced
from the excess
energy
of an deetron transition
are named
according
to the destination
shell of the moving
electron.
For example,
when
an M shell electron
moves
to the K shell,
the characteristic
x ray emitted
would
be a part
of the K series.
(Modified
from Bushberg
dl al,
1994, and reprinted
with permission.)
July-August
L
7.
permission.)
electrons
emitted
printed
K
M
6.
Figures
‘p
Vacant
1997
6, there
is a vacancy
in the
K electron
which
has a binding
electron
from the M
ing energy
-2.5 keV,
to fill the hole in the
energy
of -69.
orbital
shell,
moves
toward
K shell. The
ence is -2.5
(-69.5)
= +67
keV.
energy
of this characteristic
x ray
the tungsten
atom.
When
an electron
from
an outer
-
ward
the
nucleus
excess
energy
electron
(Fig
Iron is ejected
to fill an
inner
orbit,
5 keV. An
with a bindthe nucleus
energy
differThe 67-keY
is unique
to
shell
vacancy,
falls
to-
the
can also be released
to an orbital
When
this occurs
and the elecfrom the atom,
it is called
an
7).
McCollough
U
RadioGraphics
U
975
Electrons
Target atom
dent
electrons
2
Close inleraction:
energy
Moderate
X.rays
Figure
8.
Diagram
of a basic x-ray tube.
from Bushberg
et ah, 1994, and reprinted
(Redrawn
with per-
1
ftti nucleus:
3
Distant Interaction:
energy
Low
‘\
renergy
mission.)
V
Figure
9.
production.
Auger
electron.
The movement
of an electron
from the M shell to the K shell nets a positive
energy
of 67 keV. This energy
does not have
leave the atom as a photon
but can be transferred
to another
orbital
electron
to eject
to
the
electron
electron
keY
ergy
shell
Auger
from the atom.
Because
this ejected
was initially
bound
to the atom,
the 67
of energy
is decreased
by the binding
enof the electron.
For an electron
in the M
(binding
energy
= -2.5
keY),
the emitted
electron
has a kinetic
energy
of 64.5 keV.
U TURNING
ELECTRONS
INTO
X RAYS
In 1895, Wilhelm
Conrad
Roentgen
discovered
x rays by using
a device
simiar
to that shown
Figure
8. An x-ray tube uses a heated
filament,
typically
made
of tungsten,
to raise
of atomic
electrons
high enough
them
from their atoms.
Essentially,
boils
off
ionic
emission.
the
lively
ode).
from
tracted
x-ray
electrons,
tube.
charged
a process
A power
the
as therm-
is attached
The
filament
(cathode)
with
respect
to the
Thus,
the boiled-off
electrons
the negatively
charged
cathode
to the
positively
charged
to
is negatarget
(an-
are repelled
and at-
anode.
The
free electrons
are accelerated
toward
the anode
because
of the potential
difference
between
the
cathode
and anode
and thus acquire
substantial
kinetic
energy
(on the order
of kiloelectron
volts
to megaelectron
volts).
When
the energetic
electrons
strike
the
tungsten
target,
they hose their kinetic
energy
through
three
different
mechanisms:
excitation,
ionization,
and radiation.
In excitation,
the energy from the charged
particle
is used to move
other
electrons
to higher
energy
states
(more
external
orbital
of characteristic
loses
Technology
In ionization,
the
particle
is sufficient
from an atom.
In the
x rays,
its energy
a
the
through
charged
either
ento
case
particle
ionization
or cx-
citation;
the characteristic
x ray is produced
by
the subsequent
emission
of a photon
as the
electron
vacancy
is filled. In energy
losses
due
to radiation,
the energy
from the charged
partide 5 used to create
a photon
directly.
The
production
of x rays by means
of radiation
is
known
as the bremsstrahlungprocess.
Bremsstrahlung
ing
is a German
radiation.
mechanisms
“
word
Thus,
that
there
by which
are
The majority
the
the
energetic
electrons
the
crc-
charac-
of the x rays produced
is diagrammed
in Figure
electrons
are slowed
attracted
to the
As the
“brak-
unique
and
energized
electrons
show
target
are bremsstrahlung
are
means
two
ate x rays: the bremsstrahlung
teristic
processes.
nucleus.
& Therapeutic
shells).
ergy from the charged
remove
the electron
they
Imaging
to
an
bremsstrahlung
x ray that has the maximum
energy
(which
is equal
to the maximum
electron
energy
as
determined
by the x-ray tube potential).
