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Film-based industrial tomography
Film-based industrial tomography A. Notea X-ray and gamma-ray tomographic inspection has enormous potential for all stages of industrial quality control. Film-based industrial tomography (FIT) is simple in operation and costs less than computerized tomography by at least an order of magnitude. In FIT there is relative motion between the source and the examined object; the film is stationary relative to the object. The tomographic image is generated directly on the film. A theoretical model of the tomogram response has been developed and shows that each point of the tomogram includes information obtained from all the angular views. Tomograms of various test objects were recorded with a 160 kV constant potential X-ray unit. The slice thickness of the examined plane through the object is 0.3 to 0.5 mm. The capability of FIT to distinguish composition-density differences is demonstrated. Spatial resolution was measured with test patterns and DIN wire standards. Response of films D4 and D7 as a function of exposure was measured.
Keywords: radiographic testing, tomography, film response Tomography with X- and gamma-rays generates a material-density map (a tomogram) of a cross-sectional slice in the examined object. Variations expressed by the grey levels in the tomogram may be adjusted to yield the required contrast The technique is suitable for qualitative and quantitative inspection of structural details and defects, and its major advantage is the clear presentation of the interior of the examined object, unlike conventional radiography which is essentially a shadowgraph method. The potential of tomographic inspection for industrial products has been demonstratedl~-~°l to be large. It clearly adds a new dimension to conventional radiographic testing. In some cases the need to apply tomography should be evaluated against conventional radiography, in others it is possible to test only with tomography. Research and development efforts in the last decade were directed mainly towards computerized radiography which has revolutionized medical diagnosis. However, there are differences in the requirements of the medical unit and industryl"l. Medical computerized tomographs were developed to solve diagnostic problems in the human body where x-ray attenuation relates to bone, tissue (water) and air: industrial products to be inspected range in elemental composition from low to high atomic numbers and there is enormous variability in size and geometrical configuration. In addition, significant differences may be found in the characteristic features required from industrial tomographs: spatial resolution, slice thickness, contrast unsharpness, isoplanatics, repeatability. For industrial applications, customized tomographic systems are required as no single unit would be suitable for all industrial products. Computerized tomography has considerable limitations, however, imposed mainly by the relatively large pixel size.
In addition, its use in industry has been limited by high costs and the need for highly trained operators. The tomographic method discussed in this paper relates to image generation directly onto film1121. The image of a specific plane in the examined object is obtained by moving the radiation source relative to the object during exposure of the film. The film remains stationary relative to the object. A variety of similar approaches were considered during the first half of the century for medical diagnosticsl~3j41 and the method still arouses interestl'5,~61. Of special interest are the studiesl~7-201 of axial transverse tomography in which the inspected object and the film rotate synchronously. In the present study a non-computerized tomographic system based on film was constructed and the response obtained is discussed. The objects inspected demonstrate the characteristic features of the method.
Principles of the method Film-based industrial tomography (FIT) images a plane layer of chosen thickness through the inspected object The section visualized lies in the plane defined by the source and the surface of the film, ie the film is parallel to the plane layer through the object to be examined (Figure 1). As a result of this geometry the radiation impinging on the film is almost parallel to its surface. The radiation beam passes slantwise through the object, thus obtaining the practical thickness of the "plane layer'. The beam enters the inspected object after shaping by a slit aperture parallel to the plane layer being imaged. The beam thus produced is a fan 0.5 to 1 cm thick. In this way, blurring due to radiation scattering from planes other than the one examined is considerably reduced. During exposure the object and film or source and film are rotated synchronously. The film does not change its orientation
0308-9126/85/040179-06 $3.00 © 1985 Butterworth El-Co (Publishers) Ltd NDT INTERNATIONAL. VOL 18. NO 4. AUGUST 1985
179
Radiation
Collimator
from the source as a function of energyE, with maximum energy Emax: 0({,0) is the material density ( g c m 3) along chords passing through (X,Y), where O indicates the inclination of the chord and { is the position along its length: and la(E,{,O) is the mass attenuation coefficient along chords passing through (X,Y) (cm 2 g-*). When a monoenergetic g a m m a source is used, such as 60 keV from Am-241 or 662 keV from Cs-137, integration over the photon energy, E is unnecessary.
