By Bahman Zoofan, Tomos Technologies
Tomography is an advanced imaging technique used to isolate and visualize a particular section of an object, based on multiple exposures.¬† The term tomography explains the fundamental concept of this method; it comes from two words: tomos, which means "slice" in Greek and graphein, which means to write.¬† The current terminology for this technique is Computed Axial Tomography (CAT) or Computerized Tomography (CT).¬†
A conventional X-ray radiography is a 2D shadowgraph of a 3D object. This 2D image is a grey-level map based on the physical density or any changes in the overall thickness of the part along the direction of the X-ray.¬† A 2D image has useful information about any defects or inside details of the part, but is limited in providing exact depths and exact locations of the inside features. Figure 1 shows the inherent limitation of the conventional radiography when compared to a CT technique.¬† Internal defects A and B can be superimposed to create a single indication. To estimate the exact depth of defect C more exposures at different angles are necessary.¬†¬†
Figure 1: Shows the limitation of 2D radiography compared to tomography¬†¬†¬†¬†
Figure 2¬† shows¬† the main principle of a CT¬† scanning method. The moving¬† source¬† and¬† the detector¬† capture multiple¬† images that are called projections (P1, P2, P3).
Each projection image carries a piece of information about the object. The recorded intensities in each projection image are a map of changes in the part thickness and its physical density along the beam of X-ray at that particular angle.¬† The different slice images of the part can be reconstructed from the collected projections.¬† This representation is usually for medical application, which historically was pioneered to be a useful diagnostic tool.¬†
Figure 2: The basic principle of CT scanning
CT Method, Industrial Application
In industrial applications, the source and the detector are fixed while the part is rotating along a desired axis to acquire multiple projections. Figure 3 shows the main parts of an industrial setting for CT scanning.¬† While the basic concept of CT reconstruction seems simple, the most challenging part was to find a reliable and fast algorithm to reconstruct the slice images from a large number of acquired projections.¬†
Interestingly, in 1917 an Australian mathematician named J. Radon published a paper, from a purely mathematical standpoint, showing how to reconstruct a function from its projections data.¬† Most likely he never found that his mathematical efforts opened the window to a new and valuable imaging technique.¬† This has changed with the availability of fast computers to process the huge numbers of back-projection calculations and the introduction of faster algorithms.
The first generation of CT scanners were invented by G. Hounsfield, earning him the 1972 Noble Prize in medicine, which he shared with Allan Cormack, who independently discovered some of the algorithms.¬† The first generation of scanning was built by Hounsfield and Cormack and took nine days to produce a single slice image. Thanks to today's processors and powerful reconstruction software, CT scanning is now a vital part of daily diagnostic medical practice and a powerful tool in the field of nondestructive evaluation (NDE) of different areas of industry.
Figure 3: Basic elements of a CT system in an industrial setting
The development of high-resolution flat panel detectors with high dynamic range, relatively small pixel sizes, fast sampling rates and micro-focus tubes that provide fine focal spot size in the range of few micrometers (10-6 m) have made micro-tomography a powerful tool for different engineering set-up.
It is worthwhile to study the different features of a micro-focus tube to recognize its role in 3D micro-tomography.¬† The key to understanding the micro-focus system performance is to investigate the source of unsharpness, or lack of detail, in a radiographic image. The most dominated type of unsharpness in a radiographic system is called Geometric Unsharpness (Ug ).¬†
Figure 4: The concept of the geometric unsharpness in radiography
It is the amount of blurriness in a radiographic image due to the finite size of the focal spot or the geometrical configuration of the exposure setup. Considering the Geometric Unsharpness (Ug¬†) in a radiographic image with an effective source size (f), source-to-film or detector distance (a) and source-to-object distance (b), see Figure 4, then:
¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†Ug = f (a ‚Äď¬†b)/b¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬† (1)
Defining the image magnification like any other imaging technique as:¬†M=a/b, then the geometric unsharpness (1) can be written as:
¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬† Ug¬†= f (M ‚Äď¬†1) ,¬† (for M>1)¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬†¬† (2)
Equation (2) shows that the geometric unsharpness in a radiographic image is directly related to the tube focal spot size and the extent of the image magnification.¬† Based on this simple equation, in order to obtain large magnification for radiographic images, the focal spot size should be extremely fine in the range of micrometers (¬Ķm).¬† X-ray tubes with the focal spot sizes of 100 ¬Ķm are usually deemed micro-focus tubes.¬† Nowadays tubes with a focal spot size around 0.5 ¬Ķm have been manufactured and are capable of producing extremely high resolution images.