Another
incident
electron
(2) does not impact
with the nucleus
but travels
relatively
close to it and thus gives up a
moderate
amount
of its energy
to the bremsstrahlung x ray. For another
incident
electron
(3), which
travels
distant
to the nucleus,
only a small amount
of energy
is given up as a bremsstrahlung
x ray. (Redrawn
from Bushberg
dl al, 1994,
and reprinted
with
permission.)
charged
U
x-ray
in-
cident
electrons
are showed
down
by attraction
the positively
charged
nucleus.
In this example,
incident
electron
(1) impacts
directly
with the
nucleus
and gives up all its energy.
This produces
cess
976
brernsstrahlung
x-ray production,
energy
to release
the cathode
known
source
in
Diagram
illustrates
In bremsstrahlung
electrons
9. The negatively
down
positively
slow
when
down
or brake
in
x rays. This probecause
charged
down,
Volume
they
give
17
Number
4
EeCtd
Unfiltered
bremaatrahlung
Target
spectrum
spectrum
Filtered bramsatrahiung
(Inherent and added
0
electron
atom
fIltration)
5)
90 keV madmal
photon energy
Inddent
energy
electron wfth
greeler
than
energy
K-shell binding
4
40
50
Energy
Figure
10.
strahlung
spectra.
directly
maximum
electron
ing
the
60
70
80
90
ii
(key)
Graph
of unfiltered
and filtered
brernsThe probability
of an incoming
impacting
the nucleus
and producenergy
bremsstrahlung
x ray is
small compared
with the probability
of more
distant
interactions.
Theoretically,
the probability
increases
linearly
with decreasing
photon
energy
and produces
a triangular
spectrum.
However,
the preferential removal
of lower-energy
x rays by either
inherent or added
filtration
of the x-ray tube removes
the
majority
of low-energy
x rays from the bremsstrahlung spectrum
and produces
a curved
spectrum.
(Modified
from Bushberg
et ah, 1994, and reprinted
with permission.)
off
energy
in the
The energy
form
of bremsstrahlung
of the bremsstrahlung
x rays.
x ray is deter-
mined
by the proximity
of the electron
to the
nucleus.
Incident
electrons
that directly
impact
the nucleus
give up all their energy
to the photon. Thus,
the maximum
bremsstrahlung
x-ray
energy
is equal to the energy
of the incoming
electron
and is determined
by the tube potential.
Electrons
that
do
not
impact
the
nucleus
but that travel
close to it retain
some kinetic
energy as they are deflected
around
the nucleus.
They give off bremsstrahlung
x rays with energy less than the maximum.
The lowest
energy
bremsstrahlung
incident
lively
x rays
electron
greater
are
passes
distance.
produced
the
when
nucleus
In this
case,
the
at a relathe
incident
electron
retains
a considerable
proportion
of its
initial
energy.
A graph
of x-ray intensity
(relative
output)
as
a function
of x-ray energy
for the bremsstrahlung process
would
take the form of a triangle
(Fig 10). The maximum
bremsstrahlung
energy
is determined
by
x-ray intensity
creases
linearly
produced
at any
with decreasing
July-August
1997
the
Characterlatic
xray:
From L’K
electron transition
x-ray
tube
potential.
Figure
11.
Diagram
illustrates
characteristic
x-ray
production.
In characteristic
x-ray production,
the
incident
electron
(1) has kinetic
energy
greater
than
the binding
energy
of a K shell electron
(2). On impact of the incident
electron
with the K shell electron, a vacancy
is created
in the K orbit.
An electron
from the L shell (3) moves
into the K shell to fill this
vacancy.
The excess
energy
from the L shell to K
shell electron
transition
is emitted
as a characteristic
x ray (4). (Redrawn
from Bushberg
et al, 1994, and
reprinted
with permission.)
the theoretic
shape
of an unfiltered
bremsstrahlung spectrum.
However,
x rays produced
within
the target
material
must escape
the target and the glass envelope
enclosing
the anode.
Very low energy
bremsstrahlung
x rays are
readily
high
Thus,
absorbed
by these
probability
the
shape
materials
of not
leaving
the
of the
bremsstrahlung
and
have
x-ray
tube.
a
curve
from the theoretic
triangle
because
lowenergy
x rays are removed
due to either
inherent or added
filtration
of the x-ray tube.
The other
mechanism
by which
energetic
differs
electrons
produced
by the cathode
and accelerated toward
the anode
of an x-ray tube can produce x rays is known
as the characteristic
process (Fig 1 1). The incident
electron
must have
energy
greater
than or equal to the binding
energy of a given shell to remove
an electron
from
that
shell.
