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Computed tomography with image intensifier: imaging and characterization of materials
Nuclear Instruments and Methods in Physics Research A 437 (1999) 141}151
Computed tomography with image intensi"er: imaging and characterization of materials D.V. Rao!,",#,*, R. Cesareo$, A. Brunetti$ !Department of Physics, Sir C.R.R. Autonomous College, Eluru-534007, W.G. Dt., A.P., India "The Abdus Salam International Centre for Theoretical physics, Trieste-34100, Italy #Istituto di Matematica e Fisica, Universita di Sassari, Via Vienna, 2-1-07100 Sassari, Italy $Istituto di Matematica e Fisica, Universita di Sassari, Via Vienna, 2-1-07100 Sassari, Italy Received 24 February 1998; received in revised form 15 April 1999
Abstract Computed tomographic images, nondestructive evaluation of materials of ceramics, electrical insulators, wood and other samples obtained, using a new tomographic system based on an image intensi"er replacing earlier system (Cesareo et al., Nucl. Instr. and Meth. A 356 (1995) 573). It consists of a charge coupled device camera and an acquisition board. The charge coupled device and the acquisition board allows image processing, "ltration and restoration. A reconstruction programme, written in PASCAL is able to give the reconstruction matrix of the linear attenuation coe$cients, and simulates the matrix and the related tomography. The #ux emitted by the tube is "ltered using appropriate "lters at chosen energy and reasonable monochromacy is achieved for all the images. The e!ect of collimators is also studied at various energies with "lters and the optimum value is used for better image quality. ( 1999 Elsevier Science B.V. All rights reserved. Keywords: Computed tomographic images; Nondestructive evaluation; X-ray
1. Introduction Computed tomography with image intensi"er is well suited for nondestructive evaluation of materials. In industry it is utilised in imaging and characterization of materials [1]. The risk of sample preparation-induced artifacts is minimized because no physical sectioning of the sample is required. The spatial resolution can be achieved using conventional X-ray tubes. A series of X-ray transmis-
* Corresponding author. Department of Physics, Sir C.R.R. Autonomous College, Eluru-534007, W.G. Dt., A.P., India.
sion measurements through various parts of the moving sample can be obtained by translating and rotating the sample and the data gives rise to twodimensional maps of linear attenuation coe$cient in planes through the sample. The linear attenuation coe$cient expresses the probability per unit length for a photon to undergo an X-ray interaction process. This requirement is of the same order of magnitude as the thickness of the sample being studied to obtain good contrast. The linear attenuation coe$cient depends on both the material composition as well as the density of the samples. After a mathematical process called reconstruction, the data constituting the tomograms can be presented
0168-9002/99/$ - see front matter ( 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 9 ) 0 0 5 8 0 - X
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in several ways. Medical CT scanners employ intense X-ray tubes in order to complete the measurements within run times of a few seconds, but the bremsstrahlung spectrum gives rise to beam hardening artifacts which degrade the quality of the image. Further in medical applications the range of X-ray energy is relatively small ((100 keV), the dose limitation is severe and the time interval is small. However, in nondestructive testing these restrictions may not prevail. Monoenergetic radiation can be produced using X-ray tube with appropriate "lters [2]. A new X-ray system is developed to produce considerable amount of monoenergetic radiation using "lters and suppressing the K and the associated #uorescent b X-rays. A new method is developed to estimate the degree of monochromaticity, e$ciency and geometrical e!ects of the measuring system, solid angle correction and some considerations which are necessary in experiments using a X-ray tube with "lters at a chosen energy. The need of these parameters are thoroughly discussed and reported elsewhere [3]. The amount of scattering and artifacts are reduced and the quality of the image is improved considerably. For the last few years our laboratory is active in developing new tomographic methods using conventional X-ray tubes [4]. These methods are extensively applied in the "elds of nondestructive testing, soil science, archaeometry and conservation of works of art. Continuous radiation from a tube source of X-rays and a tomographic image intensi"er has been used to obtain the images of various objects. However, an ideal monoenergetic radiation for this purpose would come from a synchrotron source, whose mean energy can be tuned across the absorption edge of the element. Recently, computed tomography has been applied to a piece of Fontaineblease sandstone in order to determine the geometrical structure of the pores using synchrotron radiation [5]. A new tomographic system based on image intensi"er is developed. Using this system several images of the objects, for example, ceramics, electrical insulators, wood and a perspex sample are obtained. Also the e!ect of the collimator on the image is studied using a perspex sample with and without water (iodine) solutions.