Object being examined
source Film holder
"o
x,r
z
~
7
x' Y
Synchronous rotation Fig. 1 Configurationof a film-based tomographicsystem. The fan-like beam definesthe plane-sliceof the object to be imaged
The density D of the film at the point (x:r) is proportional to l(x,)'). D(x,y) obtained represents the image of the examined plane-layer in the object In the'linear-range" of the fihn characteristic curve, D is describable by
(2)
D(x,y) ~ K + "/ log I ( x , y ) relative to the examined object thus every point or pixel
(x,y) of the image on the film corresponds to a point (X,Y) in the plane-slice through the examined object The prime requirements for the type of motion used are that: (1) the examined plane area remains in the radiation beam during the motion: (2) the radiation beam passes through each point (X,Y) from all directions, indicated by 0 <~ 0 ~< rr, during the motion. Only a rotation of 180° is necessary to complete the tomogram. A further rotation only yields the projections of 0-rr, therefore no additional information is provided. In practice, however, it is convenient to rotate the object many times within the exposure period. In the present study more than 100 rotations were perlbrmed for each tomogram. The process of generating the tomographic image is first explained for a needle object represented by a two dimensional 8 function (impulse function). The needle is located at (X, Y) on the object table. For a given sourceobject position the needle generates a projected line-like image on the film plane. This line has an inclination 0 to thex direction. Only one point(x,y) on the film plane~sees" the projection from the needle object for the whole 0 range. This results in a film density which is highest at (x,y), while other points of the film are considerably less dense. Thus, all received images from the different 0 are superimposed and a tomogram is obtained for 0 from 0 to rr. Every object may be expressed by a superposition of impulse functions, generating a corresponding tomographic image on the film. Mathematically the superposition of the projection from different exposure angles can be expressed as described below. During the exposure the chord length 1 defined by the beam passing through (X,I0 changes with 0, and is a function of the object shape, source-object geometry and object density. This function is given by lx,r (8). The intensity of the transmitted radiation reaching the point (xy) on the film during the exposure in which 8 varies from 0 to rr is given by l(x,y) =
Io(x,y) [
dE}dO
(1)
where I0 is the intensity of the incident source radiation reaching (x,y) with the object removed; s(E) is the normalized distribution function of the radiation emitted
180
The magnification of the image in the tomogram depends on the source-object and object-film distances. As in conventional radiography the size of the source contributes to unsharpness in the image and sets a limit on the magnification that can be used. High magnification, x 10 and more, may be obtained using a microfocus X-ray unit As an example, l(x,y) was determined for a cylindrical rod of radius R, homogeneous in composition and density'. The plane-slice to be inspected is a cut through the cylinder perpendicular to its axis of symmetry. The plane examined is circular in shape and due to the symmetry it is sufficient to examine the radiation impinging on points along a radial axis taken as (X,0), where (0,0) is the centre of the circle. The chord length 1(0) at points along the radial axis, inside (X/R < l) and outside (X/R ~> 1) the circle, is given by 2R
1-
sin20 X
Zx, o (o)
and0~<0~
R
=
X t> 1 and 0~<0 ~
X/> 1 ~-
0 ~ 0ma x
where 0max = arc sin (R/X). The chord length as a function of O is presented in Figure 2. 0max can be seen clearly tbr X/R > 1. All chords passing through (0,0) are of the same length l = 2R (and appear as a horizontal line in Figure 2). To determine L I0 was taken to be invariant within the fan beam spreading angle, which covers the greatest amplitude of the cylinder motion in the examined plane during the exposure. The value o f / a t the centre(0,0) according to Equation (1) becomes
11(0,0)/lo =
s(E)exp
[- 6(x'Y(°) p({O)p(E, {0) d(]
where K is a constant depending on the intensity, exposure time and film efficiency, and g is the film representative gradient.
(4)
rr e x p ( - 2p#R)
where tt is the mass attenuation factor for a monoenergetic photon source. If the source is not monoenergetic, it is possible to calculate an ellective constant attenuation coefficient through a non-linear stretching transformation based on the fact that the transmitted intensity decreases monotonically as the thickness increases. At other points along the radial axis where the chord length
NDT INTERNATIONAL
. AUGUST
1985
XIR
1.0 ~
0 0.33
A tomogram of a cylindrical iron rock 12.7 mm diameter, in a plane perpendicular to the symmetric axis, was measured with 662 keV gamma-rays from Cs-137 and is shown in Figure 4. The tomogram was obtained with film D7 and the source 2 m from the symmetric axis of the cylinder. The response at the edge and the cupping at the centre are as was foreseen from the calculations for 2/,pR=l.5. The data contain nmse, mainly film noise.
0.8-
-o.,
"
0.4
The generation of the tomogram through the accumulation of radiation on the film differs from the approach used in computerized tomography where the two-dimensional image is reconstructed from its one-dimensional integral projections.
0.2
0
function, however, which does not have an equivalent in conventional radiography. Image processing techniqueslZl'ZZl based on the expected response may be applied to the tomogram to enhance detail such as the edges of discontinuities.
o
30
60
90
Measured tomograms
0(0) Fig. 2 Chord length /{0) of radiation path through the points (X,0) in the examined plane through a cylindrical object of radius R
6l
The film-based industrial tomography system was operated with an Andrex 160 kV constant potential x-ray unit. The film was exposed with the X-ray beam parallel to the film plane. The film response for such exposure is shown in Figure 5 fora source-film distance of 3.5 m. The
2FpR 0
0.1
u
II
i. 2
C
I
i
,
0
,
I
0.5
~
i
i
,
,
,
l.O
I
1.5
=
,
I
I
2.0
xlR Fig. 3 Radiation intensity impinging on the film as 0 varies from 0 ° to 180 °, as a function of distance from the centre of a cylindrical homogeneous object with radius R. The determination follows Equation ( 1 )
is not constant, Equation (1) becomes
l(x,O)/Io
= 2
j
exp [-
laPlx,o (0)1 dO
(5)
0
The intensity proliles l(x,O)/lo for various 2p.pR values are shown in Figure 3. It is obvious that the film density, at every point (x,v) is influenced by the radiation transmission through every, point (X.Y) in the examined planeslice of the object. In other words, information from the whole of the examined plane-slice is accumulated at each point of the image. The curves of Figure 3 show that the edge atx = R is more pronounced for large values of 2,ttpR. Hence, the energy of the source and the film type may be chosen to yield an image of acceptable quality. The method has an inherent contribution to the point spread
NDT INTERNATIONAL. AUGUST 1985
H
Fig. 4 Tomogram through a cylindrical iron rod, 12.7 mm diameter, obtained with a Cs-137 source on film D7. The profile was taken along the diameter
181
----
magnification factor was 1.1, and all dimensions in the tomogram were found to increase by the same factor.
