TABLE OF CONTENTS

Summary Basic physical principles Experimental set-up X or g - ray sources detector or detection system (2) translation and rotation system Results and discussion Acknowledgements References

Summary

X and g-ray computerized tomography (CT) is a method employing a beam of X or g-rays for "looking inside an object".
The basic principles of CT involve production, detection, digitization, and processing of X or g-rays, and computer image reconstruction and presentation.
X or g-rays crosse a movable specimen and are attenuated at different rates by different materials. The attenuated radiation is then collected by a detector or system of detectors and converted into numbers. The digital data are fed into a computing device for image reconstruction.
When a pencil-beam type is employed, the radiation is simply scanned along a line at a given direction or view. To achieve several different angles of perspective or projection data, the scanning is repeated to each given angular view by simply rotating the specimen, or both the X-ray tube and detector (or detectors).
When a fan-beam is employed, and an array of detectors (or a mosaics of detectors as for example in the case of the image intensifier), then at each angle or projection the complete serie of data is automatically obtained , and only rotations are required.
In the cases of pencil-beam or fan-beam, a two dimensional image is finally obtained, generally giving the distribution of physical density in the section of the object crossed by the radiation.
When finally a conical beam is employed, and a mosaics of detectors, then a three-dimensional image can be reconstructed, giving the density distribution in the whole object volume.
In this paper, the applications of CT in the field of imaging of works of art is described, both from the theoretical point of view of study of materials and from the practical point of view of optimizing the radiation versus the object to be visualized.

Basic physical principles

By considering a beam of monoenergetic and collimated X or g-rays of energy E₀ and intensity N₀ passing through a homogeneous absorber of thickness x, the emerging beam can be expressed as:

N = N0 exp [-m(r,Z,E0) x]

(1)

where N is the emerging attenuated intensity, m the linear attenuation coefficient, r the density and Z the atomic number of the absorber, respectively.
From Eq. (1), by directly counting N and N₀, and by measuring r, the linear attenuation coefficient of the absorber is determined
If the absorber is not homogeneous, then m(r,Z) is a space-variant function depending on the distribution of the various materials componing the object. By directing for example a monoenergetic X-or g-ray beam in the y direction, the output intensity N(x) can be written as:

N (x) = N0 exp [- ƒ m (x,y) dy ]

(2)

or:

ln(N0/N) = p = ƒm (x,y) dy

(3)

In digital form, Eq. (3) becomes:

p = åmi (x,y)

n = 1,2....N

(4)

Eq. (4) represents the summation of the attenuation coefficient of N-pixels along a given radiation path.


Fig 1: Physical principle of 1D-tomography

In CT the contrast is associated with the different attenuation coefficients of the material involved. Since each set of projection data represents the integral value of the attenuation coefficients along the path, the projection data taken at different views are the basis for tomographic image reconstruction. An example of a ray for the case of a single beam and N=4 pixels is illustrated in Figure 1 and a complete 2-D attenuation coefficient matrix is shown in Figure 2.

Fig 2: Physical principle of 2-D tomography. Each volume element (voxel) is characterized by its attenuation coefficient. A single measurement gives the integral attenuation of the involved pathway (at the right) and after a large number of measurements and a "reconstruction" process, the single mij values are obtained, generally corresponding to the physical density distribution.

When the beam is multienergetic, the exit beam may be expressed as:

Ni = ƒ N0i (E) exp (-åmij (E) x) dE

with 0<E<E max

(5)

Where x represents the width of a single voxel. Eq. (5) is usually simplified to the monoenergetic case and reduced to:

Ni = N0 exp[-(m11 x +m12 x +....m1n x)]

(6)

Following Eq. (1), the incident beam is attenuated by an object according to:

• incident radiation energy
• thickness of the object
• atomic number of the object components
• physical density of the object components.

Microscopically, two main effects contribute to the linear attenuation coefficient:

• photoelectric effect, prevailing at low X-ray energies, and which probability approximately depends on Z³ - Z⁴ .
• Compton effect, largely prevailing at high X-ray energies and which probability approximately depends on Z.