2. Experimental apparatus The experimental arrangement is shown in Fig. 1. It consists of an image intensi"er (Thomson TH 9412 FH), a charge coupled device camera (INLELCO) with S/N ratio of 48 dB (pixel size 10]8 mm) and 500]582 pixels, X-ray tube with 160 kV and 15 mA, a translation and rotation system and a pentium based computer. The charge coupled device provides better dynamics and these are determined from the acquisition board. The acquisition board has the same dynamics (256 levels or 48 dB) similar to the charge coupled device camera. With reduction of the time resolution the sensitivity of the charge coupled device camera is improved. The software written in PASCAL was implemented according to the characteristics of the acquisition board. The shading phenomenon due to di!erent intensities of the pixels in uniform illumination conditions, grey level distortion, linearity of the system and veiling glare is corrected using the software. In order to overcome the defects of the image, the distance between the sample and the image intensi"er is adjusted to very small and the distance between the X-ray source and the sample was large.
3. Monoenergetic radiation Beam hardening and artifacts are reduced by producing monoenergetic radiation using Ba target with Cs "lters in di!usion mode. The output of the secondary radiation is composed of K and K a b radiation and associated #uorescence spectra. Nearly monoenergetic radiation is obtained with the insertion of an absorber at the output. A well collimated Hp Ge detector (active diameter 10 mm: eV (FWHM) of 155 eV at 5.96 keV) has been used to measure the intensity. The absorber is having the energy of the photoelectric discontinuity between the energy values of K and K . Fig. 2 shows the a b spectra of Ba K radiation obtained using Cs at a various concentrations. The K and the associated b #uorescence spectrum is completely reduced. Fig. 3 shows the continuous spectra of the X-ray tube operated at 40 kV. Fig. 3a shows the variation of the attenuation coe$cient of silver "lters and
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Fig. 1. Schematic diagram of the experimental arrangement and tomographic device with image intensi"er.
Fig. 3b shows the spectra of the monoenergetic radiation obtained at operating voltage. The beam is heavily collimated using a cylindrical brass collimator with possibility of inserting required collimation at the brass-lead support, at the output of the X-ray tube. Collimators with cylindrical holes with 10 mm long and with internal holes varying from 2 to 0.2 mm are used at the output of the X-ray tube. The above analysis is employed for rapidly increasing the contrast. The scattered radiation has a negative in#uence on the contrast and it is reduced considerably by selecting the energy interval of the photons.
4. Corrections
Fig. 2. Monoenergetic radiation of Ba K radiation with water a solutions Cs at 1, 5 and 10% concentration.
To obtain better quality of the image the following corrections are implemented for veiling glare, nonlinearity of grey levels and shading. The required arrays of the factors for the correction of the shadow have been built by acquiring a number of sets of images and calculating for each set an image [6]. The average, pixel by pixel for each set, over
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Fig. 3. Bremsstrahlung spectrum emitted by an X-ray tube at an operating voltage of 40 kV. (a) Linear attenuation coe$cient of silver versus energy; (b) e!ect of Ag "lter on the X-ray spectrum.
D.V. Rao et al. / Nuclear Instruments and Methods in Physics Research A 437 (1999) 141}151
the number of images can be written as +nBk (E ) A (E )" i ij i ij i n
(1)
where Bk (E ) is the pixel (i, j) of the total sum of the ij i n images at the beam intensity E . i A number of images were obtained with better S/N ratio, since the signal increases with the number of images and the noise level drops with the square root of the image. The images were obtained with free "eld exposure changing the X-ray tube current, in order to have di!erent photon #ux with the same beam spectrum. This procedure is necessary to take into account the nonlinear response of the image intensi"er to the beam intensity. Finally, a set of correction arrays (C (E )) were obtained by ij i dividing each set of images by the average of the number of the images considered. A (E ) C " ij i . (2) ij A(E ) i The pixels with e$ciency greater than the mean value were multiplied by a factor lower and greater than one. This correction was performed using a virtual disk (RAM), the process is very fast and the time required for the construction of the arrays is about 20 s, virtually instantaneous and the correction factor is recalculated every time for a change in the experimental system. The calibration and nonlinearity grey level correction are performed using measurements of the beam intensity with free "eld exposure. A point spread function (PSF) is employed for veiling glare correction and through a linear regression, an expression for the point spread function is obtained. The real image l(x, y) can be considered as a deconvolution between the image l(x, y) and the point spread function. I@(x, y)"I(x, y) PSF
(3)
where l(x, y) and l@(x, y) are the deconvoluted and the detected image, respectively. In spatial frequency space (u, v) this expression can be written as FI@(u, v)"FI(u, v) PSF (u, v)
(4)
where FI@ is the Fourier transform of the detected image, calculated using a FFT algorithms. Fourier
145
transform of the deconvoluted image through a frequency-to-frequency division. Finally, performing the inverse of the FFT the deconvoluted image is obtained and during this correction the virtual disk is also used. With the above system we have made a series of measurements and tested the signal-to-noise ratio, MTF and PSF. The principle source of noise in the present system is the charge coupled device camera and it is about 2-bit peak to peak. The actual signal-to-noise ratio is 44 dB, 4 dB less than the S/N of the manufacturer. The modulation transfer function or MTF describes the frequency of the system (i.e., the MTF describes the contrast produced by an imaging system as a function of the spatial frequency of the object or input signal). The modulation transfer function (MTF) is measured using standard test pattern of thick Pb (0.05 mm) and the measured value is the spatial resolution of the system. The spread component of the impulsive response of image intensi"er phosphor is o PSF" e~r@k 2kr
(5)
where o is the veiling glare scatter fraction and k is a parameter pertaining to the range of the scattering process. Fig. 4 show the variation of the point spread function with distance using Eq. (5). It quanti"es the response function of the imaging system as regards the frequency of the object under investigation. The asymptotic nature of the function de"nes a cut o! frequency that estimates the minimum detectable limits in detail.