D4
D7
-
j
t"
j
.-y.'lOO
s
60 kV
.
,oo
C~
#
...<'.'.V/
~----"--TU-__-- 30 - - - . - - - - - 30
J )
I 10
i
I 20
I
A cylinder of lucite, 5 cm diameter, with seven rows each with five identical boreholes, was imaged with 140 kV. The hole diameters are 3.0, 2.5, 2.0, 1.75, 1.5, 1.25 and 1.0 ram. Figure 7 illustrates the capability of lhe method 1o distinguish holes down to 1 mm in diameter. The ability to distinguish components which differ in material density and atomic n u m b e r is demonstrated by the combination of a lucite pipe of 6.4 cm outer diameter,
I 30
Exposure (mA min) Fig. 5 Film response D as a function of exposure for different X-ray energies
iiliii....
Fig. 7 Tomogram of lucite cylinder, 5 cm diameter, with rows of boreholes 3.0. 2.5, 2 . 0 1.75. 1.5, 1.25. 1.0 mm diameter. Generated at 1 4 0 kV
Fig. 6 Tomogram of PVC cylinder, 5 cm diameter, with 3,4,5,6,7,8 m m diameter. Generated at 1 4 0 kV
boreholes
measurements were performed for films D4 and D7 simultaneously with each covering half of the t o m o g r a m area. There was no absorbing material between the source and film. The thickness of the slice which defines the plane is adjustable: in the present study 0.35 to 0.55 m m was used. This turns out to be an important parameter on which the quality of the image largely depends. For thinner slices finer detail in the vertical direction is distinguishable. The practical limitation on the slice thickness is the n u m b e r of photons per cm 2 impinging on the film, which reduces linearly with thickness. The thickness chosen for a particular tomographic inspection depends on the details that need to be distinguished, eg lower limit of diameter of voids or foreign particles. To investigate the resolution and the capability of FIT to distinguish betweeen light and heavy elements (low and high Z number) a n u m b e r of test objects were imaged. The first consisted of 5 cm diameter PVC cylinder containing holes with diameters of 3,4,5,6~7 and 8 mm. The t o m o g r a m taken perpendicular to the symmetric axis was generaled with 140 kV and film D4 (Figure 6). The source-object distance was 3 m, and object-film distance 0.4 in. The
182
t
Fig. 8 Tomogram of lucite pipe (6.4 outer diameter, 2 m m wall thickness), three iron wires (3 and 1 m m diameter) and a tygon pipe (1.1 cm diameter). Generated at 1 4 0 kV
NDT INTERNATIONAL.
AUGUST 1985,
The quality of the tomograms from FIT depends largely on the optimization of the parameters involved, such as photon energy, geometrical distances, type of motion and slice thickness. The energy considerations involved in FIT are quite different from those of conventional radiography. This becomes obvious when comparing the chord length distributions of the radiation passing through an object in both techniques, especially when the object is thin and very wide. As has been shown. FIT introduces new parameters: some are inherent in the technique, others are also present in conventional radiographic techniques but must be revaluated in the light of their effect o n FIT results. FIT has unique features which prove it to be an attractive tomographic technique for industrial NDT operators:
Fig. 9
Tomogram of lucite pipe (9.5 cm diameter)
(a)
All the components and most of the concepts used are familiar to the radiographic inspector: eg radiation units, films, screens, processing machines, intense light viewers, edge enhancement systems, film density, contrasL resolution, etc.
(b)
NDT inspectors with experience in radiography need a relatively short training period to master the FIT technique.
(c)
Marking and filing procedures for the tomograms are identical to those for conventional radiographs,
(d)
Interpretation oftomograms, as well as comparison with tomograms showing the history of the object, is convenient as both tomograms and radiographs may be viewed simultaneously on the light viewer.
(e)
The tomogram may be visualized by commercial edge enhancement or image processing systems developed for conventional radiography.
and DIN 62
standards: FE 1/7, 6 / 1 2 and 10/16. Generated at 140 kV
2 mm wall thickness, with adjacent to it on the periphery, an iron rod 3 mm in diameter, an iron wire of 1 mm diameter and a tygon pipe 11 mm diameter, 1.5 mm wall thickness, with inside it an iron rod of 3 mm diameter. The tomogram obtained is shown in Figure 8. Another object was composed of three iron wire DIN 62 standards which were attached to a lucite pipe of 9.5 cm outer diameter and 2 mm wall thickness. The wire diameters are: in the first DIN FE 1/7: 2.5, 2.0, 1.6, 1.25, 1.0 and0.8 mm; in the second DIN FE 6/12: 1.0, 0.8, 0.63, 0.5, 0.4, 0.32 and 0.25 mrn` and in the third DIN FE 10/16: 0.4, 0.32, 0.25, 0.2, 0.16, 0.125 and 0.1 mm. In the tomogram obtained (Figure 9) the wires are observed as circles. The 0.125 mm wire is still visible. The change in grey level observed from the wires of DIN FE 6/12 is due to the contrast reduction caused by the point spread function effect as explained previously123,241. Following these explanations the actual diameter for the small wires should be measured from the grey level and not from the observed circles. Tomograms were generated with densities of nearly 2, and inspected with an intense light viewer. The quality, of the tomograms obtained from the system is higher than that of the photographs reproduced here.