Once
a characteristic
atomic
the
electron
x ray
electron
fills
ejected
electron
ence as a photon.
and
has
is produced
the
emits
been
removed,
when
vacancy
heft
the
energy
another
by
the
differ-
The
other
energy
inenergy.
This is
McColiough
U
RadioGraphics
U
977
Molybdenum
Characteristic
radiation
0.
target
Bremsstrahlung
30 kVp
(30 keV electrons)
lines
Bremsstrahlung
spectrum
continuous
0
10
Binding energies
K--2OkeV
L-.3 keV
5)
5)
10
20
30
40
50
.
60
70
80
100
90
In the
typical
keY),
ray tube
the
diagnostic
x-ray
is distributed
shown
in Figure
1 2. The
maximum
mined
the
the
x-ray
Bremsstrahlung
nant
role
tube
mize
duced
spectrum.
and
plays
minimize
of bremsstrahlung
kVp).
predomispectra.
x-ray
the
the
can
shell
the
incoming
electron
ejects
an electron
from
K shell of a molybdenum
atom,
the shell
be filled with an electron
from either
the L
or M shell. The energy
difference
between
binding
energies
of the M shell (-0.5
keY)
and
K shell
(-20
difference
to
is as monoenergetic
as
keY)
between
L shell
(-3
keY)
keY. Thus,
and
17- and
opti-
rays
radiation
bremsstrahlung
pro-
This
narrow
band
istic
x rays
is the
target
x rays.
In the
mate-
which
use a relakVp). The two
x-ray spectra
which
30-keY
the positively
a broad
energy
If, however,
are
from
energy
(-20
keY)
of the
is
+
characteristic
from
useful
of the
17
x
a molybdenum
of energy
discussion
The
energies
target.
the
character-
in mammography.
distribution
of ener-
gies produced
in the bremsstrahlung
and characteristic
processes,
the spatial
distribution
of
the x rays was not mentioned.
For an extremely
thin
target
in which
the
ejected
electrons
leave
out further
interactions,
leave
ure
Technology
K shell
most
keV.
binding
19.5-keY
produced
the
tube
axis.
1 4, when
cause
the
trons
to undergo
produced
the
produced
(ie,
However,
target
and
at 90#{176})
to the
as shown
is thick
x rays
further
photons
the target
material
withthe majority
of x rays
perpendicular
anode-cathode
& Therapeutic
is +19.5
the
tubes
is a typical
rial for mammographic
tubes,
lively low tube potential
(25-30
components
of a mammographic
are illustrated
in Figure
1 3, in
electrons
are slowed
down
by
charged
nucleus
and produce
spectrum
the
it is important
of characteristic
the broad
Molybdenum
x rays
is deter(90
x-ray
x-
(ksV)
Figure
13.
Diagrams
illustrate
bremsstrahhung
and
characteristic
x-ray production
with a molybdenum
target,
typically
used in mammography.
As in general
radiography,
the mammographic
spectrum
is
composed
of both a bremsstrahlung
and a characteristic portion.
However,
in mammography,
the characteristic
x rays at 17 keV and 19.5 keY provide
the
majority
of x rays for the imaging
process.
e = dcctron. (Modified
from Bushberg
ci al, 1994, and reprinted
with permission.)
as
process,
on top of
spectrum.
(90 keY)
mammographic
the amount
axis
of the
potential
radiographic
However,
in mammography,
have an x-ray beam that
Thus,
energy
majority
radiation
in most
possible.
the
(50by the
bremsstrahlung
x-ray lines ride
bremsstrahlung
x-ray energy
from
range
produced
along
are produced
from
and the characteristic
the large, continuous
The
energy
intensity
.
Radiation
Energy
Figure
12.
General
radiographic
spectrum
produced
with a tube potential
of 90 kVp. The continuous bremsstrahlung
spectrum
encompasses
a broad
range
of energies,
and the characteristic
x rays reside in narrow
energy
bands.
(Modified
from Bushberg et al, 1994, and reprinted
with permission.)
200
.
1L
M
(key)
Energy
Imaging
30
(keV)
Characterasbc
MO.5keV
U
20
Energy
5)
978
Radiation
and
in Fig-
enough
ejected
interactions,
Volume
to
dccthe
17
spa-
Number
4
a___#___Cable
500 kV
sockets
20 MV
stream
Figure
14.
Diagram
depicts
the spatial
distribution
of x rays produced
within
a thick target.
