U.S. patent application number 09/902385 was filed with the patent office on 2002-02-14 for "x-ray computed tomography apparatus with correction for beam hardening".
This patent application is currently assigned to Siemens Aktiengesellschaft. Invention is credited to Stierstorfer, Karl.
Application Number | 20020018540 09/902385 |
Document ID | / |
Family ID | 7650014 |
Filed Date | 2002-02-14 |
United States Patent
Application |
20020018540 |
Kind Code |
A1 |
Stierstorfer, Karl |
February 14, 2002 |
"X-ray computed tomography apparatus with correction for beam
hardening"
Abstract
In an X-ray computed tomography apparatus having a radiation
filter, a patient attenuation value representative of the linear
beam attenuation by a patient under examination is determined in an
equation containing a correction function The correction function
is determined by first determining a set of reference overall
attenuation values that, for a given different thicknesses of a
reference material and different thicknesses of the radiation
filter arrangement, represent the actual overall attenuation by the
two materials. Then, an appertaining attenuation error value is
determined for each reference overall attenuation value.
Subsequently, a variable is defined changes in a direction
transverse to straight lines of constant attenuation error values
in a characteristic field of the attenuation error. Then, data
about an error function dependent on the variable are determined,
the error function representing the curve of the attenuation error
along a reference curve placed into the attenuation error
characteristic field.
Inventors: |
Stierstorfer, Karl;
(Erlangen, DE) |
Correspondence
Address: |
Schiff Hardin & Waite
Patent Department
6600 Floor Sears Tower
233 South Wacker Drive
Chicago
IL
60606
US
|
Assignee: |
Siemens Aktiengesellschaft
|
Family ID: |
7650014 |
Appl. No.: |
09/902385 |
Filed: |
July 10, 2001 |
Current U.S.
Class: |
378/16 ; 378/159;
378/19; 378/901 |
Current CPC
Class: |
G01N 2223/419 20130101;
Y10S 378/901 20130101; A61B 6/032 20130101; G01N 23/046 20130101;
A61B 6/583 20130101 |
Class at
Publication: |
378/16 ; 378/19;
378/901; 378/159 |
International
Class: |
G21K 001/12; H05G
001/60; A61B 006/00; A61B 006/00; G01N 023/00 |
Foreign Application Data
Date |
Code |
Application Number |
Jul 24, 2000 |
DE |
10 035984.1 |
Claims
I claim as my invention:
1. X-ray computed tomography apparatus comprising an X-ray radiator
having a focus from which X-rays, in a beam path, are emitted, at
least said focus being adapted for rotation around a subject for
irradiating said subject with said X-rays from a number of
different projections; a radiation filter arrangement disposed in
said beam path; a detector arrangement that detects X-rays in said
beam path that have passed through said subject and emits a set of
measured intensity values for each projection, each of said
measured intensity values being representative of the intensity of
the detected X-rays in a respective projection sub-region of the
projection; and an electronic evaluation unit that is programmed to
determine an overall attenuation value g for each of the measured
intensity values that is representative of an actual overall
attenuation of the X-radiation in the respective projection
sub-region effected by the radiation filter arrangement and the
subject and that determines a patient attenuation value p corrected
for beam hardening for each of the overall attenuation values g
that is representative of a theoretical, linear attenuation of the
X-rays by the subject in the respective projection sub-region, said
evaluation unit having data about a correction function k(z)
dependent on a variable z stored therein, and the evaluation unit
being programmed to determine a respective patient attenuation
value for each overall attenuation value according to the
equation:p=g-f-k(.alpha.g+.beta.f)wherein p is the patient
attenuation value to be respectively determined, g is the
respective overall attenuation value, f is a filter attenuation
value that is representative of a theoretical linear attenuation of
the X-rays by the radiation filter arrangement in the respective
projection sub-region, k(.alpha.g+.beta.f) is the value of the
correction function at the location z=.alpha.g+.beta.f, and .alpha.