The values of the linear attenuation coefficient versus energy for various typical components of works of art, as for example wood, stone or marble, bronze or brass is shown in Table 1 (1). The best energy of X or g-rays for a good tomography is also shown. It corresponds to the approximate semiempirical condition:

m x» from 3 to 6

(7)

E(keV)	Air	Water	Wood	Concrete (*)	Copper (**)
5	0.052	45	15	390	1577
10	0.0067	5.1	1.8	60	1840
15	0.00021	1.65	0.6	18	631
20	0.001	0.8	0.31	8.4	288
30	0.00046	0.37	0.2	2.8	93
40	0.00033	0.27	0.15	1.4	41
50	0.00027	0.22	0.12	0.9	22
60	0.00023	0.205	0.11	0.67	13.5
80	0.00022	0.18	0.094	0.55	6.5
100	0.0002	0.17	0.085	0.5	3.9
150	0.00018	0.15	0.08	0.32	1.9
200	0.00016	0.135	0.06	0.295	1.34
300	0.00014	0.12	0.052	0.25	0.95
400	0.00012	0.105	0.045	0.22	0.8
500	0.00011	0.096	0.04	0.2	0.72
600	0.000106	0.09	0.038	0.19	0.66
800	0.000091	0.077	0.035	0.165	0.57
1000	0.000085	0.072	0.032	0.15	0.51
Table 1: Linear attenuation coefficient (in cm -1) of air, water, wood, concrete and Cu versus energy (density values of 0.0013, 1, 0.5, 2.2, 8.6 g/cm3 were respectively assumed).

(*) marble and stone have approximately the same m-values
(**) bronzes and brasses have approximately the same m-values

Experimental set-up

A CT-scanner is generally characterized by the following parts:
• an X or g-ray source
• one or more detectors, or a detection system
• a rotation and translation mechanics
• a PC for the reconstruction process
• a PC for presentation and analysis of the image.

X or g - ray sources
X or g-ray sources of various energy are generally needed, according to the sample, its size and composition.
When X-rays are employed (energy from 10 to 100 keV) , then radioactive X-ray sources may be used, or X-ray tubes, which maximum voltage and current are depending on the problem.
For big size objects,g rays must be employed for their higher energy ,and, therefore, higher penetration.
A list of useful X and g radioactive sources is shown in Table 2.

Radionuclide	Half-life	Energy of emitted radiation (in keV)
Cd-109	453 d	22
Am-241	433 y	59.5
Co-57	270 d	122 (85%) 136 (11%)
Ir-192	74 d	316 (83%) 302 (60%)468 (47%)
Cs-137	30 y	662
Co-60	5.3 y	1173 (100%) 1333 (100%)
Table 2:List of useful X and g - ray radioactive sources for tomography

Typical photon output of radioactive sources is 10⁶ - 10⁷ photons/s sr mCi.

X-ray tubes are emitting a continuum photon spectrum from few keV to a value (in keV) equal to the maximum high voltage of the tube anode (in kV); the maximum intensity is at about half the maximum high voltage. A typical X-ray tube for tomography is characterized by a W-anode, a high-voltage from 20 to 200 kV, and an anodic current of 1-100 mA. The photon output is therefore several orders of magnitude higher than that of a radioactive source.

detector or detection system (2)
The most simple detection system is a single, collimated X or g-rays detector. Typically a NaI(Tl) or BGO scintillators or a HpGe or CZT semiconductor detectors may be employed.
However the use of a single detector requires a large number of movements (both rotations and translations) and therefore the scanning time will be generally extremely high, of the order of many hours.
Much more convenient will be a multi-detector array, as employed in medical tomography (with thousands of detectors and related electronics) or multi-detector systems, such as a radiographic film (3) or an image intensifier.
The multi-detector array is generally very expensive and complicated, and is only justified by the very short time required for a medical image. For non-medical samples, an array of a reduced number of detectors (for example 50-100) or an image intensifier will be the best solution, in terms of image quality and costs. The Image Intensifier (I.I.) system is completed by a CCD video camera (if possible cooled) and an Optics coupling the I.I. and the CCD-camera.
Other systems under study are composed by a phosphor with a taper and a CCD camera, by mosaics of detectors and by a radiographic film.
A CT-scanner was constructed by us, composed of a Gilardoni 160 kV X-ray tube, a 6"x 6" Thompson Image Intensifier and a rotation system (Figure 3) (4).

Figure 3 - Photo of the CT-scanner constructed by Gilardoni and composed of a 160 kV X-ray tube, a 6"x 6" Image Intensifier and a cooled CCD-camera.

translation and rotation system
With a single detector, the sample may be translated and rotated. In the case of the systems of detectors, only the rotation table is required. Accuracy and precision of the movements should be selected according to the space resolution of the image, which (keeping constant the number of translations and rotations) is correlated to the size of the object.