5. Experimental and theoretical methods In order to make a quantitative comparison between the various methods of imaging a standard perspex phantom (4 cm side) has been constructed with 4]4 cylindrical holes of 1 cm depth orthogonal to the surface that can be "lled by liquids, mixtures, metals or left void. The energy of the photon beam (monoenergetic or quasi monoenergetic) is selected according to the thickness, mass attenuation coe$cient, density of the matrix and of the material introduced in the
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Fig. 4. Variation of the veiling glare point spread function with distance.
holes, in such a manner that (k/o)oX+2
(6)
where (k/o) is the mass attenuation coe$cient, o the physical density of the ith element of the sample, and X the thickness of the sample. The diameter of the cylindrical hole is *x"(x/10)"1/[5(k/o)o]. For the phantom it turns out to be x"40 mm, *x"4 mm, E "24 keV, if the holes are "lled with 0 water (k/o of water at 24 keV is 0.5 g/cm2). Therefore, monoenergetic rays in the energy region 25}35 keV will be suited for imaging the present perspex test sample. However, a central voxel in the phantom is assumed as reference voxel and can be "lled or left void in a di!erent manner from other holes and from the matrix. Indicating the matrix with the index &0' and the material in the reference voxel with index &1' the following expressions may be deduced. The number of photons transmitted through the matrix is given by N "N e~2 (7) 1 0 when the reference voxel of area (*x)2 is "lled instead of the matrix material with a material indicated by the index &1', then N "N e~2e~*xc1 x (k/o ) o !(k/o )oy 2 0 1 1 0 0
(8)
where c , (k/o) and o are the concentration, mass 1 0 attenuation coe$cient and density of the material. The number of photons transmitted through the matrix and the matrix plus a voxel "lled with the material &1' is given by *N"N e~2M1!e~*xc1[(k/o ) o !(k/o )o ]N (9) 0 1 1 0 0 and when *x c @1 1 (10) *N"N e~2*x c [k !k ] 0 1 1 0 and the minimum detection limit at the level of three standard deviations is given by p"(3JN /*N)c "3e/JN (1/*x (k !k )). (11) 1 0 1 0 1 Eq. (11) can also be written as p"15e/JN (k /k !k ) 0 0 0 1
(12)
p"40.88n/JN (k !k ) (13) 0 1 0 where n is the number of linear holes. If the matrix is water or a material with the same attenuation coe$cient, then Eq. (10) turns out to be *N"N e~2 *xc [k !0.5] 0 1 1 and Eq. (12)
(14)
p"(15e/JN )[0.5/(k !0.5)]. 0 1
(15)
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6. Results and discussion The images obtained with the present system at an optimum value and variation of intensity with pixel number are displayed on Figs. 5}20. Fig. 5 show the variation of intensity with pixel number, for the ceramic cylinder with a central hole for injecting the iodine. The images at optimum value are shown in Figs. 6}8. Figs. 9 and 10 show the variation of intensity with pixel number, for the big (PVC) electrical insulator and the small (ceramic) electrical insulator. The insets in the above "gures
Fig. 7. Images of the ceramic cylinder at 40 kV and 4.5.
Fig. 5. Projections versus counts for the ceramic cylinder, the inset show the shape of the object.
Fig. 8. Images of the ceramic cylinder at 40 kV and 4 mA.
Fig. 6. Images of the ceramic cylinder at 40 kV and 5 mA.
show the structure of the samples used in the present study. The images of small and big electrical insulators are displayed in Figs. 11 and 12. The variation of intensity with pixel number, for the ceramic cup and wood sample, with the needle "xed in the middle are shown in Figs. 13 and 14. Figs. 15
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Fig. 9. Projections versus counts of the big (PVC) electrical insulator, the inset show the shape of the object.