Author Professor Notea is in the Department of Nuclear Engineering, Technion - Israel Institute of Technology, 32000 Haifa, Israel.
References 1
Summary The major advantage of tomographic inspection is the clear presentation of details in the depth dimension of the examined object while in conventional radiography such details are projected on to the same location of the film. In addition, when optimized the method might detect details of adjacent parts or discontinuities which on account of small differences in density or composition cannot be revealed by conventional techniques. The relatively low cost and simplicity, of operation make film-based industrial tomography an inspection technique which is within reach of eveu industrial plant and it should be considered lor application at the various stages of production.
NDT INTERNATIONAL. AUGUST 1985
Ellinger, H., Morgan, I.L., Klinksiek, 1~, Hopkins, F. and Thompson, J.N. "Tomographicanalysis of structural materials', SPIE Imaging Applicationsfor A utomated Industrial Inspection and Assembly 182 (1979) pp 179-186
2 3 4
Kruger,ILP., Wecksung, W. and Morris, A. 'Industrial applications of computed tomography in Los Alamos Scientific Laboratory' Opt Eng 19 No 3 (1980) pp 273-282 Sato, T., Ikeda, O., Yamakoshi, Y. and Tsubouchi, M. 'X-ray tomography for microstructural objects', Appl Opt 20 No 22 (1981) pp 3880-3883 Hopkin, F.F., Morgan, I.L., Ellinger, H.D., Klinksiek, R.V., Meyer, G.A. and Thompson, J.N. "Industrial tomography
5
applications" IEEt£ Trans Nucl Sci NS--28 No 2 (1981) pp 1717-1720 Burstein, P., Bjorkholm, P.J., Chase, R.C. and Seguin, F.H. 'The largest and smallest X-ray computed tomography systems'Nucl lnstrum and Methods in Phys Res 221 (1984) pp 207-212
6
Vaynberg, E.L Kazak, 1.A., Klyuev, V.V., Kurozayev, V.P. and
Plotkina, G.Z. 'Nondestructive testing of the quality of industrial products by means of X-ray computerized tomography' Proc lOth World Conf on NDT, Moscow (1982) 2 pp 93-102
183
7
Vainberg, E.I. "Sensitivity of X-ray computerized tomography in inspection oi thin layers, joints, cracks, laminations, and coatings" Soy J NDT No 12 (19821 pp 969-973 Gilhoy, W.B. "X and gamma ray tomography in NDE applicalions" Nucl Instrum and Method.~ in Phys Re~ 221 (1984) pp 193-211/I
8
9
14 15 16 17
Reimers, P., Goebbels, J., Weise, H.P. and Wilding, K. "Some aspects of industrial non*destructive evaluation by X and gamma computed tomography' Nucl lnstrum and Methods in Phys Re~"221 (1984) pp 201-206 Reimers, P., Gilboy, W.B. and Goebbels, J. "Recent developments in the industrial application of computerized tomography with ionizing radiation" NDTInternafiona117 No4 (1984) pp 197-207
20
I1
Kitadate, K. and Tanimoto, Y. "Industrial application of X-ray computed tomography" A'DTJapan 1 No 3 (1983) pp 149-153
21
12
Barrett, H.H. and Swindeli, W. "Analog reconstruction methods lbr transaxial tomography" Proc 1EEE 65 (1977) pp 89-107
22
13
Andrews, J.R. 'Planigraphy: Part 1. Introduction and histors' Am J Roentgenol and Rad Ther 36 (Nov. 1936) pp 575-587: Andrews, J. and Stava, R.J. "Part [I. Mathematical analyses olthe methods, description of apparatus and experimental prooClbid 38 (July 1937) pp 145-151
23
10
18 19
24
Kieffer, J. "Analysis oflaminographic motions and their values' Radiology 33 (1939) pp 560-585 Smith, W.V.J. "A review of tomography and zonography" Radiolow 37 (1971) pp 5-15 Hasenkamp, F.A. "Radiographic laminography' Mawr l!ral 32 1[974) pp 169-180 Lindeganrd-Andersen, A. "Grazing incidence tomograph}" Lab Appl Phys 11£ Technical Uni~: Denmark. lecture at the I'echnion. Israel ([984) Craig, D.R. and Sirkis, M.P. "Simplified apparatus li)r producing transaxial tomograms" ,~lalcr Eval 36 No I1 (197~) pp 20-23 Bates, R.H.T. and Peters, T.M. 'Towards improvements in tomography' New Zeahmd J o/Sci 14 ( 1971) pp 883-896 Rulmont, F. and Amaury, H. Tomogruphic X sur fihns J Nationale.~ du ('off'end. Grenobh, (Jan. 1985) pp 15-19 Rosenfeld, A. and Kak, A.C. Digital Picture Processing Academic Press, NY (1976) Pratt, W.K. Digital Image Processing John Wiley. NY, USA (1978) Segak E., Notea, A. and Segak Y. 'Dimensional information through industrial computerized tomography" Mater Eval 40 (1982) pp 1268-1279 Notea, A. "Evaluating radiographic systems using the rcsol',ing power function" NDT lnternatwnal 16 No 5 (1983} pp 263-2711
Paper received 21 November 1984. Revised 7 May 1 9 8 5
