Objectives: To understand;
1
The defined quantities related to scatter
2
How scatter depends on the imaging parameters
3
How scatter affects contrast and required exposure
4
The role of grids in scatter reduction
5
Alternate means of scatter reduction
6
Scatter modeling
In this section we will examine the problem of x-ray scatter
and its effects on image quality. One of the main effects of
scatter is degradation of image contrast. This is illustrated
below as a reduction in the differential signal produced by
an object when scatter is present.
The shadow of the object is filled in by the scatter
originated outside of the object shadow and contrast is
reduced.
Figure 1
Is
Ip
Detected
signal
Without scatter
With scatter
The amount of scatter detected in an image depends on several factors.
Referring to Figure 2, these include;
Focal spot
t(x,y)
Air gap
1
2
3
4
5
Detector
W
Figure 2
KVp
Field Size W
patient thickness t(x,y)
solid angle, which depends
on W and the air gap
patient composition
Referring to Figure 1 the total intensity It at the detector is the sum of
the primary (unscattered) intensity, Ip, and the scattered intensity Is.
(1)
The scatter fraction F is given by
(2)
The scatter to primary ratio R is given by
(3)
Suppose we have an object with transmitted primary intensity I2 with
adjacent intensity I1 as shown below .
I2
I1
The physical contrast, in the absence of scatter, is given by
(4)
Although we are defining the contrast in terms of intensity, similar
definitions can be made in terms of fluence.
For mono-energetic beams the two the intensity and fluence are
linearly related by the energy.
For polyenergetic beams, the situation is complicated by the details of
the spectrum. We will sometimes use intensity and sometimes use
fluence to try discuss these basic concepts.
In a real imaging situation, the details of the detector energy
response has to be taken into account.
In general, when making calculations of quantum noise it is a
convenient simplification to pretend that we are dealing with monoenergetic beams of some effective energy.
We will resort to this later in this section.
The contrast Cs observed in the presence of scatter is given by
We have assumed that the amounts of scatter detected along with I2
and I1 are approximately the same. This is reasonable since scatter is
known to vary slowly spatially, resembling a very blurred version of
the primary image.
.
The ratio of contrasts with and without scatter is given by
(6)
where we have added and subtracted the expression for the scatter
fraction to achieve the result.
Therefore the contrast observed in the presence of scatter is degraded
by a factor 1-F . The reciprocal of this quantity is sometimes referred
to in the literature as a contrast degradation factor which we will call
CDF, defined by
(7)
(8)
For example, if the scatter fraction is 0.8, CDF = 5.
CDF can also be expressed in terms of scatter to primary ratio R. From
equations 6 and 8 we get
(9)
CDF depends on field size, Kvp, patient thickness and scatter
fraction. Figure 4 below is adapted from Figure VIII-18 in Ter
Pogossian and corresponds to a 30cm x 30 cm phantom of uniform
thickness . It shows a large dependence on patient thickness and
some variation over the typical range of kVp values indicated by the
shaded areas.
Figure 4
The fact that the primary radiation is more directional than scatter is
the basis of the use of anti-scatter grids which consist of septa which
allow most of the primary radiation to pass, but which intercept the
more divergent scattered radiation. The basic idea is illustrated in
Figure 5.
Is
Ip
The grid shown in Figure 4 is called a parallel grid and usually consists
of numbers in the range of 100 septa per inch made of lead or tantalum.
The advantage of a parallel grid is that it is easily positioned.
A disadvantage is that for large fields of view, the primary transmission
decreases at the edges of the field of view where the primary radiation
enters the grid at appreciable angle leading to “grid cutoff”.
Other options include focused grids in which the grid septa are
focused toward the x-ray source and crossed grids with septa going in
each direction. These are shown in Figure 6.
Focused grids have improved transmission of primary radiation but
must be carefully aligned. Obviously, putting a focused grid in upside
down would result in very poor transmission. The crossed grid
provides the lowest resultant scatter fractions, but provides reduced
primary transmission.
The factor by which the mAs must be increased to achieve the same
detector exposure following the reduction of scatter and, to a lesser
extent, primary radiation is called the Bucky factor.
This has nothing to do with the University of Wisconsin mascot but is
derived from the name of the inventor of the grid.
An important parameter characterizing a grid is the grid ratio Rg
defined as the ratio of the septal length to the septal spacing. Figure 7
shows the typical transmission Ts for scattered radiation as a function
of grid ratio.
Most of the scatter reduction is achieved at the lower grid ratios.
Further reduction comes at the expense of increased Bucky factor.
Air gaps are sometimes used instead of grids. The extra distance
between the patient and detector allows the more divergent scattered
radiation to miss the detector.