Fig. 12. Image of small (ceramic) electrical insulator at 40 kV and 5.5 mA.
Fig. 10. Projections versus counts of the small (ceramic) electrical insulator, the inset show the shape of the object.
Fig. 13. Projections versus counts of the ceramic cup with needle in the middle, the inset show the shape of the object.
Fig. 11. Image of big (PVC) electrical insulator at 35 kV and 4 mA.
Fig. 14. Projections versus counts of the wood sample with needle in the middle, the inset show the shape of the object.
D.V. Rao et al. / Nuclear Instruments and Methods in Physics Research A 437 (1999) 141}151
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Fig. 17. Image of the perspex sample few holes "lled with water at 30 kV and 4 mA. Fig. 15. Image of the ceramic cup with needle in the middle at 35 kV and 4.5 mA.
Fig. 18. Image of the above sample with one empty hole with 2 mm collimator.
Fig. 16. Image of the wood sample with needle in the middle at 35 kV and 3.5 mA.
and 16 are the images for the ceramic cup and wood sample with needle in the middle. In both cases the needle of the image occupied a small area. The images are obtained by line selection at various positions of the object. The objects are imaged with
varying line selection, for example, at the top of the object, middle, bottom and the two extreme ends. The ceramic cylinder is injected with iodine and the images are obtained at various concentrations and the distribution at the top, middle and bottom of the cylinder. The distribution of the iodine is very slow and it is concentrated mainly at the top of the cylinder. The image of the small electrical insulator is considerably good at various line selection
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D.V. Rao et al. / Nuclear Instruments and Methods in Physics Research A 437 (1999) 141}151
of wood the image of the needle is observed at the center of the image. Considerable work is in progress on various objects in order to obtain good images. Fig. 17 shows the image of the perspex sample studied with a collimator and a few holes "lled with water. Fig. 18 is the image of the perspex sample with one empty hole and rest were "lled with water and the size of the collimator hole is 2 mm. Fig. 19 is the image obtained with 2.5 mm collimator and Fig. 20 is the image obtained with 3 mm collimator. As distinguished from Fig. 19, the image in Fig. 18 is clearly visible but with some scattering. The e!ect of collimator is easily observed on the images. The above analysis is applied to all the objects and the images are considerably good. Fig. 19. Image of the above with 2.5 mm collimator.
7. Conclusions
Fig. 20. Image of the above with 5 mm collimator.
positions. However, in the case of a big (PVC) electrical insulator the projections are obtained in the middle of the object to know the hollow nature of the object and the distribution of the solid material around the hollow. At the extreme ends the projections are inconsistent and the image is unclear. The image of the needle in the middle of the ceramic cup occupy a small area in the form of a circle at the center of the image. Also in the case
It is interesting to note that monoenergetic X-ray source may o!er better imaging performance than polyenergetic sources. Polyenergetic X-ray spectrum is composed of photons which vary widely in energy. It is not possible to precisely match the X-ray energy to the detectors ideal absorption energy. The present observations suggest that a monoenergetic or near monoenergetic X-ray source might provide new information at optimum value. The acquisition time of the image is considerably less with image intensi"er and the e!ect of artifacts are reduced. The potential use of monoenergetic source allows substantially more #exibility in technique optimization due to their narrow energy distributions. However, polyenergetic X-ray beam will lead to errors in the reconstructed values of attenuation coe$cients. In view of this monoenergetic X-ray beams have a de"nite advantage over a polyenergetic X-rays for the imaging. The present study is focused mainly on strongly attenuating objects at an optimum operating voltage. At optimum value and with the aid of the tomographic image the size and location of the void could be ascertained. With this system we have been able to reduce the beam hardening artifacts considerably and with increased monochromacy the quality of the images are improved. It
D.V. Rao et al. / Nuclear Instruments and Methods in Physics Research A 437 (1999) 141}151
o!ers a new nondestructive method using ionization radiation techniques. Acknowledgements We are very grateful to Prof. Dr. G. Furlan for providing the "nancial assistance to carryout the experimental work. One of us (DVR) undertook this work with the support from the The Abdus Salam ICTP programme for training and research in Italian laboratories, Trieste, Italy and University Grants Commission, New Delhi, India.