184
NDT INTERNATIONAL . AUGUST 1 9 8 5
Keywords: radiographic testing, tomography, film response Tomography with X- and gamma-rays generates a material-density map (a tomogram) of a cross-sectional slice in the examined object. Variations expressed by the grey levels in the tomogram may be adjusted to yield the required contrast The technique is suitable for qualitative and quantitative inspection of structural details and defects, and its major advantage is the clear presentation of the interior of the examined object, unlike conventional radiography which is essentially a shadowgraph method. The potential of tomographic inspection for industrial products has been demonstratedl~-~°l to be large. It clearly adds a new dimension to conventional radiographic testing. In some cases the need to apply tomography should be evaluated against conventional radiography, in others it is possible to test only with tomography. Research and development efforts in the last decade were directed mainly towards computerized radiography which has revolutionized medical diagnosis. However, there are differences in the requirements of the medical unit and industryl"l. Medical computerized tomographs were developed to solve diagnostic problems in the human body where x-ray attenuation relates to bone, tissue (water) and air: industrial products to be inspected range in elemental composition from low to high atomic numbers and there is enormous variability in size and geometrical configuration. In addition, significant differences may be found in the characteristic features required from industrial tomographs: spatial resolution, slice thickness, contrast unsharpness, isoplanatics, repeatability. For industrial applications, customized tomographic systems are required as no single unit would be suitable for all industrial products. Computerized tomography has considerable limitations, however, imposed mainly by the relatively large pixel size.
In addition, its use in industry has been limited by high costs and the need for highly trained operators. The tomographic method discussed in this paper relates to image generation directly onto film1121. The image of a specific plane in the examined object is obtained by moving the radiation source relative to the object during exposure of the film. The film remains stationary relative to the object. A variety of similar approaches were considered during the first half of the century for medical diagnosticsl~3j41 and the method still arouses interestl'5,~61. Of special interest are the studiesl~7-201 of axial transverse tomography in which the inspected object and the film rotate synchronously. In the present study a non-computerized tomographic system based on film was constructed and the response obtained is discussed. The objects inspected demonstrate the characteristic features of the method.
Principles of the method Film-based industrial tomography (FIT) images a plane layer of chosen thickness through the inspected object The section visualized lies in the plane defined by the source and the surface of the film, ie the film is parallel to the plane layer through the object to be examined (Figure 1). As a result of this geometry the radiation impinging on the film is almost parallel to its surface. The radiation beam passes slantwise through the object, thus obtaining the practical thickness of the "plane layer'. The beam enters the inspected object after shaping by a slit aperture parallel to the plane layer being imaged. The beam thus produced is a fan 0.5 to 1 cm thick. In this way, blurring due to radiation scattering from planes other than the one examined is considerably reduced. During exposure the object and film or source and film are rotated synchronously. The film does not change its orientation
0308-9126/85/040179-06 $3.00 © 1985 Butterworth El-Co (Publishers) Ltd NDT INTERNATIONAL. VOL 18. NO 4. AUGUST 1985
179
Radiation
Collimator
from the source as a function of energyE, with maximum energy Emax: 0({,0) is the material density ( g c m 3) along chords passing through (X,Y), where O indicates the inclination of the chord and { is the position along its length: and la(E,{,O) is the mass attenuation coefficient along chords passing through (X,Y) (cm 2 g-*). When a monoenergetic g a m m a source is used, such as 60 keV from Am-241 or 662 keV from Cs-137, integration over the photon energy, E is unnecessary.
