Bundesanstalt für Materialforschung und -prüfung

International Symposium (NDT-CE 2003)

Non-Destructive Testing in Civil Engineering 2003
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Multi-energy radiography for non-destructive testing of materials and structures for civil engineering

Sergey Naydenov, Institute of Single Crystals of UAS, 60 Lenin avenue
Kharkov, 61001, Ukraine, e-mail: naydenov@isc.kharkov.com
Vladimir Ryzhikov, Institute of Single Crystals of UAS, Kharkov, Ukraine


Development of the technological base of modern non-destructive testing require new methods allowing determination of specified properties of materials and structures under study. A traditional direction of works is determination of internal spatial structure of the materials and other constructions. Restoration of this geometrical information is of qualitative character, though provides for determination of technical parameters affecting physical properties of the system. Reconstruction of the chemical composition, density and atomic structure (effective atomic number) is an inverse problem of direct quantitative determination of properties starting from data obtained by means of non-destructive testing. In the present work, we propose the use of multi-energy radiography for reconstruction of the substantial structure of materials. In framework of simple theoretical model it is shown that, using multi-channel absorption of X-rays, important substantial characteristics of materials and multi-compound structures can be readily reconstructed. The results obtained show high efficiency of 2-energy radiography for non-destructive testing in civil engineering.

1. Introduction

Development of modern construction technologies and expansion of building activities in the civil sphere impose higher requirements to quality and reliability of building constructions. Among the most efficient methods of control, one should note various radiographic methods [1-3]. Their important advantage is high penetrating ability of X-ray or gamma-radiation from radioactive sources or accelerators. Traditionally, technical radiography is used for inspection and image reconstruction of the internal structure of objects and materials in a broad range of thickness (from several millimeters to tens of centimeters in steel equivalent. However, as a rule, it is limited to reconstruction of only the spatial structure, i.e., determination of the relative location of elements and details in the tested objects, as well as of various defects, cavities, non-uniformities, etc. Principally new possibilities are related with monitoring of atomic and chemical structure of the tested objects. This is a direct quantitative monitoring of their substantional structure. Obviously, the reconstructed internal physical parameters of the objects can be used as control parameters in the development of more reliable and accurate methods of non-destructive testing of construction elements, ensuring determination of the quality of their fabrication, degree of degradation, functionability, service time, etc.

Among these parameters, on should specially note the effective atomic number Zeff of the material. Local distribution of Zeff(r) in the object allows identification of its effective atomic (chemical) composition. In other words, it is possible to distinguish organics from inorganics, light alloys from heavy alloys, to control higher or lower content of specified chemical elements (e.g., content of calcium in raw materials used in construction works) in the main substance or in mixtures of several substances, to realize virtual (digital) separation of the images of physically overlapping materials in composites, etc. Separation of images of simple components (with subsequent routine control of their spatial distribution in the complex objects under study) increases the contrast sensitivity of radiographic images by an order of magnitude. All this provides new possibilities in the non-destructive testing.

Conventional radiography does not allow reconstruction of the effective atomic number and many other parameters of the substance structure. To do this, one should use multi-energy radiography (spectroscopy) of the materials. It appears that multi-energeticity, i.e., inspection of an object using not one, but several characteristic energies (or ranges) of radiation, allows us to obtain full information about these parameters. In this work, it has been shown (theoretically) how such inverse problem can be solved within the framework of 2-radiography. New algorithms for reconstruction of these parameters require development of modern multi-energy introscopes using scintillation detectors and digital data processing for radiation detection.

2. Effective atomic number

Among the most important substantional structure parameters, one should specially note the effective atomic number Zeff. In fact, it roughly determines the chemical composition of a material. Higher Zeff ³20 correspond to inorganic compounds and metals, lower Zeff £10 correspond to organic substances. Normally, in radiography the material is irradiated in the ranges corresponding to the photo-effect and Compton effect (from 20-50 keV to 200-400 keV). The effective atomic number of a compound of known chemical formula is determined from the relationship


where Ak and Zk are the atomic mass and atomic number of simple elements, P is the total quantity of simple elements, ak - relative atomic (molar) concentrations, i.e., the number of atoms of each kind in one molecule. In Table 1, data are collected on the effective atomic number of some substances that are often present in materials of the inspected objects under study.

Material Chemical formula Zeff
Inorganic substances    
Stainless steel Fe 66%;Cr 10%;Ni 16%;Ti 8% 26.57
Black steel Fe 92%; C 8% 25.97
Calcium phosphate; bone tissue Ca(PO4)2 17.38
Table salt NaCl 15.66
Quartz glass; sand SiO2 12.30
Aluminum and light alloys Al2O3 11.70
Glass Na2SiO3 11.49
Water H2O 7.98
Air mixture O2; N2 etc. 7.6
Organic substances    
Polyvinyl chloride (C2H3Cl)n 15.85
Soft tissue (med.) CNO-organics; H2O 80-95% 7.8
Glucose C6H12O6 7.37
Saccharose C12H22O11 7.38
Cellulose (wood, paper, fabrics) (C6H10O5)n 7.31
Organic glass (C5H8O2)n 6.96
Polyamide (nylon) (C6H11NO2)n 6.85
Polystyrene (C8H9)n 5.95
Polyethylene (plastics) (C2H4)n 5.94
Table 1: Effective atomic number of various substances with respect to the photo effect.