and .beta. are constants, and wherein the evaluation unit is
programmed to determine correction function k(z) by: determining a
set of reference overall attenuation values for a combination of a
material of the radiation filter arrangement and a reference
material, said reference overall attenuation values being
representative of the overall attenuation of the X-radiation
effected by said combination for different thicknesses of the
filter material and of the reference material, at least taking the
beam hardening into consideration; determining an appertaining
attenuation error value for each of the reference overall
attenuation values according to the equation:e(d.sub.w,
d.sub.t)=g'(d.sub.w)-w(d.sub.w,d.sub- .t)-t(d.sub.t)wherein
e(d.sub.w, d.sub.t) is the attenuation error value given a
thickness d.sub.w of the reference material and a thickness d.sub.t
of the filter material, g'(d.sub.w, d.sub.t) is the reference
overall attenuation value given the thickness d.sub.w of the
reference material and the thickness d.sub.t of the filter
material, w(d.sub.w) is a first individual attenuation value that
is representative of the theoretical linear attenuation of the
X-radiation by the reference material given the thickness d.sub.w
of the reference material, and t(d.sub.t) is a second individual
attenuation values that is representative of the theoretical linear
attenuation of the X-radiation by the filter material given the
thickness d.sub.t of the filter material; defining the constants
.alpha. and .beta. are defined such that a value of a
variablex=.alpha.g'(d.sub.w, d.sub.t)+.beta.t(d.sub.t)change- s in
a direction transverse to lines of constant attenuation error in a
(g'(d.sub.w, d.sub.t), t(d.sub.t)) characteristics field of the
attenuation error; determining data about an error function u(x)
dependent on the variable x, said error function u(x) representing
a curve of the attenuation error along a reference curve v(x)
placed into the attenuation error characteristics field; and
determining the correction function k(z) according to the
equation:k(z)=u(x=z)
2. An apparatus as claimed in claim 1 wherein the reference overall
attenuation values (g') are determined by computer simulation.
3. An apparatus as claimed in claim 1, wherein the reference
overall attenuation values (g') are determined by measurement.
4. An apparatus as claimed in claim 1 wherein said reference
material is water.
5. An apparatus as claimed in claim 1 wherein said evaluation unit
is programmed to define .alpha. and .beta. as coordinates of a
vector (n) that is substantially normal to a line of constant
attenuation error in the attenuation error characteristics field,
whereby .alpha. is the coordinate of said vector along the
g'(d.sub.w, d.sub.t) axis of the characteristics field and .beta.
is the coordinate of the vector (n) along the t(d.sub.t) axis of
the characteristics field.
6. An apparatus as claimed in claim 1 wherein said evaluation unit
is programmed to place the reference curve v(x) at least partially
into a region of the attenuation error value characteristics field
wherein a significant part of the pairs of overall attenuation
value (g) and filter attenuation value (f) is anticipated in an
examination of said subject.
7. An apparatus as claimed in claim 1 wherein said evaluation unit
is programmed to select a straight line Cx as the reference curve
v(x), whereby C is a constant.
8. An apparatus as claimed in claim 1 wherein said error function
u(x) as a mathematical equation stored in the evaluation unit.
9. An apparatus as claimed in claim 8, wherein said evaluation unit
is programmed to determine the error function u(x) by polynomial
approximation.
10. An apparatus as claimed in claim 1 wherein the error function
u(x) is determined in table form and is stored in the evaluation
unit.
11. An apparatus as claimed in claim 1 wherein said filter material
is polytetrafluoroethylene.
12. An apparatus as claimed in claim 1 wherein said filter material
is aluminum.
Description
BACKGROUND OF THE INVENTION
[0001] 1. Field of the Invention
[0002] The present invention is directed to correcting beam
hardening in an X-ray computed tomography apparatus.
[0003] 2. Description of the Prior Art
[0004] As a consequence of the spectral dependency of the beam
attenuation behavior in an irradiated object, a shift of the
average or mean energy of the X-radiation emerging from a
transirradiated body toward higher energy values occurs given
polychromatic X-radiation. This effect is referred to as beam
hardening. In computed tomography, beam hardening causes gray scale
deviations in the reconstructed image of the body compared to the
theoretical case of linear, spectrally independent beam
attenuation. These gray scale deviations--or beam hardening
artifacts--in the reconstructed image interfere with the diagnostic
content of the image and can lead to misinterpretations in the
worst case.
[0005] Numerous approaches are proposed in the literature for
correcting image artifacts caused by beam hardening. For example,
one approach disclosed in U.S. Pat. No. 4,709,333 is known as
polynomial correction. Using an attenuation value obtained by
measurement that indicates the actual beam attenuation of a body
affected by beam hardening, a corrected attenuation value that is
employed as the basis of the image reconstruction is calculated by
inserting this attenuation value into a suitable polynomial
identified in a calibration phase.