Object being examined
source Film holder
"o
x,r
z
~
7
x' Y
Synchronous rotation Fig. 1 Configurationof a film-based tomographicsystem. The fan-like beam definesthe plane-sliceof the object to be imaged
The density D of the film at the point (x:r) is proportional to l(x,)'). D(x,y) obtained represents the image of the examined plane-layer in the object In the'linear-range" of the fihn characteristic curve, D is describable by
(2)
D(x,y) ~ K + "/ log I ( x , y ) relative to the examined object thus every point or pixel
(x,y) of the image on the film corresponds to a point (X,Y) in the plane-slice through the examined object The prime requirements for the type of motion used are that: (1) the examined plane area remains in the radiation beam during the motion: (2) the radiation beam passes through each point (X,Y) from all directions, indicated by 0 <~ 0 ~< rr, during the motion. Only a rotation of 180° is necessary to complete the tomogram. A further rotation only yields the projections of 0-rr, therefore no additional information is provided. In practice, however, it is convenient to rotate the object many times within the exposure period. In the present study more than 100 rotations were perlbrmed for each tomogram. The process of generating the tomographic image is first explained for a needle object represented by a two dimensional 8 function (impulse function). The needle is located at (X, Y) on the object table. For a given sourceobject position the needle generates a projected line-like image on the film plane. This line has an inclination 0 to thex direction. Only one point(x,y) on the film plane~sees" the projection from the needle object for the whole 0 range. This results in a film density which is highest at (x,y), while other points of the film are considerably less dense. Thus, all received images from the different 0 are superimposed and a tomogram is obtained for 0 from 0 to rr. Every object may be expressed by a superposition of impulse functions, generating a corresponding tomographic image on the film. Mathematically the superposition of the projection from different exposure angles can be expressed as described below. During the exposure the chord length 1 defined by the beam passing through (X,I0 changes with 0, and is a function of the object shape, source-object geometry and object density. This function is given by lx,r (8). The intensity of the transmitted radiation reaching the point (xy) on the film during the exposure in which 8 varies from 0 to rr is given by l(x,y) =
Io(x,y) [
dE}dO
(1)
where I0 is the intensity of the incident source radiation reaching (x,y) with the object removed; s(E) is the normalized distribution function of the radiation emitted
180
The magnification of the image in the tomogram depends on the source-object and object-film distances. As in conventional radiography the size of the source contributes to unsharpness in the image and sets a limit on the magnification that can be used. High magnification, x 10 and more, may be obtained using a microfocus X-ray unit As an example, l(x,y) was determined for a cylindrical rod of radius R, homogeneous in composition and density'. The plane-slice to be inspected is a cut through the cylinder perpendicular to its axis of symmetry. The plane examined is circular in shape and due to the symmetry it is sufficient to examine the radiation impinging on points along a radial axis taken as (X,0), where (0,0) is the centre of the circle. The chord length 1(0) at points along the radial axis, inside (X/R < l) and outside (X/R ~> 1) the circle, is given by 2R
1-
sin20 X
Zx, o (o)
and0~<0~
R
=
X t> 1 and 0~<0 ~
X/> 1 ~-
0 ~ 0ma x
where 0max = arc sin (R/X). The chord length as a function of O is presented in Figure 2. 0max can be seen clearly tbr X/R > 1. All chords passing through (0,0) are of the same length l = 2R (and appear as a horizontal line in Figure 2). To determine L I0 was taken to be invariant within the fan beam spreading angle, which covers the greatest amplitude of the cylinder motion in the examined plane during the exposure. The value o f / a t the centre(0,0) according to Equation (1) becomes
11(0,0)/lo =
s(E)exp
[- 6(x'Y(°) p({O)p(E, {0) d(]
where K is a constant depending on the intensity, exposure time and film efficiency, and g is the film representative gradient.
(4)
rr e x p ( - 2p#R)
where tt is the mass attenuation factor for a monoenergetic photon source. If the source is not monoenergetic, it is possible to calculate an ellective constant attenuation coefficient through a non-linear stretching transformation based on the fact that the transmitted intensity decreases monotonically as the thickness increases. At other points along the radial axis where the chord length
NDT INTERNATIONAL
. AUGUST
1985
XIR
1.0 ~
0 0.33
A tomogram of a cylindrical iron rock 12.7 mm diameter, in a plane perpendicular to the symmetric axis, was measured with 662 keV gamma-rays from Cs-137 and is shown in Figure 4. The tomogram was obtained with film D7 and the source 2 m from the symmetric axis of the cylinder. The response at the edge and the cupping at the centre are as was foreseen from the calculations for 2/,pR=l.5. The data contain nmse, mainly film noise.
0.8-
-o.,
"
0.4
The generation of the tomogram through the accumulation of radiation on the film differs from the approach used in computerized tomography where the two-dimensional image is reconstructed from its one-dimensional integral projections.
0.2
0
function, however, which does not have an equivalent in conventional radiography. Image processing techniqueslZl'ZZl based on the expected response may be applied to the tomogram to enhance detail such as the edges of discontinuities.
o
30
60
90
Measured tomograms
0(0) Fig. 2 Chord length /{0) of radiation path through the points (X,0) in the examined plane through a cylindrical object of radius R
6l
The film-based industrial tomography system was operated with an Andrex 160 kV constant potential x-ray unit. The film was exposed with the X-ray beam parallel to the film plane. The film response for such exposure is shown in Figure 5 fora source-film distance of 3.5 m. The
2FpR 0
0.1
u
II
i. 2
C
I
i
,
0
,
I
0.5
~
i
i
,
,
,
l.O
I
1.5
=
,
I
I
2.0
xlR Fig. 3 Radiation intensity impinging on the film as 0 varies from 0 ° to 180 °, as a function of distance from the centre of a cylindrical homogeneous object with radius R. The determination follows Equation ( 1 )
is not constant, Equation (1) becomes
l(x,O)/Io
= 2
j
exp [-
laPlx,o (0)1 dO
(5)
0
The intensity proliles l(x,O)/lo for various 2p.pR values are shown in Figure 3. It is obvious that the film density, at every point (x,v) is influenced by the radiation transmission through every, point (X.Y) in the examined planeslice of the object. In other words, information from the whole of the examined plane-slice is accumulated at each point of the image. The curves of Figure 3 show that the edge atx = R is more pronounced for large values of 2,ttpR. Hence, the energy of the source and the film type may be chosen to yield an image of acceptable quality. The method has an inherent contribution to the point spread
NDT INTERNATIONAL. AUGUST 1985
H
Fig. 4 Tomogram through a cylindrical iron rod, 12.7 mm diameter, obtained with a Cs-137 source on film D7. The profile was taken along the diameter
181
----
magnification factor was 1.1, and all dimensions in the tomogram were found to increase by the same factor.
