Flaw Geometry Reconstruction Using a Limited Set of X-Ray Radiographic Projections

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Wallingford, Richard
Basart, John
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Review of Progress in Quantitative Nondestructive Evaluation
Center for Nondestructive Evaluation

Begun in 1973, the Review of Progress in Quantitative Nondestructive Evaluation (QNDE) is the premier international NDE meeting designed to provide an interface between research and early engineering through the presentation of current ideas and results focused on facilitating a rapid transfer to engineering development.

This site provides free, public access to papers presented at the annual QNDE conference between 1983 and 1999, and abstracts for papers presented at the conference since 2001.


Flaw detection using x-ray radiography has traditionally been based on a qualitative assessment of the x-ray image features [1]. This approach, although reliable in many cases, has limitations due to the relatively small amount of information contained in a single projected image, the variability of inspection results based on the radiographer’s experience level and intuition, and the inability to extract quantitative information about the flaw. One way to help alleviate these limitations is to use x-ray computed tomography (CT) where the flaw can be reconstructed, sized, and located within the part [2,3.4,5]. The drawback of using CT is that the hardware required is very complex and expensive. In addition, the computational power required to execute a CT algorithm in a reasonable amount of time is very high [6,7]. A compromise between the use of a single x-ray projection and CT for flaw reconstruction is to model the flaw, a priori, as a geometric figure or solid and reconstruct the model from a reduced set of x-ray projections [8]. The number of projections required to deduce the geometric model parameters may vary with the complexity of the model, but it will be shown that only two projections are required to reconstruct a straight line of arbitrary orientation. In this paper we present the reconstruction formulation for a crack modeled as a straight line or series of straight lines. We also present the analysis for reconstruction errors caused by film measurement errors and system geometry errors. Experimental results of flaw reconstruction with a microfocus x-ray machine are also presented.

Sun Jan 01 00:00:00 UTC 1989