Since air gaps and grids eliminate some of the same radiation, the
effects of simultaneous use of air gaps and grids are not
multiplicative.
The use of an air gap increases magnification which can either
increase or decrease spatial resolution depending upon whether
resolution is limited by focal spot blurring or the detector.
The effectiveness of a grid depends on the details of the imaging
situation.
In general when there is a large scatter fraction present, it makes sense
to use a grid. For small scatter fractions, the decrease in primary
transmission might be too large a detriment. The grids physical
transmission properties are described by the selectivity  which is
defined in terms of the primary tranmission Tp and the scatter
transmission Ts as
(10)
The grid produces the following intensity transformations,
(11)
Rewriting the scatter fraction in terms of the scatter to primary ratio
using equations 2 and 3, we can calculate the new scatter fraction with
the grid in place. Without the grid we have,
(12)
With the grid the scatter fraction becomes,
(13)
Figure 8 shows the improvement in scatter fraction FG achieved with
grids of various selectivities for various scatter fractions F.
For  =10, F=0.8 which gives R =4, we get FG of about 0.3.
The contrast after insertion of a grid CG is related to the contrast in the
presence of scatter
by the
(note missing words in text)
contrast improvement factor KG defined as
(14)
From equation 6 we had
Similarly we can write
(15)
Dividing, we obtain
(16)
Plugging in for FG from equation 13
(13)
and doing a little algebra, we obtain,
(17)
The selectivity  is a more fundamental property of the grid than KG
which, as can be seen from equation 17, is highly dependent on the
scatter to primary ratio.
The dependence of KG on  is shown in Figure 8 for three values of R.
The dependence of KG on  is shown in Figure 8 for three values of R.
QUESTION--Can insertion of a grid reduce the required exposure?
Since contrast is improved and required exposure depends on contrast
we might expect that under certain circumstances, the use of a grid
might reduce exposure requirements. First we will consider the case of
an ideal grid with perfect scatter rejection and complete primary
transmission. Then we will consider the case of a real grid. We will
consider a mono-energetic x-ray beam so that we can easily calculate
the quantum noise.
Suppose with no scatter present it is possible to see an object of
contrast Cp. We previously derived the fact that the required detected
fluence Np for a given SNR, object area A and primary subject
transmission is given by
(18)
Recall that in this equation s is understood to be the differential
signal due to the attenuation of the low contrast object as opposed
to S, the total signal detected.
In the case where scatter is detected and the contrast is reduced in
accordance with equation 6, the new required exposure, including the
detected scatter N’s is
(19)
where
(20)
and  is the factor by which the exposure must be increased in order to
compensate for the increased scatter fraction.
A common mistake (made in one of my own early publications) is
to argue that since the required exposure is increased by a factor of
1 / (1-F ) 2 , the mAs must be increased by this factor in order to see
the object, and therefore, the insertion of a grid would reduce
exposure by a factor of 1 / (1-F ) 2.
However, this argument ignores the fact that, whereas only primary
radiation was used to satisfy the exposure requirement in the case
with no scatter, when scatter is present it contributes to the detected
exposure and alters the fractional quantum fluctuations. Lets look at
this more carefully.
From F = Ns / ( Np + Ns) we get
(21)
Using equation 20 and the fact that scatter fraction is not altered by
the mAs increase we get
(22)
But since from equations 18 and 19
(23)
It follows that
(24)
Therefore, by eliminating the need to increase the mAs by a factor of
, the use of an ideal grid reduces the required exposure by a factor
of 1 / (1-F) rather than 1 / (1-F) 2.
Another way of calculating this result is to consider absolute signal
and quantum noise amplitudes rather than contrast. In that case,
scatter does not change the differential signal, (the attenuation by the
low contrast object) but it does increase the absolute size of the noise
since the square root of the total detected fluence increases. Let’s try
this.
For the case of no scatter the differential signal to noise ratio is given
by
(25)
With scatter and mAs increased by a factor of 
(26)
The object will be detected equally well provided that the signal to
noise ratio is the same. Therefore we can equate the two expressions
in equations 25 and 26 to obtain  = 1/(1-F) as above.
Because real grids do not completely reduce scatter and do not
transmit all of the primary radiation, they do not automatically reduce
the exposure required to detect a given small contrast and, in some
circumstances, can increase the required exposure.
The Bucky factor B is given by
(27)
Where in and out refer to the grid and Ts and Tp are the grid
transmissions for scatter and primary respectively.
For systems such as film which generally require a narrow range of
exposure to remain in the linear range, exposure must be increased
by the Bucky factor just to satisfy exposure conditions.
For systems such as phosphor plates and image intensifiers which
can approach quantum limited systems in certain circumstances we
can apply our previous analysis to determine the factor  by which
exposure must be altered to provide equivalent low contrast object
detection.