SUMMARY OF THE INVENTION
[0006] An object of the present invention is to provide a computed
tomography apparatus which is operable to effectively correct for
beam hardening.
[0007] This object is inventively achieved in an X-ray computed
tomography apparatus having an X-ray radiator, a radiation filter
arrangement arranged in the beam path of the X-rays emitted by the
X-ray radiator, a detector arrangement that detects the X-rays that
pass through a patient under examination and provides a set of
measured intensity values for each slice projection, each of these
measured intensity values being representative of the intensity of
the detected X-rays in a respective projection sub-region of the
slice projection, and has an electronic evaluation unit that
determines an overall attenuation value for each of the measured
intensity values that is representative of the actual overall
attenuation of the X-rays in the respective projection sub-region
effected by the radiation filter arrangement and the patient, and
that determines a patient attenuation value corrected for beam
hardening for each of the overall attenuation values that is
representative of the theoretical, linear attenuation of the X-rays
by the patient in the respective projection sub-region.
BRIEF DESCRIPTION OF THE DRAWINGS
[0008] FIG. 1 shows an exemplary attenuation characteristics field
in which a number of lines of constant attenuation error are
entered, in accordance with the invention.
[0009] FIG. 2 shows a characteristics field wherein lines of
constant residual error are entered, wherein the function u(x) was
implemented as a look-up table, in accordance with the
invention.
[0010] FIG. 3 shows a characteristics field wherein lines of
constant residual error are entered, wherein the function u(x) was
implemented as a polynomial of the fourth degree table, in
accordance with the invention.
[0011] FIG. 4 is a block diagram schematically illustrating the
basic components of an X-ray computed tomography apparatus
constructed and operating in accordance with the principles of the
present invention.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0012] In accordance with the invention, data about a correction
function k(z) dependent on a variable z are stored in an evaluation
unit, and the evaluation unit is configured for determining the
respectively appertaining patient attenuation value for each
overall attenuation value according to the following equation:
p=g-f-k(.alpha.g+.beta.f) (1)
[0013] wherein p is the patient attenuation value to be
respectively determined, g is the respective overall attenuation
value, f is a filter attenuation value that is representative of
the theoretical linear attenuation of the X-rays by the radiation
filter arrangement in the respective projection sub-region,
k(.alpha.g+.beta.f) is the value of the correction function at the
location z=.alpha.g+.beta.f, and .alpha. and .beta. are constants.
The correction function k(z) is determined according to the
following method:
[0014] a) first, a set of reference overall attenuation values is
determined for a combination of the material of the radiation
filter arrangement and a reference material, the reference overall
attenuation values being representative of the overall attenuation
of the X-rays produced by this combination of materials for
different thicknesses of the filter material and of the reference
material, taking at least the beam hardening into
consideration;
[0015] b) an appertaining attenuation error value is then
determined for each of the reference overall attenuation values
according to the following equation:
e(d.sub.w, d.sub.t)=g'(d.sub.w, d.sub.t)-w(d.sub.w)-t(d.sub.t)
(2),
[0016] wherein e(d.sub.w, d.sub.t) is the attenuation error value
given a thickness d.sub.w of the reference material and a thickness
d.sub.t of the filter material, g'(d.sub.w, d.sub.t) is the
reference overall attenuation value given the thickness d.sub.w of
the reference material and the thickness d.sub.t of the filter
material, w(d.sub.w) is a first individual attenuation value that
is representative of the theoretical linear attenuation of the
X-radiation by the reference material given the thickness d.sub.w
of the reference material, and t(d.sub.t) is a second individual
attenuation values that is representative of the theoretical linear
attenuation of the X-radiation by the filter material given the
thickness d.sub.t of the filter material;
[0017] c) subsequently, the constants .alpha. and .beta. are
defined such that the value of a variable x with
x=.alpha.g'(d.sub.w, d.sub.t)+.beta.t(d.sub.t) (3)
[0018] changes in the direction transverse to lines of constant
attenuation error in a (g'(d.sub.w, d.sub.t), t(d.sub.t))
characteristics field of the attenuation error,
[0019] d) subsequently, information about an error function u(x)
dependent on the variable x are determined, said error function
u(x) representing the curve of the attenuation error along a
reference curve v(x) placed into the attenuation error
characteristics field;
[0020] e) finally, the correction function k(z) is determined
according to the following equation:
k(z)=u(x=z) (4).