151
References [1] K.W. Jones, in: R.E. Van Grieken, A.A. Markowicz (Eds.), Handbook of X-ray Spectrometry, Methods and Techniques, Marcel Dekker, New York, 1992, p. 443 (chapter 8). [2] R. Cesareo, A.L. Hansob, G.E. Gigante, L.J. Pedraza, S.Q.G. Mahtaboally, Phys Rep. 213 (1992) 117. [3] D.V. Rao, R. Cesareo, G.E. Gigante, Phys. Scripta 55 (1997) 265. [4] R. Cesareo, D.V. Rao, C. Appolini, A. Brunetti, Nucl. Instr. and Meth. A 356 (1995) 573. [5] P. Spanne, J.F. Thovert, C.J. Jacquin, W.B. Lindquist, K.W. Jones, P.M. Adler, Phys. Rev. Lett. 73 (1994) 2001. [6] J.M. Boone, J.A. Seibert, W.A. Barrett, E.A. Blood, Med. Phys. 18 (2) (1991) 236.
Computed tomography with image intensi"er: imaging and characterization of materials D.V. Rao!,",#,*, R. Cesareo$, A. Brunetti$ !Department of Physics, Sir C.R.R. Autonomous College, Eluru-534007, W.G. Dt., A.P., India "The Abdus Salam International Centre for Theoretical physics, Trieste-34100, Italy #Istituto di Matematica e Fisica, Universita di Sassari, Via Vienna, 2-1-07100 Sassari, Italy $Istituto di Matematica e Fisica, Universita di Sassari, Via Vienna, 2-1-07100 Sassari, Italy Received 24 February 1998; received in revised form 15 April 1999
Abstract Computed tomographic images, nondestructive evaluation of materials of ceramics, electrical insulators, wood and other samples obtained, using a new tomographic system based on an image intensi"er replacing earlier system (Cesareo et al., Nucl. Instr. and Meth. A 356 (1995) 573). It consists of a charge coupled device camera and an acquisition board. The charge coupled device and the acquisition board allows image processing, "ltration and restoration. A reconstruction programme, written in PASCAL is able to give the reconstruction matrix of the linear attenuation coe$cients, and simulates the matrix and the related tomography. The #ux emitted by the tube is "ltered using appropriate "lters at chosen energy and reasonable monochromacy is achieved for all the images. The e!ect of collimators is also studied at various energies with "lters and the optimum value is used for better image quality. ( 1999 Elsevier Science B.V. All rights reserved. Keywords: Computed tomographic images; Nondestructive evaluation; X-ray
1. Introduction Computed tomography with image intensi"er is well suited for nondestructive evaluation of materials. In industry it is utilised in imaging and characterization of materials [1]. The risk of sample preparation-induced artifacts is minimized because no physical sectioning of the sample is required. The spatial resolution can be achieved using conventional X-ray tubes. A series of X-ray transmis-
* Corresponding author. Department of Physics, Sir C.R.R. Autonomous College, Eluru-534007, W.G. Dt., A.P., India.
sion measurements through various parts of the moving sample can be obtained by translating and rotating the sample and the data gives rise to twodimensional maps of linear attenuation coe$cient in planes through the sample. The linear attenuation coe$cient expresses the probability per unit length for a photon to undergo an X-ray interaction process. This requirement is of the same order of magnitude as the thickness of the sample being studied to obtain good contrast. The linear attenuation coe$cient depends on both the material composition as well as the density of the samples. After a mathematical process called reconstruction, the data constituting the tomograms can be presented
0168-9002/99/$ - see front matter ( 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 9 ) 0 0 5 8 0 - X
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D.V. Rao et al. / Nuclear Instruments and Methods in Physics Research A 437 (1999) 141}151
in several ways. Medical CT scanners employ intense X-ray tubes in order to complete the measurements within run times of a few seconds, but the bremsstrahlung spectrum gives rise to beam hardening artifacts which degrade the quality of the image. Further in medical applications the range of X-ray energy is relatively small ((100 keV), the dose limitation is severe and the time interval is small. However, in nondestructive testing these restrictions may not prevail. Monoenergetic radiation can be produced using X-ray tube with appropriate "lters [2]. A new X-ray system is developed to produce considerable amount of monoenergetic radiation using "lters and suppressing the K and the associated #uorescent b X-rays. A new method is developed to estimate the degree of monochromaticity, e$ciency and geometrical e!ects of the measuring system, solid angle correction and some considerations which are necessary in experiments using a X-ray tube with "lters at a chosen energy. The need of these parameters are thoroughly discussed and reported elsewhere [3]. The amount of scattering and artifacts are reduced and the quality of the image is improved considerably. For the last few years our laboratory is active in developing new tomographic methods using conventional X-ray tubes [4]. These methods are extensively applied in the "elds of nondestructive testing, soil science, archaeometry and conservation of works of art. Continuous radiation from a tube source of X-rays and a tomographic image intensi"er has been used to obtain the images of various objects. However, an ideal monoenergetic radiation for this purpose would come from a synchrotron source, whose mean energy can be tuned across the absorption edge of the element. Recently, computed tomography has been applied to a piece of Fontaineblease sandstone in order to determine the geometrical structure of the pores using synchrotron radiation [5]. A new tomographic system based on image intensi"er is developed. Using this system several images of the objects, for example, ceramics, electrical insulators, wood and a perspex sample are obtained. Also the e!ect of the collimator on the image is studied using a perspex sample with and without water (iodine) solutions.
