Deconvolution Processing for Flaw Signatures

The ultimate resolution of all ultrasonic flaw detection systems is limited by transducer response. Although the system output contains detailed information about the target structure, these details are masked by the system characteristics. Since the output can be described as the convolution of the target response and the impulse response of the system, it shouldin principle be possible to reverse this operation and extract the target response. In practice, it is found that the presence of even relatively small amounts of noise make the deconvolution process impossible. If, however, the flaw detection system has an extremely high output signal-to-noise ratio it is possible to use estimation techniques in the deconvolution process to achieve a good approximation to the actual target response. Results are presented that demonstrate these techniques applied to both simulated and experimental data. Coupling deconvolution processing with feature extraction is shown to yield an order of magnitude increase in range resolution. Introduction The output of a linear flaw detection system, y{t) can be represented as the convolution of the target response, x(t), and the impulse response of the system, h(t). y(t) = x(t) * h(t} =J: x(T} h(t T)dT (1) For this type of system the convolution process can be reversed to remove the effects of the system and obtain detailed information about the target. Since the impulse response of the system can be measured, extraction of the target response from the convolu. tion tntegral by straight-forward deconvolution is achieved by taking Fourier transforms Y(w) = X(w) • H(w), (2) dividing,and taking the inverse transform 1 . x(t) = F{Y(w}/H(w)}. (3} However, in the case of real experimental data, the output y(t) is contaminated by the presence of noise, n(t), so that the measured output is y(t) = x(t}* h(t) + n(t). (4) If straight forward deconvolution of the noise contaminated output, y(t), is attempted, we obtain x(t) F-l{Y(w)/ + N(w)/ } (S} H(01) H(w} where the first term is the desired target response and the second term is the noise contribution. 312 Si nee the functions 1'1 (w} and H(w) are unrelated, their zeros can not in general coincide. Thus it is usually the case that the noise term dominates, completely obscuring the desired target response. In an actual system the noise, n{t}, is an unknown random function. Thus examination of Eq. 5 reveals that straight. forward deconvolution actually generates an entire setS of possible solutions in which each noise function yields a different approximation x( t). Virtually no useful information can be extracted from this simple processing technique. This result clearly 'demonstrates the desirability of obtaining the largest possible output signal-to-noise ratio. However it does not follow directly that a high signal-tonoise ratio implies a good approximation to the actual target response in straight forward deconvolution. For detection systems which possess a high signal-to-noise ratio, the following estimation technique can be used to advantage. If we know that the noise is bounded and assume that all the signals exist only in a finite time interval such that