At lower
tube potentials
(eg, 100 kV), the x rays are produced
isotropicahly.
As the tube potential
increases,
the x
rays
are
produced
in a more forward
direction
(ie,
following
stream).
the
direction
of the
incoming
o_
tial distribution
for a 100-kY
tube potential
is
approximately
isotropic
(equally
distributed
in
all directions).
For both thin and thick targets,
the distribution
of emitted
x rays becomes
more and more
forward
(ie, in the direction
of
the incoming
electrons)
with increasing
energy.
The energetic
in an x-ray
electrons
impinging
tube
their
lose
way of the three
basic processes
her: excitation,
ionization,
and
amount
of energy
lost through
radiation
as a percentage
on the
energy
by
discussed
earradiation.
The
bremsstrahlung
of the
Anode
of a modern
et al, 1994,
x-ray tube.
and reprinted
(Rewith
electron
ciency
target
port
Figure
15.
Diagram
drawn
from Bushberg
permission.)
total
energy
lost
of x-ray
production
with
the
bremsstrah-
lung process
increases
dramatically
ergy: At 4 McV, approximately
40%
ergy is converted
into x rays.
The
much
ray
next
article
greater
tubes.
detail
However,
in this series
the
the
with
en-
of the
describes
enin
workings
of modern
diagram
of a modern
x-
positively
ciency
charged
of x-ray
anode.
production
Because
is low
the
and
effithe
(including
losses
due to excitation
and ionization collision)
is a function
of both the target
atomic
number
and the electron
energy.
For
electrons
in the diagnostic
energy
range
(approximately
50-200
keY) and a tungsten
target,
amount
modern
only
are absorbed
by the x-ray tube and casing.
The
output
port of the x-ray tube has a reduced
amount
of attenuating
material;
it is from
this
portion
of the tube that the usefuh beam
is delivered.
1 % of the
converted
energy
nostic
to x rays. This
into heating
x rays in amounts
imaging,
to receive
makes
July-August
of the
goes
produce
heat
point
energy
and
x-ray
energy.
Tungsten,
of 3,370#{176}Cand
an
excellent
1997
tube
dissipate
electron
stream
pate
thick
means
that 99% of the
the anode.
Thus,
to
sufficient
for diaganodes
a substantial
must
be
amount
of heat deposited
in the anode
is high,
x-ray tubes
use rotating
anodes
to dissithe heat over a wider area. The relatively
targets
produce
x rays isotropically
(ic, in
all directions).
is
able
x-
ray tube shown
in Figure
1 5 provides
a review
of the principles
discussed
thus far. The energetic electrons
arc produced
by thermionic
emission
(ic, boiled
oft) from the negatively
charged
cathode
and accelerated
toward
the
Thus,
a large
number
of x rays
of
with its high melting
high atomic
number,
target
material.
The
effi-
McCollough
U
RadioGraphics
U
979
Fixed kVp
Area cxmAs
150mM
0.
0
0
I
5)
5)
60
16.
Figure
Graph
of the
effect
of varying
tube
po-
tential
(kVp)
on the x-ray spectrum.
At 60 kVp, the
electron
energy
is insufficient
to produce
characteristic x rays in a tungsten
target
(K binding
energy
of
-69.5
keY). (Modified
from Bushberg
et al, 1994,
and reprinted
with permission.)
U THE
X-RAY
An x-ray
sity
is a graph
output)
ray
and
der an x-ray
to describe
the energy
spectrum.
beam.
over
Higher-quality
a
Quality
is used
beams
to give
are
better
tube
a
of the
are more
and
quality
(ie,
for
x-ray spectrum.
These
potential,
tube current,
tance,
anode
material,
erator
type.
The
anode
electric
and
influences
the
ing x-ray
potential
cathode
imaging
applied
and
The
shape)
between
tube
quality
quantity
is also
of the
the
dramatically
of the
result-
of x rays,
or
or absence
determined
of characteristic
by
produces
of 60 keV, which
the
tube
of a tungsten
keY). The
of changes
on
trum
in tube
curve)
rent
potential
is demonstrated
quantity
is directly
the
in Figure
(area
proportional
and the exposure
times
time,
seconds).
Imaging
&
Therapeutic
Technology
atom
effect
x-ray
spec-
16.
under
the spectral
to the
or their
tube
cur-
product
Changing
the
tube current
or exposure
time has no effect on
the shape (or quality)
of the x-ray spectrum.