D4
D7
-
j
t"
j
.-y.'lOO
s
60 kV
.
,oo
C~
#
...<'.'.V/
~----"--TU-__-- 30 - - - . - - - - - 30
J )
I 10
i
I 20
I
A cylinder of lucite, 5 cm diameter, with seven rows each with five identical boreholes, was imaged with 140 kV. The hole diameters are 3.0, 2.5, 2.0, 1.75, 1.5, 1.25 and 1.0 ram. Figure 7 illustrates the capability of lhe method 1o distinguish holes down to 1 mm in diameter. The ability to distinguish components which differ in material density and atomic n u m b e r is demonstrated by the combination of a lucite pipe of 6.4 cm outer diameter,
I 30
Exposure (mA min) Fig. 5 Film response D as a function of exposure for different X-ray energies
iiliii....
Fig. 7 Tomogram of lucite cylinder, 5 cm diameter, with rows of boreholes 3.0. 2.5, 2 . 0 1.75. 1.5, 1.25. 1.0 mm diameter. Generated at 1 4 0 kV
Fig. 6 Tomogram of PVC cylinder, 5 cm diameter, with 3,4,5,6,7,8 m m diameter. Generated at 1 4 0 kV
boreholes
measurements were performed for films D4 and D7 simultaneously with each covering half of the t o m o g r a m area. There was no absorbing material between the source and film. The thickness of the slice which defines the plane is adjustable: in the present study 0.35 to 0.55 m m was used. This turns out to be an important parameter on which the quality of the image largely depends. For thinner slices finer detail in the vertical direction is distinguishable. The practical limitation on the slice thickness is the n u m b e r of photons per cm 2 impinging on the film, which reduces linearly with thickness. The thickness chosen for a particular tomographic inspection depends on the details that need to be distinguished, eg lower limit of diameter of voids or foreign particles. To investigate the resolution and the capability of FIT to distinguish betweeen light and heavy elements (low and high Z number) a n u m b e r of test objects were imaged. The first consisted of 5 cm diameter PVC cylinder containing holes with diameters of 3,4,5,6~7 and 8 mm. The t o m o g r a m taken perpendicular to the symmetric axis was generaled with 140 kV and film D4 (Figure 6). The source-object distance was 3 m, and object-film distance 0.4 in. The
182
t
Fig. 8 Tomogram of lucite pipe (6.4 outer diameter, 2 m m wall thickness), three iron wires (3 and 1 m m diameter) and a tygon pipe (1.1 cm diameter). Generated at 1 4 0 kV
NDT INTERNATIONAL.
AUGUST 1985,
The quality of the tomograms from FIT depends largely on the optimization of the parameters involved, such as photon energy, geometrical distances, type of motion and slice thickness. The energy considerations involved in FIT are quite different from those of conventional radiography. This becomes obvious when comparing the chord length distributions of the radiation passing through an object in both techniques, especially when the object is thin and very wide. As has been shown. FIT introduces new parameters: some are inherent in the technique, others are also present in conventional radiographic techniques but must be revaluated in the light of their effect o n FIT results. FIT has unique features which prove it to be an attractive tomographic technique for industrial NDT operators:
Fig. 9
Tomogram of lucite pipe (9.5 cm diameter)
(a)
All the components and most of the concepts used are familiar to the radiographic inspector: eg radiation units, films, screens, processing machines, intense light viewers, edge enhancement systems, film density, contrasL resolution, etc.
(b)
NDT inspectors with experience in radiography need a relatively short training period to master the FIT technique.
(c)
Marking and filing procedures for the tomograms are identical to those for conventional radiographs,
(d)
Interpretation oftomograms, as well as comparison with tomograms showing the history of the object, is convenient as both tomograms and radiographs may be viewed simultaneously on the light viewer.
(e)
The tomogram may be visualized by commercial edge enhancement or image processing systems developed for conventional radiography.
and DIN 62
standards: FE 1/7, 6 / 1 2 and 10/16. Generated at 140 kV
2 mm wall thickness, with adjacent to it on the periphery, an iron rod 3 mm in diameter, an iron wire of 1 mm diameter and a tygon pipe 11 mm diameter, 1.5 mm wall thickness, with inside it an iron rod of 3 mm diameter. The tomogram obtained is shown in Figure 8. Another object was composed of three iron wire DIN 62 standards which were attached to a lucite pipe of 9.5 cm outer diameter and 2 mm wall thickness. The wire diameters are: in the first DIN FE 1/7: 2.5, 2.0, 1.6, 1.25, 1.0 and0.8 mm; in the second DIN FE 6/12: 1.0, 0.8, 0.63, 0.5, 0.4, 0.32 and 0.25 mrn` and in the third DIN FE 10/16: 0.4, 0.32, 0.25, 0.2, 0.16, 0.125 and 0.1 mm. In the tomogram obtained (Figure 9) the wires are observed as circles. The 0.125 mm wire is still visible. The change in grey level observed from the wires of DIN FE 6/12 is due to the contrast reduction caused by the point spread function effect as explained previously123,241. Following these explanations the actual diameter for the small wires should be measured from the grey level and not from the observed circles. Tomograms were generated with densities of nearly 2, and inspected with an intense light viewer. The quality, of the tomograms obtained from the system is higher than that of the photographs reproduced here.