2. Experimental apparatus The experimental arrangement is shown in Fig. 1. It consists of an image intensi"er (Thomson TH 9412 FH), a charge coupled device camera (INLELCO) with S/N ratio of 48 dB (pixel size 10]8 mm) and 500]582 pixels, X-ray tube with 160 kV and 15 mA, a translation and rotation system and a pentium based computer. The charge coupled device provides better dynamics and these are determined from the acquisition board. The acquisition board has the same dynamics (256 levels or 48 dB) similar to the charge coupled device camera. With reduction of the time resolution the sensitivity of the charge coupled device camera is improved. The software written in PASCAL was implemented according to the characteristics of the acquisition board. The shading phenomenon due to di!erent intensities of the pixels in uniform illumination conditions, grey level distortion, linearity of the system and veiling glare is corrected using the software. In order to overcome the defects of the image, the distance between the sample and the image intensi"er is adjusted to very small and the distance between the X-ray source and the sample was large.
3. Monoenergetic radiation Beam hardening and artifacts are reduced by producing monoenergetic radiation using Ba target with Cs "lters in di!usion mode. The output of the secondary radiation is composed of K and K a b radiation and associated #uorescence spectra. Nearly monoenergetic radiation is obtained with the insertion of an absorber at the output. A well collimated Hp Ge detector (active diameter 10 mm: eV (FWHM) of 155 eV at 5.96 keV) has been used to measure the intensity. The absorber is having the energy of the photoelectric discontinuity between the energy values of K and K . Fig. 2 shows the a b spectra of Ba K radiation obtained using Cs at a various concentrations. The K and the associated b #uorescence spectrum is completely reduced. Fig. 3 shows the continuous spectra of the X-ray tube operated at 40 kV. Fig. 3a shows the variation of the attenuation coe$cient of silver "lters and
D.V. Rao et al. / Nuclear Instruments and Methods in Physics Research A 437 (1999) 141}151
143
Fig. 1. Schematic diagram of the experimental arrangement and tomographic device with image intensi"er.
Fig. 3b shows the spectra of the monoenergetic radiation obtained at operating voltage. The beam is heavily collimated using a cylindrical brass collimator with possibility of inserting required collimation at the brass-lead support, at the output of the X-ray tube. Collimators with cylindrical holes with 10 mm long and with internal holes varying from 2 to 0.2 mm are used at the output of the X-ray tube. The above analysis is employed for rapidly increasing the contrast. The scattered radiation has a negative in#uence on the contrast and it is reduced considerably by selecting the energy interval of the photons.
4. Corrections
Fig. 2. Monoenergetic radiation of Ba K radiation with water a solutions Cs at 1, 5 and 10% concentration.
To obtain better quality of the image the following corrections are implemented for veiling glare, nonlinearity of grey levels and shading. The required arrays of the factors for the correction of the shadow have been built by acquiring a number of sets of images and calculating for each set an image [6]. The average, pixel by pixel for each set, over
144
D.V. Rao et al. / Nuclear Instruments and Methods in Physics Research A 437 (1999) 141}151
Fig. 3. Bremsstrahlung spectrum emitted by an X-ray tube at an operating voltage of 40 kV. (a) Linear attenuation coe$cient of silver versus energy; (b) e!ect of Ag "lter on the X-ray spectrum.
