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Research
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Mathematical
Models
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The following publications discusses the limited angle tomography for reinforced concrete: P.J.M. Monteiro, C.Y.Pichot and K. Belkebir, Computer Tomography of Reinforced Concrete , Chapter 12, Materials Science of Concrete, American Ceramics Society (1998). Computer Simulations of Limited Angle Tomography of Reinforced Concrete (with K.A. Heiskanen and H. Rin), Cem. Concr. Res. Vo. 21, 625 (1991).
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X-ray tomography of reinforced concrete Tomography cames from the Greek word tomos (slice) and it has the goal of obtaining an image of an object from measurements made from slices through it. Tomography belongs to the general class of inverse problems, which often arises in the physical sciences when inferences from observations are used to obtain information about the physical world. In computed tomography, the image of an object is reconstructed from projections of the object. Most commonly the projections are obtained by using penetrating x-rays, although other modalities for measuring projection data are also available. In tomography, two basic configurations have been applied: parallel beam and fan beam geometry. |
| An image can be reconstructed when projections are available evenly from a sufficient number of directions around the object. Tomography with limited data arises when the projections cannot be measured from certain directions, for reasons such as the geometric configuration of the scanner or the object, or the movement of the object during the scan. The artifacts are more serious if the projections are missing from a contiguous sector of directions than if they are missing in a number of smaller sectors. In order to avoid or reduce the artifacts, methods have to be devised for compensating for the missing data.. | |
| Image reconstruction from projections succeeds or fails depending on the quality and quantity of projection data available. One limitation that usually is unavoidable is that the measured data are discrete, not continuous. In other words, data are measured at a finite number of angles. The finiteness of the projection data does not need to be a problem, if the data are approximately evenly distributed over the projection space, and are not too noisy. The ill-posed nature of both the Radon-transform and the X-ray transform becomes more severe if there are missing gaps in the projection data, i.e. data are not available at a regular grid. For these cases the normal reconstruction algorithms fail, and special methods are needed. So far satisfactory methods have not been developed for the fan beam geometry. | |
Examples of tomography
Radiograph (left) and CT (right) images of unloaded fiber-reinforced concrete cylinder
Radiograph (left) and CT (right) images of loaded fiber-reinforced concrete cylinder
Multiple CT scans of loaded fiber-reinforced concrete cylinder
Radiograph (left) and CT (right) images of a concrete block with multiple rebars