The effect of changes
in the tube current
and
exposure
time product
on the x-ray spectrum
is
demonstrated
in Figure
17.
The x-ray quantity
(area under the spectral
curve) is directly
proportional
to the atomic
number
of the target material.
The target material is fixed for most x-ray tubes
and is typically
an alloy consisting
of 90% tungsten
(Z = 74)
and 10% rhenium
(Z = 75). Some
mammo-
graphic
tubes allow the user to select a molybdenum
(Z = 42) or rhodium
(Z = 45) anode.
The choice
of target material
affects only the
not the quality,
of the bremsstrahhung
of an x-ray spectrum.
The target
mate-
rial, however,
determines
the position
of the characteristic
x rays and hence
fluence
x-ray quality.
U
A
electron
ento remove
ergy
an electron
from the K shell
(binding
energy
equals
-69.5
quantity,
portion
980
x
potential.
a maximum
is insufficient
beam
(milliamperes
higher-
parameters
include
tube
exposure
time, disbeam
filtration,
and gen-
of an x-ray
quantity
spectrum.
and
presence
rays
The x-ray
of higherquality.
potential,
magnitude
The
monoen-
quality
beams
produce
a better
image
and impart a lower
dose to the patient.
Various
fixed
and operator-selectable
parameters
are involved
in the production
of x rays that affect the quantity
area under
the spectral
curve,
is proportional
to
the tube potential
squared.
The maximum
photon energy
is determined
by the tube potential.
60-kVp
un-
explic-
distribution
beams
x rays. For a given
area
is not
but
energy
all x-
quality
is used
spectrum
(ie,
x-ray
and have a greater
percentage
photons
than beams
of lower
energy
with
The term
of the
of the
High-quality
ergetic
for
to the
as is quantity,
sense
inten-
of an x-ray
summed
is proportional
the shape
distribution).
defmed,
general
x-ray
energy
radiography
is provided
in
quantity
is often
used
to
the x-ray intensity
energies
itly
x-ray
An example
spectrum
for general
Figure
12. The term
describe
of the
at each
set of conditions.
given
(key)
Energy
17.
Graph
of the effect
of varying
tube current and exposure
time (or their product,
milliampere seconds
[muls])
on the x-ray spectrum.
The
area under
the curve,
not the shape
of the curve,
is
changed
as the tube current
or exposure
time or
both are increased.
Figure
SPECTRUM
spectrum
(relative
120
Volume
(energy)
does in-
17
Number
4
Average
f-.
J
and
Photon
Energy
Photon
Quantity
I mm HVI.
Increases
HVL
Fixed kVp
and mAs
Decreases
c_#{149}
Jw\+
Jw\.
M
0.
nm
m
-
-
_5
iaarun-
jnarsnfl
c-.
-
Jw.
Jw.
5)
w.
/-
-
0
wssamr
--
20
Figure
18.
Diagram
ifiustrates
the effects
of beam
hardening.
Beam hardening
is the process
in which
lower-energy
x rays are selectively
removed
from
the x-ray beam
as the beam
is passed
through
more
and more
attenuating
materials.
HVL
=
halfvalue
layer. (Redrawn
from Bushberg
printed
with permission.)
et ah, 1994,
and
re-
30 kVp Unfiltered
JMYbenum
--
Spectrum
larOet
Graph
creases
and
the
of high-
passes
and
shifts
more
because
(softer)
of increased
and
to higher
energies.
photons.
As it
more
attenuating
ma-
(softer)
x rays are abthan are the higher-energy
x-ray
spectrum
is said
exiting
to have
the percentage
photons
filtra-
on the x-ray spectrum.
As the
the area under
the curve
de-
the lower-energy
more readily
ened
Mass Attenuation
(key)
low-energy
through
100
80
effect
spectrum
sorbed
x rays. Thus,
the
tenuating
material
E
of the
tion (increased
HVL)
filtration
is increased,
terial,
0
60
Energy
19.
Figure
tion
6
40
has
been
the at-
been
hard-
of low-energy
decreased.
Beam
increases
the average
energy
of the
beam,
which
causes
an increase
in the amount
of material
required
to decrease
the number
of
photons
in the beam by a factor
of two (defmed
as the baljvalue
layer
[HYL]).
Beam
hardening
produces
a more
monoenergetic
x-ray beam,
but it decreases
the absolute
number
of photons in the beam.