D.V. Rao et al. / Nuclear Instruments and Methods in Physics Research A 437 (1999) 141}151
the number of images can be written as +nBk (E ) A (E )" i ij i ij i n
(1)
where Bk (E ) is the pixel (i, j) of the total sum of the ij i n images at the beam intensity E . i A number of images were obtained with better S/N ratio, since the signal increases with the number of images and the noise level drops with the square root of the image. The images were obtained with free "eld exposure changing the X-ray tube current, in order to have di!erent photon #ux with the same beam spectrum. This procedure is necessary to take into account the nonlinear response of the image intensi"er to the beam intensity. Finally, a set of correction arrays (C (E )) were obtained by ij i dividing each set of images by the average of the number of the images considered. A (E ) C " ij i . (2) ij A(E ) i The pixels with e$ciency greater than the mean value were multiplied by a factor lower and greater than one. This correction was performed using a virtual disk (RAM), the process is very fast and the time required for the construction of the arrays is about 20 s, virtually instantaneous and the correction factor is recalculated every time for a change in the experimental system. The calibration and nonlinearity grey level correction are performed using measurements of the beam intensity with free "eld exposure. A point spread function (PSF) is employed for veiling glare correction and through a linear regression, an expression for the point spread function is obtained. The real image l(x, y) can be considered as a deconvolution between the image l(x, y) and the point spread function. I@(x, y)"I(x, y) PSF
(3)
where l(x, y) and l@(x, y) are the deconvoluted and the detected image, respectively. In spatial frequency space (u, v) this expression can be written as FI@(u, v)"FI(u, v) PSF (u, v)
(4)
where FI@ is the Fourier transform of the detected image, calculated using a FFT algorithms. Fourier
145
transform of the deconvoluted image through a frequency-to-frequency division. Finally, performing the inverse of the FFT the deconvoluted image is obtained and during this correction the virtual disk is also used. With the above system we have made a series of measurements and tested the signal-to-noise ratio, MTF and PSF. The principle source of noise in the present system is the charge coupled device camera and it is about 2-bit peak to peak. The actual signal-to-noise ratio is 44 dB, 4 dB less than the S/N of the manufacturer. The modulation transfer function or MTF describes the frequency of the system (i.e., the MTF describes the contrast produced by an imaging system as a function of the spatial frequency of the object or input signal). The modulation transfer function (MTF) is measured using standard test pattern of thick Pb (0.05 mm) and the measured value is the spatial resolution of the system. The spread component of the impulsive response of image intensi"er phosphor is o PSF" e~r@k 2kr
(5)
where o is the veiling glare scatter fraction and k is a parameter pertaining to the range of the scattering process. Fig. 4 show the variation of the point spread function with distance using Eq. (5). It quanti"es the response function of the imaging system as regards the frequency of the object under investigation. The asymptotic nature of the function de"nes a cut o! frequency that estimates the minimum detectable limits in detail.
5. Experimental and theoretical methods In order to make a quantitative comparison between the various methods of imaging a standard perspex phantom (4 cm side) has been constructed with 4]4 cylindrical holes of 1 cm depth orthogonal to the surface that can be "lled by liquids, mixtures, metals or left void. The energy of the photon beam (monoenergetic or quasi monoenergetic) is selected according to the thickness, mass attenuation coe$cient, density of the matrix and of the material introduced in the
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Fig. 4. Variation of the veiling glare point spread function with distance.
holes, in such a manner that (k/o)oX+2
(6)
where (k/o) is the mass attenuation coe$cient, o the physical density of the ith element of the sample, and X the thickness of the sample. The diameter of the cylindrical hole is *x"(x/10)"1/[5(k/o)o]. For the phantom it turns out to be x"40 mm, *x"4 mm, E "24 keV, if the holes are "lled with 0 water (k/o of water at 24 keV is 0.5 g/cm2). Therefore, monoenergetic rays in the energy region 25}35 keV will be suited for imaging the present perspex test sample. However, a central voxel in the phantom is assumed as reference voxel and can be "lled or left void in a di!erent manner from other holes and from the matrix. Indicating the matrix with the index &0' and the material in the reference voxel with index &1' the following expressions may be deduced. The number of photons transmitted through the matrix is given by N "N e~2 (7) 1 0 when the reference voxel of area (*x)2 is "lled instead of the matrix material with a material indicated by the index &1', then N "N e~2e~*xc1 x (k/o ) o !(k/o )oy 2 0 1 1 0 0
(8)
where c , (k/o) and o are the concentration, mass 1 0 attenuation coe$cient and density of the material. The number of photons transmitted through the matrix and the matrix plus a voxel "lled with the material &1' is given by *N"N e~2M1!e~*xc1[(k/o ) o !(k/o )o ]N (9) 0 1 1 0 0 and when *x c @1 1 (10) *N"N e~2*x c [k !k ] 0 1 1 0 and the minimum detection limit at the level of three standard deviations is given by p"(3JN /*N)c "3e/JN (1/*x (k !k )). (11) 1 0 1 0 1 Eq. (11) can also be written as p"15e/JN (k /k !k ) 0 0 0 1
(12)
p"40.88n/JN (k !k ) (13) 0 1 0 where n is the number of linear holes. If the matrix is water or a material with the same attenuation coe$cient, then Eq. (10) turns out to be *N"N e~2 *xc [k !0.5] 0 1 1 and Eq. (12)
(14)
p"(15e/JN )[0.5/(k !0.5)]. 0 1
(15)
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6. Results and discussion The images obtained with the present system at an optimum value and variation of intensity with pixel number are displayed on Figs. 5}20. Fig. 5 show the variation of intensity with pixel number, for the ceramic cylinder with a central hole for injecting the iodine. The images at optimum value are shown in Figs. 6}8. Figs. 9 and 10 show the variation of intensity with pixel number, for the big (PVC) electrical insulator and the small (ceramic) electrical insulator. The insets in the above "gures
Fig. 7. Images of the ceramic cylinder at 40 kV and 4.5.
