**2. Some antecedents of ultrasonic evaluation from perpendicular planes**

Techniques for combining ultrasonic signal traces coming from perpendicular planes have few antecedents. As a precedent of this type of scanning performed from two distinct planes, the inspection of a high-power laser with critical optic components using ultrasonic transducers situated in perpendicular planes is mentioned in (Meyer and Candy 2002). In this particular case, the backscattering noise is valueless and the method seems centred in the combination from the arrival time of the ultrasonic echoes, and thus the combination is made with a time domain technique.

In (Rodríguez et al 2004), a testing piece containing a flaw was evaluated by using transducers located at two scanning planes. In this case, the receiving ultrasonic traces contain backscattering noise and the combination was performed in the time domain. Two combination options were there presented: one based on a 2D sum operator and the other 80 Applications of Digital Signal Processing

beams overlapping, were reported (Meyer and Candy 2002, Rodríguez et al 2004). But an extensive research in order to find simple and complete solutions to these problems is still needed. In particular, the authors are currently investigating techniques for ultrasonic radiation from perpendicular planes using arrays of few radiators working in near field conditions. In parallel, we are developing digital signal processing tools for improving the signal to noise ratio (SNR) in the echoes acquired in NDE of media with complex internal

In this technological context, a set of novel ultrasonic signal combination techniques have been developed to be applied in flaw detection ultrasonic systems based on multiple transducers. These combination techniques use a spatial-combination approach from the echographic traces acquired by several transducers located at different external planes of the piece under testing. In all these alternative techniques, the A-scan echo-information, received from the different transducers involved, is fused in a common integrated twodimensional (2D) pattern, in which, each spot displayed incorporates distinct grades of SNR

In this chapter, some linear and non-linear digital processing techniques to fuse echo-traces coming from several NDE ultrasonic transducers distributed on two perpendicular scanning planes are described. These techniques are also applied to the flaw detection by using a 2D combination of the ultrasonic traces acquired from the different transducers. The final objective is to increase the detection capabilities of unfavorable-orientation flaws and also to

Individual ultrasonic echo-signals are measured by sucesively exciting several transducers located at two perpendicular planes with electrical short-time pulses. Each transducer acquires a one-dimensional (1D) trace, thus it becomes necessary to fuse all the measured 1D signals with the purpose of obtaining an useful 2D representation of the material under inspection. Three combination techniques will be presented in this chapter; they are based on different processing tools: Hilbert, Wavelets and Wigner-Vile transforms. For each case, the algorithms are presented and the mathematical expressions of the resulting 2D SNRs are

Simulated and experimental results show certain combinations of simple A-scans registers providing relatively high detection capacities for single flaws. These good results are obtained in spite that the very-reduced number of ultrasonic channels involved and confirm the accuracy of the theoretical expressions deduced for 2D-SNR of the combined registers.

Techniques for combining ultrasonic signal traces coming from perpendicular planes have few antecedents. As a precedent of this type of scanning performed from two distinct planes, the inspection of a high-power laser with critical optic components using ultrasonic transducers situated in perpendicular planes is mentioned in (Meyer and Candy 2002). In this particular case, the backscattering noise is valueless and the method seems centred in the combination from the arrival time of the ultrasonic echoes, and thus the combination is

In (Rodríguez et al 2004), a testing piece containing a flaw was evaluated by using transducers located at two scanning planes. In this case, the receiving ultrasonic traces contain backscattering noise and the combination was performed in the time domain. Two combination options were there presented: one based on a 2D sum operator and the other

**2. Some antecedents of ultrasonic evaluation from perpendicular planes** 

structure (Lázaro et al 2002, Rodríguez et al 2004a, Pardo et al 2008).

improvement, depending on particular processing parameters.

deduced and evaluated by means of controlled experiments.

achieve a good 2D spatial location of them.

made with a time domain technique.

using a 2D product operator. The SNR was used as a quality index to evaluate both methods; and the resulting evaluation data showed a better performance of the product operator. Nevertheless, their performances were limited in both cases by the time representation of the signals.

A technique in this same line that introduces the combination in the time-frequency domain, based on the Wigner-Ville transform (WVT), was preliminary applied in (Rodríguez 2003). This technique took into account the temporal and the frequency information of the ultrasonic traces. A better SNR result than with the time domain method (Rodríguez et al 2004) was obtained. But this option presented two drawbacks: a lost of linearity of the processed signals and a high computational cost.

In (Rodríguez et al 2004b) a new method was presented, performing the combination in the time-frequency domain with a low computational cost by the use of a linear transform (based on the wavelet transform (Daubechies 1992); its 2D SNR performance seemed to be closed to that obtained in (Rodríguez 2003) with Wigner-Ville transforms.

The present chapter summarizes these three combination techniques previously proposed by the authors for flaw detection from perpendicular transducers. A comparative analysis (based on theoretic and experimental results) of their performances over a common set of specific experiments is made. The objective is to establish the respective advantages and inconveniences of each technique in a rather rigorous frame. For experimental evaluations, we have arranged an ultrasonic prototype to generate (from 2 planes) ultrasonic near-field beams collimated along the inspected piece, and to acquire the echoes from the transducers involved in our experiments. The different combination results calculated in each case, from the measured echo-responses, will be discussed.
