|TABLE OF CONTENTS|
The computerized industrial tomography is one of the NDT method entirely based on the computer reconstruction technique that offers a very detailed 2D and 3D graphic images of the tested object. After a brief description of a simple laboratory tomograph, we present some important features of our software package, specially developed for tomographic analysis. In the last part, some relevant 2D and 3D tomograms made with our laboratory equipment and some consideration regarding the material identification from tomograms are showed. We use the Filtred Back Projection based algorithm for reconstructing the 2D tomograms and a direct representation of the 3D-matrix method for 3D tomograms.
The computerized tomography technique is based on successive attenuation measurements of a narrow X-ray or -ray beam after it passes through a tested object in several directions. By means of an adequate mathematical tomographic algorithm, a map of attenuation coefficients for the scanned surface is reconstructed. In fact, this map of attenuation coefficients is sometimes called a "density map" of the materials from the slice.
|Fig 1: General presentation of a simplest tomographic equipment|
The laboratory tomograph we built is a 1st generation classical model (fig. 1): it has a gamma ray source and a detector, so that only one measurement is possible at a given time. With this model, the data acquisition time is relatively long, but the simplicity of its design and the low cost were the major selection criteria.
The tomograph operates in the following way. The tested object is placed on the mechanical unit enabling its translation, rotation and motion along Z-axis. The object is then exposed to the collimated beam. Two collimators are placed between the source and the detector. Accurate motion control and data acquisition is accomplished by a microcontroller equipped personal computer. A preamplifier, an amplifier and two-channel analyzers process the data collected from the detector. Data storage and processing, reconstruction algorithms and the final 2D and 3D tomograms display are carried out by specialized program packages running on the PC.
Several classes of reconstruction algorithms are available, such as algebraic, iterative, analytical, etc. We have found that one of the faster and accurate algorithms is the Filtered Back Projection (FBP) algorithm, combined with convolution filtering method. Various basic algorithm description, including the FBP, could be found in  - .
A reconstructed slice, or a 2D tomogram, is usually 0.4 - 3 mm thick which is generally determined by the radiation beam width. The scanned slice is plotted by associating a given color to every "density" value, corresponding to a given distribution of the attenuation coefficients. Thus, a tomogram becomes a "false colors" representation of the scanned slice of the object.
The 3D tomograms or, more exactly, the representation of the successive slice tomograms, is based on the 3D direct matrix representation method, described in ,  and .
We have to point some specific advantages of the tomographic reconstruction:
An NDT tomograph procedure includes motion control, data acquisition and storage, tomographic reconstruction, fault detection analysis of 2D and 3D tomograms and report generation. The program package providing all these facilities was developed in our laboratory ,  and includes the following features:
The industrial tomography apparatus TOMORAY-01 (fig.2) was built in 1992. It utilizes the mono-detector geometry and a 30 Ci192Ir radiation source. The following are its technical characteristics:
|Fig 2: TOMORAY Tomograph|
In order to illustrate the industrial application of the computerized tomography (see the general presentation from  and ) we present in following a part of the 2D (fig. 3 to fig.6) and 3D tomograms (fig.7 and fig.8) made with the TOMORAY-1 apparatus. More details are presented in ,  and .
Fig 3: Cross-section of a 90 mm diameter aluminum rod cage rotor from an asynchronous electric motor
Diameter of reconstruction: 110 mm; scanning step : 0.4 mm; number of projections : 60
Large faults consisting in air bubbles resulting form casting and some high-density material segregation possibly as a result of differences in cooling, may be seen .
Fig. 4: A cross section of an encapsulated varistor.|
Length of reconstruction area: 85 mm
Scanning step : 0.4 mm
Number of projections : 60
The size of the capped varistor and the bolt screw terminals may be clearly observed in the cross section.