The other advantage of using micro-focus tubes, which is extremely important in CT scanning, is keeping a part far away from the detector.¬† The scattered radiations that are generated inside the object cannot reach the detector. This means the build-up factor on the detector is almost negligible.¬† The reduction of scattered radiations can improve the clarity of the image dramatically¬† when compared to a conventional tube.¬† The presence of scattered radiations acts like noise in the projected image and can cause severe artifacts during the reconstruction process and makes the interpretation of the final images difficult.¬†
Integration of different elements like a micro-focus tube, high dynamic range detector with fine pixel-pitch sizes, fast algorithms software and, finally, trained operators can produce high-resolution 3D reconstruction images for different engineering applications.¬† Different branches of industries, such as aerospace, electronics, manufacturers of composite materials, automobile, jewelry, plastic, biomedical and dentistry, can benefit from this imaging technique.¬† The technique can be well adopted for any research or evaluation of micro-damage, for example the study of corrosion.¬† The two main paths of industrial application of 3D micro-tomography are:¬†¬†¬†
Nondestructive Evaluation (NDE) of very complex structures, which need different exposures at different angles in 2D radiography technique.
Reverse engineering to create volumetric structure of a part in order to improve its original design.¬†¬†
Figure 5: (a) 3D CT-reconstruction of a surgical plastic tube with 200 micro-meters opening holes, (b) a CT-slice of the tube for exact details measurement.
Figure 6: (a) 3D reconstruction of a medical devise, (b) a slice image shows the diference in the physical density of the inserted part.
CT Micro-Tomography for Reverse Engineering
The advantage of applying CT micro-tomography to reverse engineering purposes rather than surface 3D scanning methods is because the acquired slices can be used for solid reconstruction of a part, and at the same time can reveal some other internal features. Among these features are presences of any interior defects, precise inside details measurement and the difference in physical density that other surface scanning methods are not capable of detecting.¬† Figures 5 and 6 show examples of these sorts of application.
Figure 7 shows a 3D reconstruction of a medical part as a simple reverse engineering application.¬† Figure 7(a) shows the part, 7(b) shows the 3D reconstructed image and 7(c) shows the interior features of the part by X-ray tomography.¬†¬† Figure 8 shows the created solid structure of the part with the populated polygonal meshes based on the volumetric reconstruction during micro-tomography.
Figure 7: (a) shows a plastic medical part, (b) 3D-reconstructed CT image, (c) inside features of the part revealed through CT scanning
The Question Of CT Spatial-Resolution
The concept of detectability and resolution is important for any imaging system. Determining detectability for an imaging system with many parameters involved is a challenging task.¬† Detectability in radiography may be defined as the size of the smallest visible detail revealed by a detector.¬† This size may be less than the pixel size.¬† In this case, only the existence of a defect may be determined from the image, while its actual size cannot be found.¬† In a radiographic system, the concept of detectability is more complicated compared to other imaging systems because the partial absorption of the radiation by materials needs to be considered.¬† Generally, in radiography and in CT scanning as well, the overall resolution depends on the size of the details in a part, plus on its thickness (object contrast), material composition of the part and the presence of any scattered radiations.¬† As mentioned before, the degree of eliminating scattered radiations has a great effect on producing sharp CT images.¬† Therefore, detectability and contrast are interrelated. ¬†
In the case of a using a micro-focus tube, the focal size of the X-ray source, image magnification and unsharpness of the imaging chain play an important role on detectability.¬† In order to determine the detectability for a micro-tomography system, the effect of different unsharpness contributed in captured images should be well understood.¬†¬†¬†
There are different sources of unsharpness in any radiographic imaging system. The most dramatic sources of unsharpness are recognized as:
Geometric unsharpness, Ug¬†
Detector unsharpness, UD¬†
Screen or display unsharpness (combination of the computer video card and monitor) Ug¬†
Movement unsharpness, Um
Among these different sources of unsharpness, the geometric unsharpness (Ug) is the most dominate one.¬† As far as the combination of different sources of unsharpness is concerned, it has been shown that the "total unsharpness" (Ut) cannot be added arithmetically, and a proposed formula is necessary to determine the total
effective unsharpness.¬† Different mathematical models have been suggested to represent the total unsharpness due to several separated unsharpnesses. The presence of the total unsharpness in a radiographic image shows a negative effect on the overall image contrast.
