# Application of a matched filter approach for finite aperture transducers for the synthetic aperture imaging of defects

TL;DR: These studies confirm that MFA is an alternative to SAFT with little additional computational burden and can also be applied blindly, like SAFT, to effect synthetic focusing with distinct advantages in treating finite transducer effects, and in handling steered beam inspections.

Abstract: The suitability of the synthetic aperture imaging of defects using a matched filter approach on finite aperture transducers was investigated. The first part of the study involved the use a finite-difference time-domain (FDTD) algorithm to simulate the phased array ultrasonic wave propagation in an aluminum block and its interaction with side-drilled hole-like defects. B-scans were generated using the FDTD method for three active aperture transducer configurations of the phased array (a) single element and (b) 16-element linear scan mode, and (c) 16-element steering mode. A matched filter algorithm (MFA) was developed using the delay laws and the spatial impulse response of a finite size rectangular phased array transducer. The conventional synthetic aperture focusing technique (SAFT) algorithm and the MFA were independently applied on the FDTD signals simulated with the probe operating at a center frequency of 5 MHz and the processed B-scans were compared. The second part of the study investigated the capability of the MFA approach to improve the SNR. Gaussian white noise was added to the FDTD generated defect signals. The noisy B-scans were then processed using the SAFT and the MFA and the improvements in the SNR were estimated. The third part of the study investigated the application of the MFA to image and size surface-crack-like defects in pipe specimens obtained using a 45° steered beam from a phased array probe. These studies confirm that MFA is an alternative to SAFT with little additional computational burden. It can also be applied blindly, like SAFT, to effect synthetic focusing with distinct advantages in treating finite transducer effects, and in handling steered beam inspections. Finally, limitations of the MFA in dealing with larger-sized transducers are discussed.

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### Cites background from "Application of a matched filter app..."

...2510419 or optimal filter kernels can be derived [9]–[11]....

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##### References

1,168 citations

### "Application of a matched filter app..." refers background in this paper

...although larger apertures lead to higher spatial resolution capabilities, the images of small defects need to be deconvolved with the corresponding point spread function for defect sizing [3]....

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...small defects can be considered uniformly insonified to respond like point scatterers [3] having sharp sirs and uniform angular distributions....

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594 citations

### "Application of a matched filter app..." refers methods in this paper

...other methods of synthetic focusing of the received data using a post-processing approach have been reported in the literature [4], [5]....

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568 citations

### "Application of a matched filter app..." refers background or methods in this paper

...a prevalent numerical computational technique commonly used is the discrete representation array Modeling (dreaM) procedure, which is well suited for the computation of fields from planar and array transducers [6]–[8]....

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...saft, though a rapid, simple, and effective sizing technique, cannot be readily applied to the defect images obtained from a finite-size-aperture transducer because the transducer has a broader sir characteristic [6]–[8] and a shaped beam....

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299 citations

231 citations

### "Application of a matched filter app..." refers methods in this paper

...furthermore, the phased array system is emerging as a rapid and more convenient ultrasonic nondestructive evaluation technique for detection and real time imaging of defects in structural components [9]–[16]....

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