Assume that in the presence of scatter a contrast Cs is just seen with
exposure Np +Ns, we can write
=
Cs2 AT
(28)
With the grid inserted and the exposure modified by a factor of  ,
recalling that CG = CsKG, we get the following expression after the grid,
(29)
For the signal to noise ratio to be the same in each case we must have
(30)
or
(31)
For B< (KG)2, exposure is reduced by using the grid. When small
amounts of scatter are present, KG is small ( see Figure 8) and  will
be greater than 1.
Several alternate approaches to scatter reduction have been
implemented. These usually involved some sort of scanning procedure
which limits the extent of the x-ray beam to a scanning point or line. A
generic example of a line scan system is shown in Figure10.
Due to the coordinated motion of the slit pairs, most of the scattered
radiation is removed. These systems have been shown to provide
greatly improved contrast in applications such as chest radiography.
Their main drawback is that exposure times are increased by the
ratio of the field of view to the slit width and tube loading becomes
a serious problem.
Commercial systems using line scan geometries have been
introduced in connection with a process called exposure equalization
in which detected signal feedback schemes permit alteration of the
exposure on a line by line basis in order to reduce the dynamic range
of information contained in the image. This results in improved SNR
in the poorly transmissive regions of the image. Because the highly
transmissive areas are reduced in intensity, their contribution to the
scatter fraction in nearby, less transmissive areas is reduced. The
result is that low contrast objects such as lung tumors can be
detected more easily.
Other manufacturers have used point scanned systems which remove
essentially all effects of scatter. These systems had extremely high
tube loading and were generally limited to pediatric patients.
There are several applications where it is advantageous to estimate
the amount of scatter present in order to perform quantitative image
processing. Examples of this include dual energy imaging for
determination of bone mineral, dual energy chest imaging, where
images of differing energies are used to remove bone or soft tissue,
and dual energy DSA where it is desired to remove the effects of
soft tissue misregistration.
One technique is to simply place an array of small lead absorbers in
the image and take an extra exposure in which the signal behind the
absorbers can be used to estimate the local amount of scatter.
Since the finite size of the absorbers perturbs the scatter field to some
extent, such measurements are usually tried on phantoms using
absorbers of decreasing size and then extrapolating to the scatter value
which would be obtained with absorbers of zero radius.
Another calculational approach is to use a point spread function
method which assumes that, associated with every point in the
detected primary radiation field, there is a well defined distribution
of scattered radiation as shown in Figure 11.
For a single primary transmission ray at the point x,y there is an
associated amount of scatter P(x-x’,y-y’) at point x’,y’. This function
is called the scatter point spread function and can be used to estimate
the scatter image if the primary image is known.
This is described by equation 32.
(32)
There are two difficulties with trying to calculate a scatter image by
this method
1
The primary intensity is not available since it is Ip + Is that is
measured.
2
The point spread function depends on thickness.
A first approximation to the scatter image is to blur the detected image
and pretend that the detected image is the primary image.
This works well if the scatter fraction is small, provided that the right
amount of blurring is used.
More accurate methods such as those used by Naimuddin and Molloi
attempt to establish a relationship between the detected image
intensity and the scatter fraction.
This makes use of the knowledge that scatter fractions are typically
higher in the regions of decreasing transmission.
Typically a chest phantom with lead blockers is used to get a graph of
scatter fraction versus detected intensity as shown schematically in
Figure 12.
The spread in data points around the fitted curve reflects the fact that
detected intensity alone is not an absolute predictor of scatter fraction.
Scatter fraction also depends on the configuration of scattering material
in adjacent regions. Nevertheless, the variations from a polynomial fit
to the chest phantom data are not excessively large in the chest.
When corrections for patient thickness and beam energy are made,
scatter fraction and therefore the scatter image can be estimated fairly
reliably.
Separate polynomial estimators are required for different imaging sites
in the body.
The scatter correction scheme of Molloi is shown in Figure 13.
Note that before the scatter image is subtracted from the detected
image to produce a scatter free estimate it is blurred to remove
detail not physically present in the actual scatter image.
The use of such a scheme to estimate the scatter image is
shown in Figure 14 for the case of chest radiography.
Note that the scatter image is essentially a blurred version of the
original image containing only low spatial frequencies.
Capillary Optics
X RAY
HOLLOW GLASS
CAPILLARY
POLYCAPILLARY CONTAINING
1 MICRON CAPILLARIES
IMAGE
INTENSIFIER
OPTICS
PRIMARY
SCATTER
NORMAL
MAGNIFICATION
BLUR
REDUCED
BLUR DUE
TO OPTICS
PATIENT
EXIT
BLUR
PATIENT
EXTENDED FOCAL SPOT