[0021] In the inventive solution, a correct value for the linear
patient attenuation p could be derived from Equation (1) when the
correction value k is equal to the attenuation error between the
overall attenuation g and the sum of the linear filter attenuation
f and the linear patient attenuation p. For examination of a
patient, however, the value of this attenuation is not known
because of ignorance about the spatial distribution of the
attenuation coefficient in the examined body slice. In the
inventive solution, an attenuation error that is acquired in the
course of an examination of, in particular, a homogeneous reference
material having known attenuation behavior is therefore employed
for the correction value k. It is expedient to select a reference
material whose attenuation properties are similar to those of body
tissue, for which reason water is preferably employed as the
reference material. As used herein, the term `patient` stands for
arbitrary examination subjects.
[0022] In order to acquire information about this attenuation
error, the attenuation behavior of the material combination of the
reference material and a filter material employed in the radiation
filter arrangement is determined in a calibration phase with a
tandem arrangement of the reference material and the filter
material employed in the radiation filter arrangement. This can
ensue either by computer simulation but it is also possible to
undertake concrete measurements in an experiment. Reference overall
attenuation values are thereby determined for a number of different
thicknesses of the filter material and for a number of different
thicknesses of the reference material, the reference overall
attenuation values respectively indicating the overall attenuation
of the X-rays affected by beam hardening effected by the material
combination of filter and reference material given the respective
thicknesses of the two materials. It is self-evident that only the
material thickness effective in the sense of a radiation
attenuation is employed as the thickness of the filter or reference
material, i.e. the material thickness in the direction of the beam
path of the X-rays. A set of reference overall attenuation values
g'(d.sub.w, d.sub.t) is thus obtained that are dependent on the
thickness d.sub.w of the reference material and on the thickness
d.sub.t of the filter material and are respectively allocated to a
pair combination of thickness d.sub.w of the reference material and
thickness d.sub.t of the filter material. The attenuation error is
then calculated according to Equation (2) from the difference
between reference overall attenuation g'(d.sub.w, d.sub.t) and the
sum of linear attenuation w(d.sub.w) by the reference material and
linear attenuation t(d.sub.t) by the filter material. The following
applies to these two linear attenuations:
w(d.sub.w)=.mu..sub.wd.sub.w (5)
w(d.sub.t)=.mu..sub.td.sub.t (6),
[0023] wherein .mu..sub.w is an attenuation coefficient of the
reference material effective for linear attenuation and .mu..sub.t
is the corresponding effective attenuation coefficient of the
filter material.
[0024] It is theoretically possible, during use of the X-ray
computed tomography apparatus, to determine the value of the
attenuation error for the current value of the overall attenuation
g in a projection sub-region and the appertaining, current value of
the filter attenuation f, this attenuation error having been
derived given identical values of the reference overall attenuation
g' and the attenuation t by the filter material, and to utilize the
attenuation error value e determined in this way as the correction
value k for the respective projection sub-region. This, however,
would require that the attenuation error value e be present in
table form dependent on two variables, namely on the reference
overall attenuation g' and the filter material attenuation t. In
order to be sufficiently exact, such a table would have to contain
attenuation error values for an extremely large number of (g',
t)-value pairs. The realization outlay for this would be
considerable.
[0025] With the inventive solution, by contrast, dependency of the
attenuation error value e is reduced to dependency on a single
variable. To this end, the variable x is introduced according to
Equation (3), this being interpreted as the scalar product of a
vector (.alpha., .beta.) with a vector (g'(d.sub.w, d.sub.t),
t(d.sub.t)). The value of the variable x, accordingly, is a
criterion for the length of the vector (g'(d.sub.w, d.sub.t),
t(d.sub.t)) in the direction of the vector (.alpha., .beta.. In
order to obtain an unambiguous allocation between the variable x
and the attenuation error e, the vector (.alpha., .beta.) is
defined such that it is directed transverse to lines of constant
value of the attenuation error e in a (g', t) characteristics field
of the attenuation error e. This is equivalent to the amount that
the variable x changes from one line of constant attenuation error
value to the next.
[0026] FIG. 1 shows an exemplary (g', t) attenuation
characteristics field into which a number of lines of constant
attenuation error e are entered with a specification of the
respective value of the attenuation error. It should be noted that,
due to the definition of the attenuation error according to
Equation (2), its value is always negative. The amount of the
attenuation error also steadily increases toward higher values of
g' and t. It can be seen from FIG. 1 that, to a very good
approximation, the value of the attenuation error is constant on a
family of parallel straight lines. This unanticipated perception
favors the coordinate transformation according to Equation (3).