Fig. 5. Projections versus counts for the ceramic cylinder, the inset show the shape of the object.
Fig. 8. Images of the ceramic cylinder at 40 kV and 4 mA.
Fig. 6. Images of the ceramic cylinder at 40 kV and 5 mA.
show the structure of the samples used in the present study. The images of small and big electrical insulators are displayed in Figs. 11 and 12. The variation of intensity with pixel number, for the ceramic cup and wood sample, with the needle "xed in the middle are shown in Figs. 13 and 14. Figs. 15
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Fig. 9. Projections versus counts of the big (PVC) electrical insulator, the inset show the shape of the object.
Fig. 12. Image of small (ceramic) electrical insulator at 40 kV and 5.5 mA.
Fig. 10. Projections versus counts of the small (ceramic) electrical insulator, the inset show the shape of the object.
Fig. 13. Projections versus counts of the ceramic cup with needle in the middle, the inset show the shape of the object.
Fig. 11. Image of big (PVC) electrical insulator at 35 kV and 4 mA.
Fig. 14. Projections versus counts of the wood sample with needle in the middle, the inset show the shape of the object.
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Fig. 17. Image of the perspex sample few holes "lled with water at 30 kV and 4 mA. Fig. 15. Image of the ceramic cup with needle in the middle at 35 kV and 4.5 mA.
Fig. 18. Image of the above sample with one empty hole with 2 mm collimator.
Fig. 16. Image of the wood sample with needle in the middle at 35 kV and 3.5 mA.
and 16 are the images for the ceramic cup and wood sample with needle in the middle. In both cases the needle of the image occupied a small area. The images are obtained by line selection at various positions of the object. The objects are imaged with
varying line selection, for example, at the top of the object, middle, bottom and the two extreme ends. The ceramic cylinder is injected with iodine and the images are obtained at various concentrations and the distribution at the top, middle and bottom of the cylinder. The distribution of the iodine is very slow and it is concentrated mainly at the top of the cylinder. The image of the small electrical insulator is considerably good at various line selection
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of wood the image of the needle is observed at the center of the image. Considerable work is in progress on various objects in order to obtain good images. Fig. 17 shows the image of the perspex sample studied with a collimator and a few holes "lled with water. Fig. 18 is the image of the perspex sample with one empty hole and rest were "lled with water and the size of the collimator hole is 2 mm. Fig. 19 is the image obtained with 2.5 mm collimator and Fig. 20 is the image obtained with 3 mm collimator. As distinguished from Fig. 19, the image in Fig. 18 is clearly visible but with some scattering. The e!ect of collimator is easily observed on the images. The above analysis is applied to all the objects and the images are considerably good. Fig. 19. Image of the above with 2.5 mm collimator.
7. Conclusions
Fig. 20. Image of the above with 5 mm collimator.
positions. However, in the case of a big (PVC) electrical insulator the projections are obtained in the middle of the object to know the hollow nature of the object and the distribution of the solid material around the hollow. At the extreme ends the projections are inconsistent and the image is unclear. The image of the needle in the middle of the ceramic cup occupy a small area in the form of a circle at the center of the image. Also in the case
It is interesting to note that monoenergetic X-ray source may o!er better imaging performance than polyenergetic sources. Polyenergetic X-ray spectrum is composed of photons which vary widely in energy. It is not possible to precisely match the X-ray energy to the detectors ideal absorption energy. The present observations suggest that a monoenergetic or near monoenergetic X-ray source might provide new information at optimum value. The acquisition time of the image is considerably less with image intensi"er and the e!ect of artifacts are reduced. The potential use of monoenergetic source allows substantially more #exibility in technique optimization due to their narrow energy distributions. However, polyenergetic X-ray beam will lead to errors in the reconstructed values of attenuation coe$cients. In view of this monoenergetic X-ray beams have a de"nite advantage over a polyenergetic X-rays for the imaging. The present study is focused mainly on strongly attenuating objects at an optimum operating voltage. At optimum value and with the aid of the tomographic image the size and location of the void could be ascertained. With this system we have been able to reduce the beam hardening artifacts considerably and with increased monochromacy the quality of the images are improved. It
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o!ers a new nondestructive method using ionization radiation techniques. Acknowledgements We are very grateful to Prof. Dr. G. Furlan for providing the "nancial assistance to carryout the experimental work. One of us (DVR) undertook this work with the support from the The Abdus Salam ICTP programme for training and research in Italian laboratories, Trieste, Italy and University Grants Commission, New Delhi, India.
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