The effect of beam
hardening,
hardening
I
I
30 kVp Filtered Spectrum
Molybdenum
Target
0.03 mm Molybdenum
Filter
25
Photon
Figure
x-ray
20.
spectra
energy
36
(key)
Unfiltered
and
and graph
of molybdenum
coefficient
as a function
the effects
of beam
filtered
of x-ray
mammographic
or filtration,
attenuation
energy
crease
demonstrate
to higher
filtration.
Filtration
is important
in optimizing
the mammographic
x-ray
clinically
spectrum.
The initial unfiltered
spectrum
from a molybdenum
target
contains
both the narrow
characteristic energy
bands
and the broad bremsstrahlung
spectrum.
Filtration
with a molybdenum
filter seleclively removes
much
of the broad
bremsstrahlung
spectrum
and produces
a spectrum
with fewer
photons occupying
a narrower
energy
range.
(Modified
from Bushberg
et al, 1994, and reprinted
with permission.)
through
tially,
July-August
an attenuating
an
x-ray
1997
spectrum
material
contains
(Fig
18).
some
the
quantity
x-ray
while
energies
(Fig
spectrum
is to de-
shifting
the spectrum
19). The maximum
en-
ergy
of the spectrum
remains
unchanged.
Mammographic
x-ray spectra
provide
an cxcellent
example
of the utility
of beam filtration
(Fig 20). The initial beam
containing
both the
broad
bremsstrahlung
spectrum
and the narrow
characteristic
x-ray spectrum
passes
through
a
thin
(approximately
ter that
has
0.03-mm)
a K shell
binding
keV. The graph
in the center
the
attenuation
coefficient
sus
energy
absorption
Beam hardening
is the process
in which
x-ray spectrum
changes
shape after passing
on
the
and
indicates
at a given
molybdenum
energy
fil-
of -20
of Figure
20 plots
of molybdenum
the
energy.
likelihood
The
verof x-ray
attenuation
an
Ii-
distribu-
McCollough
U
RadioGraphics
U
981
coefficient
ing energy
use
increases
sharply
at the
(“K edge”)
of molybdenum.
of a molybdenum
creases
and 30
the
keY
filter
K shell bindThus,
dramatically
bremsstrahlung
and produces
de-
x rays between
a more
monoenerge-
20
0.
0
5)
tic
spectrum
containing
the
energies
best
suited
5)
for mammography.
A subsequent
ray
physics
5)
article
discusses
properties
in this
series
in detail
of x-ray
the
generators.
which
the
generators
means
that
maximum
means
that
tials
are
ode,
and
the
(peak
at some
times
at other
the maximum
value.
from
the
This
Energy
0 to
poten-
anode
and
cath-
potential
reaches
type of waveform
spectrum
with
a higher
per-
centage
of lower-energy
pared
with generators
nearer
to the maximum
erator
should
produce
to the peak kilovoltage.
(softer)
x rays comthat produce
voltages
potential.
Ideally,
a gena constant
voltage
equal
More typically,
triplephase
or high-frequency
generators
have
an approximately
5% ripple
and produce
an x-ray
spectrum
with a greater
proportion
of high-energy x rays than that produced
by a singlephase
generator
(Fig
2 1). Because
x-ray
increases
with tube potential
squared,
generator
type (voltage
waveform)
affects
quantity
as well as the quality
of the x-ray
trum.
x
rays
emanating
from
a point
source
by the
states
that
tional
to the
the
inverse
exposure
distance
square
varies
squared
law,
inversely
a factor
of four
pling the distance
posure
by a factor
The
982
U
Imaging
inverse
square
& Therapeutic
(1/22)
to 22.5
mR/h,
law affects
the x-ray
Technology
not
affect
in Table
produce
est
the
Distance
of the
on the x-ray
x-ray
spec-
spectrum
parameters
dose,
are
the goal
quality
a diagnostic
radiation
of the
summarized
of radiography
image
at the
different
diagnostic
is to
low-
tasks
and
scenarios
require
various
equipment
of this is the need
avoid
motion
the
sure
different
optimizations
parameters.
An cxto optimize
anode
madifferently
for mammogra-
fihm
blur
For
during
the
screen-film
density
to the
and
and
dark
or too
light).
is chosen,
some
other
must
radiographic
detection
is related
patient
characteristics
too
cx-
decreases
squared.
phy and general
radiography.
Another
example
is the desire
to minimize
exposure
time
to
is
tri-
of photons
quality
7. Because
patient
of the
ample
propor-
spec-
quantity
equipment
amination.
and
(key)
of distance
The influences
various
which
reduces
the
to 10 mR/h.
the
inverse
teriah and filtration
-). This prim22, in which
an cx-
100
trum.
the
dis-
(1/d
to the source
of nine (1/32)
the
does
are
ciple is illustrated
in Figure
posure
equal to 90 mR/h
is measured
at 2 feet
from the source.