[0027] The vector (.alpha., .beta.) under discussion is then
defined such that it is essentially normal to the straight lines.
The length of this normal vector in the direction of the g'-axis of
the (g', t) characteristics field is thereby selected for the value
of .alpha., whereas the length of the normal vector in the
direction of the t-axis of the (g', t) characteristics field is
selected for the value of .beta.. For the sake of simplicity,
.alpha.=1 can thereby be applied. The variable x then has
essentially the same value for each value pair (g', t) lying on one
of the straight lines in the family of straight lines. This means
that, in this case, the coordinate transformation according to the
above Equation (3) enables an unambiguous allocation of each of the
straight lines from the family of straight lines to an x-value and,
consequently, enables an unambiguous allocation of an attenuation
error value to each x-value. For illustration, a normal vector n to
the straight line e=-0.06 is entered as an example in FIG. 1.
Further, a vector q is entered that belongs to a value pair of g'
and t lying on the straight line e=-0.06. It can be easily
replicated that each vector directed onto the straight line e=-0.06
has an identical projection in the direction of the normal vector n
and, thus, an identical x-value.
[0028] After the two variables g' and t have been reduced to the
variable x by the coordinate transformation according to Equation
(3), the relationship between the value of the attenuation error e
and the value of the variable x must still be found. To this end, a
reference curve v(x0 dependent on the variable x is defined and
along which the profile of the attenuation error e is to be
determined. v(x) should be selected such that a separate function
value v(x) is allocated to each value of x. Moreover, the reference
curve v(x) should be placed such into the (g', t) characteristics
field that it passes through a region of this characteristics field
wherein a significant part of the pairs of overall attenuation
value g and filter attenuation value f occurring given examination
of a patient is anticipated. In particular, the reference curve
v(x) should lie in the proximity of the most important value pairs
of g and t. In the simplest case, the reference curve v(x) is
defined as a straight line, i.e.
v(x)=Cx (7),
[0029] wherein C is a constant. The value of this constant C will
be selected dependent on the aforementioned demands made of the
position of the reference curve v(x).
[0030] It is self-evident that, instead of a straight line, some
other, arbitrary shape can be fundamentally selected for the
reference curve v(x). When a rectangular x-y coordinate system is
defined with
y=.beta.g'(d.sub.w, d.sub.t)+.alpha.t(d.sub.t) (8)
[0031] and when the reference curve is described by
y=v(x) (9),
[0032] then the following is generally valid for an error function
u(x) that indicates the value of the attenuation error e along the
reference curve v(x): 1 u ( x ) = e ( g ' ( x , v ( x ) , t ( x , v
( x ) ) ) ) = ( x - v ( x ) 2 + 2 , x + v ( x ) 2 + 2 ) . ( 10
)
[0033] In the above Equation (10), the first term in the argument
of e indicates the coordinate value of the attenuation error along
the g'-axis of the characteristics field according to FIG. 1,
whereas the second term indicates the t-coordinate value. The error
function u(x) can be modeled as look-up table. However, it is also
conceivable to express the curve of the attenuation error e along
the reference curve v(x) with the assistance of a mathematical
equation. A polynomial approximation can lead to good results here.
It has been shown that a polynomial of the fourth degree having the
form
u(x)=a.sub.4x.sup.4+a.sub.3x.sup.3+a.sub.2x.sup.2+a.sub.1x (11)
[0034] often suffices in order to approximate the error curve along
the reference curve v(x) with acceptable precision.
[0035] It is to be noted that, in practice, the lines of constant
attenuation error e will usually not be exact straight lines and
will also not proceed exactly parallel to one another. For this
reason, a function value u(x=.alpha.g'+.beta.t) that essentially
corresponds to the exact value of the attenuation error e for the
respective value pair (g', t) can in fact be obtained for value
pairs of g' and t that lie on the reference curve v(x). For value
pairs of g' and t that do not lie on the reference curve v(x),
however, a function value u(x=.alpha.g'+.beta.t) will be obtained
that, under certain circumstances, deviates slightly from the
actual value of the attenuation error for the appertaining value
pair (g', t). The coincidence between the function value u(x) and
the actual value of the attenuation error e is especially high in
the proximity of that straight line of constant attenuation error e
for which the normal vector n and, thus, the values of .alpha. and
.beta. were determined. It is therefore recommendable to determine
the normal vector n for a straight line of constant attenuation
error e that passes through the principal region of the value pairs
of g and f to be anticipated in the examination of a patient. Given
the characteristics field of FIG. 1, a beneficial selection would,
for example, would be the straight line e=-0.2.