Also, the angle at whick X-ray beam exposes a part during acquiring projections has influence on the resolution of the final CT reconstructed image.¬† For relatively larger parts, a lower spatial resolution can be expected at the periphery of the part compared to the central part due to the extreme edges of the beam.
It is clear that the complexity of all these factors limits the ability to identify a specific resolving number for all CT scanning tasks.¬† Sometimes resolving power of CT has been expressed as Modulation Transfer Function (MTF) with the number of lines per millimeter, which in most cases is less than 2D radiography images. This can misrepresent the better detectability of CT compared to 2D radiography.¬† Detection of flat surface defects (particularly fine cracks) in 2D radiography depends on the direction of X-ray beams and plane of the defect. The CT technique overcomes this limitation by acquiring multiple exposures at different angles.
The following example shows a simple approach in finding the resolution of a CT reconstructed image. To simplify the case, a few assumptions are considered here.
The scattered radiations are completely eliminated in final reconstructed image.¬†
The unsharpness of the display system is extremely small and negligible.
For an image magnification of 8X with a focal spot size of 5 ¬Ķm and a detector with 14-bit dynamic range and a pixel pitch of 254 ¬Ķm2 then:
The Object Pixel Resolution = 254/8,
which gives a value of 31.8 ¬Ķm.
This provides a rough estimation¬†of the resolution in the reconstructed image, as far as the detector pixel size, is larger than the geometric unsharpness, i.e.
¬† ¬†Ug= F(M-1)= 5(8-1)=35 ¬Ķm
Figure 8: Solid 3D-reconstructed features of the same plastic part
The most practical method to judge the final resolution of the reconstructed scans for each particular case is to examine the image's fine details or sharp edges¬† The comparison of these fine details with actual parts can be used to confirm the acceptability of the obtained contrast and accuracy in 3D reconstructed images.¬†
Examples are shown in Figures 9 and 10, highlighting some fine features inside two reconstructed images.
Figure 9:¬† (a) original object, (b)reconstructed 3D images
CT scanning with a micro-focus tube can produce sharp, reconstructed images as a valuable NDE tool. Different branches of industries benefit from this advanced imaging technique in their quality assurance activities.¬† The availability of fast algorithms and software packages for fast and accurate reconstruction of final 3D scanning makes the technique an efficient tool. The sharp and high-contrast reconstructed images can be used for reverse engineering to reconstruct solid CAD models for improving design efficiency.¬†
Figure 10: Reconstructed 3D scanned image
Large magnification images acquired by micro-focus tubes can enhance detectability, particularly in the case of relatively small parts.¬† Due to a low applied flux on a micro-focus, the technique is limited to low-absorbent materials like plastic, rubber, electronic components, small electrical assemblies, biomedical substances, composite materials and thin metallic parts.¬† The advances in technology of manufacturing high resolution detectors with small pixel pitch, exact pixel shape and having large dynamic range are continually enhancing this imaging method. Due to the complexity of a variety of factors, substantial training of the micro-tomography operators is essential.¬†
For more information, contact Tomos Technologies, Inc. Bellingham, WA¬† or visit www.tomostech.com. ¬†¬†¬†¬†¬†¬†¬†¬†
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