Doubling
the distance
from
the source
to 4 feet reduces
the exposure
rate
by
in that
by
the
the
spec-
uniformly
distributed
in all directions.
Thus,
amount
of x rays measured
depends
on the
tance
from the point
source.
This relationship
summarized
trum
quan-
tity
60
40
Figure
21.
Graph
of the effects
of generator
type
on the x-ray spectrum.
Single-phase
generators,
which
have 100% voltage
ripple,
produce
a spectrum
more heavily
weighted
with lower-energy
photons than do triple-phase
generators,
which
have an
approximately
5% voltage
ripple.
(Modified
from
Bushberg
et al, 1994, and reprinted
with permission.)
This
how electric
the
times
an x-ray
varies
20
is
ripple,
kilovoltage).
between
and
however,
generators
waveform.
100%
voltage
value
applied
produces
have
x-
operation
Briefly,
one distinguishing
feature
of x-ray
the amount
of ripple
in the voltage
Single-phase
on basic
to the
the
be
radiation
patient
expo-
transmission
optimized
If a short
variable
cx-
systems,
(ic,
exposure
may
not
time
need
to be
changed
to increase
the photon
fluence
and to
achieve
appropriate
film darkening.
Either
the
tube current
or the tube potential
could
be increased
or the distance
between
the patient
and the detector
could
be decreased.
The operator
must understand
the ramifications
of
each of these
scenarios
to make the best
choice.
Volume
17
Number
4
Table
7
Summary
of Influenc
es on
X-ray
Variable
Quantity
Anode
Tube
material
potential
Tube
current
Time
Distance
Filtration
(Z)
(kVp)
Quality
Affects
position
(energy)
of characteristic
x rays
Determines
presence
or absence
of characteristic x rays; determines
maximum
x-ray energy
None
None
None
Increased
percentage
of high-energy
x rays with
increased
filtration
(higher
HVL)
a Z
a kVp2
(mA)
a mA
a time
cx 1/distance2
Decreases
with increasing
filtration
(higher
HVL)
(HVL)
Waveform
Inverse
Spectrum
Increases
with decreasing
voltage
ripple
(flatter
waveform)
square
Increased
decreased
percentage
filtration
of high-energy
x rays
(flatter
waveform)
law:
(1/distance)2
Exposure
3’
Figure
22.
Diagram
illustrates
the
inverse
square
law. The inverse
square
law dictates
that the exposure
(L) is inversely
proportional
to the
distance
(D) squared.
In this cxample,
doubling
the distance
from
the source
from 2 to 4 feet reduces
the exposure
by a factor
of four
(from
90 mR/h to 22.5 mR/h).
(Modi-
Source
E-9O
mRlhr (5)5
fled from
reprinted
10 mRlhr
Bushberg
et al, 1994,
with permission.)
It is often
desirable
to provide
information
regarding
the x-ray spectrum.
This can be done
with regard
to either
the quantity
or quality
of
the spectrum.
X-ray quantity,
or intensity,
is
A particularly
useful descriptor
spectrum
is the effective
energy
The effective
energy
is determined
surement
of the
most
material
required
easily
measured
and
described
in terms
of
exposure.
It is easier
to measure
charge
duced in an ion chamber
than to count
proindividual
photons.
To describe
quality,
citing
a
single
value is convenient
but incomplete.
A
graph
of the actual
x-ray spectrum
is the only
complete
representation
of the energy
distribution of the x-ray beam.
However,
if target
material, filtration,
and waveform
are similar
for the
x-ray tube spectra
being
compared,
the tube potential
can be used as a reasonable
indicator
of
the energy
characteristics
of the x-ray beam.
Typically,
the
average
tron volts)
is equal
the tube potential.
July-August
with
1997
x-ray
to one-third
energy
(in
by a factor
of two.
HVL,
which
If one
of an x-ray
of the beam.
from a mea-
is the
to decrease
amount
the photon
knows
and
the
HVL,
of
flucnce
an ef-
fective
attenuation
coefficient
of the entire
beam
can be estimated.
Although
the photons
at each
energy
all have a different
attenuation
coefficient
for
a given
material,
the
effective
attenuation
co-
efficient
reflects
the global behavior
of the beam
and ignores
the individual
energies.