[0036] FIGS. 2 and 3 shows (g', t) characteristics fields wherein
lines of constant residual error are entered, with the residual
error being defined from the difference between the function value
u(x) determined for a respective value pair of g' and t and the
actual value of the attenuation error e for this value pair (g', t)
taken from the characteristics field of FIG. 1. FIG. 2 thereby
shows an example wherein the function u(x) was implemented as
look-up table, whereas the function u(x) in the example of FIG. 3
was implemented as polynomial of the fourth degree. One can see
that the amount of the residual error is negligibly slight in broad
regions of the characteristics fields in both instances.
Particularly in FIG. 2, one can see that the residual error
approximately disappears along a straight line g'=(1/.gamma.)t
(whereby .gamma. is approximately 0.1) that was employed as
reference curve for the determination of the profile of the
attenuation error.
[0037] Points of value pairs (g', t) that were acquired from
projections of three central water phantoms having diameters of 10,
20 or, respectively, 30 cm are also entered in FIGS. 2 and 3. The
dot-dash line referenced P1 was thereby obtained given the water
phantom with a 10 cm diameter, the dot-dash line referenced P2 was
obtained given the water phantom with a 20 cm diameter and the
dot-dash line referenced P3 was obtained given the water phantom
with a 30 cm diameter. It can be clearly seen that the value pairs
of g' and t obtained for all three water phantoms lie in a region
of the characteristics field wherein the residual error is
decidedly slight both given implementation of the error function
u(x) as look-up table as well as given modeling of the error
function u(x) by a polynomial function.
[0038] The results shown in FIGS. 1 through 3 were obtained given
employment of water as reference material and Teflon.RTM.
(polytetrafluoroethylene) as the filter material. It has been
shown, however, that the lines of constant attenuation error e in
the (g', t) characteristics field can also be approximately assumed
as a family of straight lines parallel to one another given other
filter materials, for instance aluminum, so that the procedure
described up to now for determining the error function u(x) can
also be applied given other filter materials. It is also not
precluded that reference materials other than water be
employed.
[0039] FIG. 4 schematically shows the fundamental structure of an
X-ray computed tomography apparatus operating according to the
invention. An X-ray radiator 10 that emits a fan-shaped X-ray beam
12 onto a patient 14. A form filter 16 arranged between the X-ray
radiator 10 and the patient 14 attenuates the X-rays toward the
edge regions of the ray fan 12 in order to produce a uniform
radiation load on all transirradiated regions of the patient 14. A
detector arrangement 18 arranged in the beam path behind the
patient 14 detects the intensity of the X-rays that have passed
through the patient 14. The detector arrangement 18 is composed of
a number of detector elements 20 arranged next to one another in
the direction of the fan angle of the ray fan 12 that cover
respective projection sub-regions of the entire projection region
represented by the ray fan 12. Each of the detector elements 20
supplies a measured intensity value indicating the radiation
intensity in the respective projection sub-region to an electronic
evaluation unit 22. Using the received measured intensity values,
the evaluation unit 22 calculates the initially described overall
attenuation values g in a known way, these values g indicating the
actual overall attenuation of the X-rays in the respective
projection sub-region caused by the patient 14 and by the form
filter 16. The values of the linear patient attenuation p required
for the image reconstruction are then calculated by the evaluation
unit 22 according to Equation (1). The value of the error function
u(x=z) is utilized according to Equation (4) for the correction
value k(z=.alpha.g+.beta.f). The error function u(x) is stored for
this purpose in the evaluation unit 22, as described above either
in table form or in the form of an algorithm. It is self-evident
that the error function u(x) was determined for the filter material
of which the form filter 16 is composed.
[0040] In the case of a simulation of the reference overall
attenuation values g'(d.sub.w, d.sub.t), stray radiation effects
also can be additionally simulated in addition to beam hardening
effects. When the reference overall attenuation values g'(d.sub.w,
d.sub.t) are experimentally determined in the framework of a test
series, such stray radiations effects, of course, enter into the
measured values anyway.
[0041] Although modifications and changes may be suggested by those
skilled in the art, it is the intention of the inventor to embody
within the patent warranted hereon all changes and modifications as
reasonably and properly come within the scope of his contribution
to the art.
* * * * *