3. A physical model of two-energy radiography

Let us consider the main peculiar feature of two-energy radiography [4-7]. Detectors of this system record the attenuated ionizing radiation not in just one, but in two separated ranges of the energy spectrum. This corresponds to a general scheme of 2-radiography presented on Fig. 1. Each range (channel) of detection corresponds to some characteristic energy of radiation. Methods of energy separation depend upon the detector design and the choice of radiation sources. In the classical design [1] with X-ray tubes, metal filters are used. In new developments [7] the role of filter may be played by a low-energy detector array (e.g., based on zinc selenide). The better are the ranges separated, the higher is inspection efficiency and quality of reconstruction of the object.

Fig 1: General scheme of two-energy radiography with reconstruction of the effective atomic number of the material. Conventional "synthesis" scheme consists in mixing of the fitting basic elements with L - "light", M - "middle" and H - "heavy" atomic mass. "Black-and-white" synthesis corresponds to the two-energy radiography, "three-color" scheme (R - red, G- green, and B- blue) corresponds to 3-radiography, etc. For our direct method ("analysis") proposed in this work, 2-radiography is sufficient.

Our physical model of multi-energy radiography uses the property of exponential attenuation of hard ionizing radiation in the inspected object. The character of the energy dependence of the linear attenuation coefficient is shown in Fig.2.

Fig 2: Linear mass attenuation coefficient of radiation (full and without back-scattering).

An important feature of multi-energy systems is digital processing of data arrays coming simultaneously from several detectors. The computer also presents the output signal in the most convenient form (logarithmic and normalized). Theoretically, the multi-energy radiography can be described by a system of linear equations [4]


where Ri = R(Ei) = In [F0(Ei) / F(Ei)] is the reflex of the system, F0 and F are output signals from the background (in the absence of object) and from the object, respectively, Ei is one of the selected radiation energies, M is the order of multi-energeticity. For 2-radiography, i=1,2; and j=1,2; Ei = {E1,E2}. The unknown X correspond to controlled physical parameters of the object. The monitoring matrix does not depend upon properties of the inspected object. It depends only upon the chosen "energy" configuration of the monitoring, i.e., upon energies {E1,E2}, and properties of the detectors. Its components are defined after calibration measurements using samples of known composition (effective atomic number Zk and density rk) and geometry (thickness Lk) by the coefficients of the "calibration" matrix .

In the two-energy radiography, the effective atomic number of an unknown material can be reconstructed using the expression derived from the general system


Here we have introduced auxiliary constants D1 = (Z2/Z1)3 (r2L2/ r1L1) and D2 = D1 (Z1/Z2)2. The value Y is a reduced (relative) output signal. The expressions obtained depend only upon data of radiographic measurements carried out using a detector pair R1,2 = R(E1,2), calibration (reference) data - components of the calibration matrix C11,C12,C21,C22 and constants D1,D2. It is essential that in general it is a direct method for quantitative determination of the effective atomic number. The reconstruction will be unambiguous and without artifacts, because the dependence Z(Y) is strictly monotonously increasing (positive derivative, dZ/dY > 0). The calibration defines the ranges of effective atomic number reconstruction with high sensitivity for distinction between organic compounds (Z=1-10), inorganic compounds (Z=18-40), and compounds of intermediate composition (Z=10-18), as well as for the full range (Z=1-40). Fig.3 shows a characteristic view of the dependence of dual-energy radiography law of reconstruction Zeff (with a some model calibration for interval Z=1-81).

Fig 3: Theoretical plot (in formal calibration) of the effective atomic number Zeff as function of the ratio R = R1/R2 of two output signals in the two-energy radiography inspection of Zeff.

It should be noted that existing developments of 2- and even 3-energy radiography are mainly using methods of qualitative determination of the effective atomic number. Their accuracy is of the order of 50% for compounds with large Zeff (a scheme of such "synthesis" is presented in Fig.1). It is possible to efficiently distinguish only between organics and inorganics or heavy alloys (iron, Zeff"26) and light alloys (aluminum, Zeff"13). Possibilities of the two-energy radiography are much wider. The approach proposed by us - a method for direct reconstruction of Zeff (indicated in Fig.1 as "analysis") - allows to more fully realize the broad possibilities of multi-energy radiography.

4. Prospects and advantages of the multi-energy approach

Our analysis shows that the effective atomic number of a material can be reconstructed (using the formula (3)) with accuracy of ~5%. Among practical applications of this method, one can note detection of plastic explosives inside postal parcels and letters, commercial goods and loads, etc.

Theoretical analysis also proves inefficiency of traditional radiography for such problems. Higher multi-energy modifications (3-, 4-energy) increase the accuracy and reliability of the monitoring and provide us with additional information about properties of the inspected objects. In particular, it is possible to reconstruct concentration of simple chemical elements, i.e., make a direct determination of the chemical composition of the material.

Thus, remaining within the limits of 2-energy radiography, it is possible to carry out quantitative diagnostics of the effective atomic number of materials with accuracy of 5-10% . There are two controlling parameters, and not just one. This also increases the monitoring efficiency. Moreover, passing from the 2-energy to 3-energy radiography allows improved monitoring not only of the effective atomic number, but also of atomic (molar) concentrations of simple components of a complex chemical compound. The number of reconstructed parameters always corresponds to the order of multi-energeticity.


The research described in this publication was made possible in part by Award No.UE2-2484-KH-02 of the U.S. Civilian Research & Development Foundation for the Independent States of the Former Soviet Union (CRDF).


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