After one determines
the effective
attenuation
coefficient,
the energy
corresponding
to the effective
attenuation coefficient
is used as the effective
energy
kihoehec-
to one-half
of
McCollough
U
RadioGraphics
U
983
of the
ray
entire
beam
beam.
The
is a helpful
tenuation
of the
effective
tool
beam
for
energy
of an x-
predicting
for a given
the
at-
object.
article
ciples
reviewed
inherent
physics
fundamental
physics
discussion
of radiologic
to the
and
described
as the
loss
across
an electric
the
of energy
production
from
potential
sult
of electrons
influence
Characteristic
down
positively
x rays
from
an atom,
atomic
shell.
Outer
fall into
vacancies.
The electron
tion yields excess
energy
that can be released
from the atom in the form of characteristic
x
rays.
An x-ray
versus
spectrum
the
x-ray
is a plot
energy
and
of x-ray
potential
squared,
tube
a broad,
current,
expo-
sure time, and anode
material
and inversely
proportional
to the distance
(from
the source)
squared.
The x-ray quantity
decreases
with increasing
filtration
(a higher
HVL) and increases
with decreasing
voltage ripple (a flatter voltage
waveform).
The distribution
of photon
energies
within
an x-ray
spectrum
anode
material,
potential,
waveform.
Increasing
creases
the maximum
and
determines
characteristic
984
U
Imaging
&
the
Therapeutic
filtration,
by the
and
tube
voltage
the tube potential
inx-ray energy
produced
presence
x rays.
This article
meets
Award.
To obtain
is affected
The
or absence
atomic
number
the criteriafor
1.0 credit
credit,
see the questionnaire
Technology
it determines
the
broad
bremsthe
posi-
articles
addressing
the
basic
physics
of imaging
with x rays provide
the user of radiographic
equipment
with a deeper
understanding of the tools used in clinical
radiology.
intensity
includes
continuous
bremsstrahlung
spectrum
and marrow, discrete
energy
bands
(lines)
produced
by
characteristic
x rays. The quantity
of photons
produced
by an x-ray beam
is proportional
to
the tube
affect
but
subsequent
are
in an
the
not
transi-
ehectrons
a vacancy
does
spectrum,
atom
of the
nucleus.
when
leaving
electrons
to fill the created
characterisis the rc-
because
charged
occur
ejected
mechanisms:
and the
radiation
slowing
of the
accelerated
by two
the bremsstrahlung
process
tic process.
Bremsstrahlung
prim-
of x rays
electrons
material
strahlumg
tion of the narrow
energy
band of characteristic
x rays. Finally,
an increased
percentage
of highenergy x rays occurs
with increased
beam
filtration or decreased
voltage
ripple.
These
basic principles
of x-ray production
form the foundation
for the effective
use of radiographic
equipment
in clinical
practice.
Understanding
the effects
of equipment
parameter
choices
allows
the user to optimize
the radiographic
examination
in terms
of both image
quality
and patient
dose and to reduce
the need
for repeat
exposures.
In addition,
knowledge
of
the principles
that govern
equipment
operation
can be of substantial
benefit
when
medical
equipment
is purchased.
This article
and the
U SUMMARY
This
anode
of
of the
hour
Acknowledgment:
sistance
of Candra
manuscript.
The author
appreciates
K. Jones
in the preparation
U SUGGESTED
Several
excellent
the
topics
which
listed
asof the
READINGS
texts
presented
are
the
are available
in this
that
article,
some
address
of
below.
Bushberg
JT, Seibert
JA, Leidholdt
EM Jr, Boone
JM.
The essential
physics
of medical
imaging.
Baltimore,
Md: Williams
& Wilkins,
1994.
Curry
TS III, Dowdey
JE, Murry
RC Jr. Christensen’s
physics
of diagnostic
radiology.
4th ed. Philadelphia, Pa: Lea & Febiger,
1990.
Hendee
WR, Ritenour
ER. Medical
imaging
physics.
3rd ed. St Louis,
Mo: Mosby-Year
Book,
1992.
Huda W, Sloan RM. Review
of radiologic
physics.
Baltimore,
Md: Wihhiams
& Wilkins,
1995.
Johns
HE, Cunningham
JR. The physics
of radiology.
4th ed. Springfield,
Ill: Thomas,
1983.
Sprawls
P Jr. Physical
principles
of medical
imaging. 2nd ed. Gaithersburg,
Mo: Aspen,
1993.
in Category
onpp
961-966
1 ofthe
AMA
Physician’s
Recognition
Volume
17
Number
4