Author Professor Notea is in the Department of Nuclear Engineering, Technion - Israel Institute of Technology, 32000 Haifa, Israel.
References 1
Summary The major advantage of tomographic inspection is the clear presentation of details in the depth dimension of the examined object while in conventional radiography such details are projected on to the same location of the film. In addition, when optimized the method might detect details of adjacent parts or discontinuities which on account of small differences in density or composition cannot be revealed by conventional techniques. The relatively low cost and simplicity, of operation make film-based industrial tomography an inspection technique which is within reach of eveu industrial plant and it should be considered lor application at the various stages of production.
NDT INTERNATIONAL. AUGUST 1985
Ellinger, H., Morgan, I.L., Klinksiek, 1~, Hopkins, F. and Thompson, J.N. "Tomographicanalysis of structural materials', SPIE Imaging Applicationsfor A utomated Industrial Inspection and Assembly 182 (1979) pp 179-186
2 3 4
Kruger,ILP., Wecksung, W. and Morris, A. 'Industrial applications of computed tomography in Los Alamos Scientific Laboratory' Opt Eng 19 No 3 (1980) pp 273-282 Sato, T., Ikeda, O., Yamakoshi, Y. and Tsubouchi, M. 'X-ray tomography for microstructural objects', Appl Opt 20 No 22 (1981) pp 3880-3883 Hopkin, F.F., Morgan, I.L., Ellinger, H.D., Klinksiek, R.V., Meyer, G.A. and Thompson, J.N. "Industrial tomography
5
applications" IEEt£ Trans Nucl Sci NS--28 No 2 (1981) pp 1717-1720 Burstein, P., Bjorkholm, P.J., Chase, R.C. and Seguin, F.H. 'The largest and smallest X-ray computed tomography systems'Nucl lnstrum and Methods in Phys Res 221 (1984) pp 207-212
6
Vaynberg, E.L Kazak, 1.A., Klyuev, V.V., Kurozayev, V.P. and
Plotkina, G.Z. 'Nondestructive testing of the quality of industrial products by means of X-ray computerized tomography' Proc lOth World Conf on NDT, Moscow (1982) 2 pp 93-102
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7
Vainberg, E.I. "Sensitivity of X-ray computerized tomography in inspection oi thin layers, joints, cracks, laminations, and coatings" Soy J NDT No 12 (19821 pp 969-973 Gilhoy, W.B. "X and gamma ray tomography in NDE applicalions" Nucl Instrum and Method.~ in Phys Re~ 221 (1984) pp 193-211/I
8
9
14 15 16 17
Reimers, P., Goebbels, J., Weise, H.P. and Wilding, K. "Some aspects of industrial non*destructive evaluation by X and gamma computed tomography' Nucl lnstrum and Methods in Phys Re~"221 (1984) pp 201-206 Reimers, P., Gilboy, W.B. and Goebbels, J. "Recent developments in the industrial application of computerized tomography with ionizing radiation" NDTInternafiona117 No4 (1984) pp 197-207
20
I1
Kitadate, K. and Tanimoto, Y. "Industrial application of X-ray computed tomography" A'DTJapan 1 No 3 (1983) pp 149-153
21
12
Barrett, H.H. and Swindeli, W. "Analog reconstruction methods lbr transaxial tomography" Proc 1EEE 65 (1977) pp 89-107
22
13
Andrews, J.R. 'Planigraphy: Part 1. Introduction and histors' Am J Roentgenol and Rad Ther 36 (Nov. 1936) pp 575-587: Andrews, J. and Stava, R.J. "Part [I. Mathematical analyses olthe methods, description of apparatus and experimental prooClbid 38 (July 1937) pp 145-151
23
10
18 19
24
Kieffer, J. "Analysis oflaminographic motions and their values' Radiology 33 (1939) pp 560-585 Smith, W.V.J. "A review of tomography and zonography" Radiolow 37 (1971) pp 5-15 Hasenkamp, F.A. "Radiographic laminography' Mawr l!ral 32 1[974) pp 169-180 Lindeganrd-Andersen, A. "Grazing incidence tomograph}" Lab Appl Phys 11£ Technical Uni~: Denmark. lecture at the I'echnion. Israel ([984) Craig, D.R. and Sirkis, M.P. "Simplified apparatus li)r producing transaxial tomograms" ,~lalcr Eval 36 No I1 (197~) pp 20-23 Bates, R.H.T. and Peters, T.M. 'Towards improvements in tomography' New Zeahmd J o/Sci 14 ( 1971) pp 883-896 Rulmont, F. and Amaury, H. Tomogruphic X sur fihns J Nationale.~ du ('off'end. Grenobh, (Jan. 1985) pp 15-19 Rosenfeld, A. and Kak, A.C. Digital Picture Processing Academic Press, NY (1976) Pratt, W.K. Digital Image Processing John Wiley. NY, USA (1978) Segak E., Notea, A. and Segak Y. 'Dimensional information through industrial computerized tomography" Mater Eval 40 (1982) pp 1268-1279 Notea, A. "Evaluating radiographic systems using the rcsol',ing power function" NDT lnternatwnal 16 No 5 (1983} pp 263-2711
Paper received 21 November 1984. Revised 7 May 1 9 8 5
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