Results and discussion

Various artifacts were analyzed, and materials of interest in the field of works of art.
• wood
  Attenuation coefficient of wood versus energy is shown in Table 1, for a wood of density r = 0.5 g/cm³. Samples with maximum size of 10 cm can be images with X-rays of about 20 keV, and sizes untill about 1 m can be analyzed with X-rays of 100 keV. A X-ray tomography of wood is able to detect in a very clear manner the annual rings (Figure 4)(5), and simple attenuation measurements can also give details of them (Figure 5) (6).

  Figure 4 - Image of a tree trunk, carried out at 45 kV, with the Gilardoni CT-scanner described in Figure 3. The annual rings are clearly visible.

  Figure 5 - Densitometric scan of the wood rings of a chestnut sample of 1 mm thickness with 5.6 keV photons.

• marble, stone or concrete
  Attenuation coefficients of marble, stone or concrete, are similar, and are shown in Table 1, for samples of density r = 2.2 g/cm³ . For samples of 1 and 10 cm maximum size, 25 keV and 75 keV X-rays are respectively needed, and samples of a maximum size up to 20 cm can be visualized by means of X-rays. For bigger sizes (untill about 30-40 cm), g-rays are needed. The image of a stone sample is shown in Figure 6.
  

  Figure 6 - Tomography of a stone sample. Internal structures are visible. It would be possible to study porosity and water absorption of porous stones by computed tomography.

• copper alloys (bronzes and brasses)
  The attenuation coefficient of copper is shown in Table 1. Attenuation coefficient of bronzes and brasses, mainly composed of copper, do not differ noticeably. It is much higher than that of wood or marble, due to the much higher density and mean atomic number of copper. Samples with a maximum size of 1-1.5 cm can be visualized by X-ray tomography. For bigger sizes, g-rays are required. For example, using a Cs¹³⁷ radioactive source, sizes up to about 10 cm can be tomographed. A typical example of a bronze statue is shown in Figure 7 (7).

  Figure 7 - Tomography of a hermes bronze statue (after Illerhaus ref. 6).The wall thickness can be measured exactly.

• terracotta and ceramics
  The attenuation coefficient of ceramics is not too different from that of concrete, and depends on the composition of the employed soil. The tomography of a vase is shown in Figure 8 (8).

  Figure 8 - Tomography of various sections of a terracotta vase (after ref. 7). From top left, a radiography of the vase showing the levels of the tomographs. Various defects and inhomogeneities are visible.

• papier mâché
  The attenuation coefficient of papier mâché is low, but difficult to define, because of the inhomogeneity of the sample. The huge statue of S. Giuseppe Patriarca (Lecce) was tomographed (9), which is considered the biggest statue on papier mâché all over the world. The image is shown in Figure 9. The internal structure of the statue is clearly visible, composed of various layers of papier mâché and a wood support
  

  Figure 9 - Tomography of a section of the huge statue of S. Giuseppe Patriarca (Lecce), after ref. 8.

Acknowledgements

This work was partially carried out with the support of the National Research Council, Piano Finalizzato Beni Culturali.

References

1. M.J. Berger, J.H. Hubbll: XCOM: photon cross sections on a personal computer; US Dept. Of Commerce, NBSIR 87-3597
2. R. Cesareo: X-Ray Physics; to be published in "Rivista del Nuovo Cimento" (2000)
3. A.Castellano, F. Quarta Colosso,A. Brunetti, R. Cesareo: to be published (2000)
4. CT 2000 scanner; Gilardoni, 23826 Mandello del Lario (LC) , Italy
5. R. Cesareo et al: X and g-ray tomography for non destructive material testing; submitted to IEEE Trans. on medical imaging; 1999
6. R. Cesareo et al.: Thermoelectrically cooled semiconductor detectors for portable energy-dispersive X-ray fluorescence equipments; SPIE Conf., S. Diego, CA, 31 july- 1 august 1997, Proc. Vol. 3115,274
7. B. Illerhaus:The principle of computerized tomography and its applications in the reconstruction of works of art; in "College on advanced techniques in archaeometry and conservation of works of art", Trieste 17-28 October 1994
8. A. Castellano and P. Quarta Colosso: private communication
9. A. Castellano, P. Quarta Colosso; Kermes XI, n. 32, may/june 1998