Fig 5: A cross section of a high sensitivity Hall transducer.|
Length of reconstruction area: 98 mm
Scanning step : 0.4 mm
Number of projections : 60
Several coils and some ferromagnetic material showing very well shaped geometry, may be observed.
|Fig 6: A cross section of a pine tree trunk. Diameter of reconstruction: 160 mm; Projections: 180; Scanning step: 0.4 mm. The annual rings of the tree and an internal crack can be clearly observed.|
Fig 7: A roman statue from the National Museum of Romanian History.
The statue, 12 cm high and made of bronze, was reconstructed using 167 successive longitudinal planes. The resolution was 0.4 mm|
Scanning step : 0.4 mm
Number of projection : 60
3D-array size : 6.2 MB
Fig 8: 3D plot and analysis of a circular weld of a 44 mm diameter 4 mm thick steel pipe; Number of planes: 25; Scanning step : 0.4 mm; Number of projections : 90
Fig 9: A tomogram and histogram of a specimen containing different materials, such as: silicon, steel, aluminum, carbon, copper, ceramic, bronze, molybdenum and different mixtures
The most interesting and spectacular results of tomography reconstruction technique are the plots and analyses of 3D scanned objects. The method consists of successive slice scans and the reconstruction of the object by means of an original reconstruction algorithm, named 3D array direct plotting (and ). This means that 3D scanning of an object results in an array (3D matrix) containing voxels (elementary volumes) that describe every internal or external detail of the object, so that any interesting surface or view of the object can be plotted subsequently. In order words, the object with its every internal or external detail is stored in a 3D array and may be fully displayed using any view angle or lighting source, may be partially or fully cut through. Some materials or any part of the object may be removed, magnified or represented in a semitransparent manner. Using this procedure, the object is 3D fully digitized and stored.
Reconstruction details are remarkable, so that internal and even external analysis may be directly carried out using computer's display. During analysis, various interesting internal details, obtained by adequate choice of plotted positions and surfaces, were pointed out. Cutting performed through the statue, in some interesting areas, showed hidden internal details. Its middle area was studied in order to check the hypothesis that the statue was made by joining or by soldering two pieces. The hypothesis was contradicted by 3D tomographic analysis as may be observed in the illustrated images. The 3D analysis of the statue also pointed to another interesting detail: the left leg was apparently broken and repaired by gluing the pieces together. Using the data processing program, the gluing material was removed, and an image of a perfectly circular hole was reconstructed. The hole was drilled with a 2 mm spiral drill, possibly with the intention of inserting a reinforcement bolt.
The high resolution of the 3D plot is pointed out by weld scales and drops. A "software" cutting method may be used to observe internal caverns caused by the welding process, as well as one high-density material inclusion, which possibly came from the welding electrode. The investigation went on, by choosing the adequate plan to measure the maximum size of the gap occurring in the most significant section.
Another direction we work on was the development of an accurate algorithm for tomographic identification of constituent materials. Two methods were investigated. The first method involves the attenuation coefficient value correction , in order to have a linear response across the full range of the material attenuation coefficients. Using this compensation method we are able to identify materials, sufficiently represented in a tomogram, with less then 2% accuracy. An example is shown in fig. 9 where a test specimen composed of many materials, such as silicon, steel, aluminum, ceramic, carbon, copper, bronze, molybdenum and other composite materials, was reconstructed. The histogram (placed on the upper right side) shows the distribution of the materials of the tomogram and has a very clear separation between the corresponding peaks.
We developed also a more accurate method for materials identification for our equipment, similar to the dual energy method, which is based on the data correlation from two tomograms made at different energy. This algorithm, described in  and  is able to identify the density and Zeff (effective atomic number) values for the materials contained in tomograms with 3-5 % accuracy.
After many experiments in the tomography domain, despite of high equipment costs, it appears that for every class of objects to be studied by Computerized Tomography, there is an adequate configuration leading to optimum affordable cost/performance ratio.
The Computerized Tomography results obtained until present have been well received by the NDT specialists, who expressed their interest in testing this method in various industrial applications.