EFECTO DEL OXIGENO Y ALCALINIDAD DE LA SOLUCION.

Commonly, ultrasonic NDT procedures rely on the use of a short time-duration voltage impulse to excite the ultrasonic probe and to retrieve information about the internal structure of the sample. A single transducer is often used to excite the sample under test, leading to a Pulse Echo inspection. A short pulse allows the sample to be excited across a broad frequency range. This is because a short time duration pulse is a good approximation to the Dirac Delta function, whose frequency spectrum can be considered ideally flat over the frequency range of interest [1]–[3]. Figure 2.1 shows an example of a pulsed signal and its corresponding frequency spectrum:

Figure 2.1: Pulsed signal and its frequency spectrum.

The signal recorded by using a single pulse input signal x(t) after its path into the

sample it is called Impulse Response h(t) of the sample. If the excitation amplitude is not high enough to cause non-linear phenomena within the sample under test, then its behaviour can be considered Linear and Time Invariant (L.T.I.). Under these conditions, the Impulse Response represents ideally how the sample reacts across the frequency range of interest:

Figure 2.2: Illustration of the impulse response definition.

However, there are some limitations on the use of such pulsed techniques. When a test is performed either in highly attenuating environments (by using air-coupled ultrasound) or to inspect challenging materials such as composites, steel forgings and concrete, there is the need to enhance the amount of energy input into the sample, to maximize the SNR. In principle, this can be done by increasing the voltage excitation level. Industrial transducers can be excited by voltage levels of up to 1000 V peak-to-peak, but the resultant input energy is still not enough for many such applications. An alternative method to enhance the SNR consists of matching the signal to the resonant frequency of the sample under test, so as to maximize the transmitted acoustic energy. This can be done by means of a Tone Burst signal (Frequency Stopped Output) [4]–[6]. Figure 2.3 shows the time waveform and the frequency spectrum of a Tone Burst signal whose central frequency is 200 kHz:

Figure 2.3: an example of a 200 kHz central frequency Tone Burst signal and its frequency spectrum.

However, when a test involves scanning a transducer over a given sample, a change in the local properties (such as density or thickness for example) leads to a change in the local resonance frequency. Therefore, it is difficult to use Tone Burst signals in real time applications. Moreover, the signal band is limited both from the transducer frequency properties and the time duration T of the signal used, i.e. the value T*B (where B effective signal bandwidth) is about unity for Tone Burst signal.

To cope with these problems, the use of the Pulse Compression (PuC) technique has been proposed [7], [8]. PuC consists of the application of a matched filter to retrieve the impulse response of the systems, even in low SNR cases. In a standard PuC scheme, the sample under test is excited by a Coded Excitationsignal x(n), whose frequency spectrum can be considered flat across a broad range frequencies and which has an arbitrary time duration. The signal recorded after travelling within the sample (y(n)) is thus convolved with the matched filter Ψ(n). In this way, an estimate of the impulse response of the system is

retrieved. Note that both discrete-time, i.e. (n), and continuous-time domains, i.e. (t), will

A generic PuC scheme can be depicted as shown in Figure 2.4. Here, would be equivalent to the ideal impulse response h(n) if (i) the coded signal has an infinite time duration and (ii)its frequency spectrum is flat for all the frequency band considered. In other words, it happens when the time-frequency domain characteristics of the coded signal tends to match those of the ideal impulse.

Figure 2.4: Pulse compression generic scheme. The red-crossed circle represents the convolution algorithm.

The key-point is that shows an amplitude gain proportional to the length of the coded signal used. This means that a low voltage level can be used and a high SNR can be reached simply by changing the signal length. The coded signals enhance the T*Bvalue as

the input signal duration is increased for a given available bandwidth. This means that the SNR can be increased, compared with SNRPulse-Echo, as follows:

∗ (2.1)

Although a deeper analysis will be given in section 2.3, equation (2.2) summarizes the PuC procedure:

Ψ ⨂ Ψ ⨂ ⨂

where e(n) represents noise of arbitrary type (environmental, quantization, instrumental,

etc.) and is the approximation of Dirac’s delta function. The matched filter Ψ(n) is the one which has the impulse response:

∙ Δ (2.3)

where k and Δ are arbitrary constants. This corresponds to perform a convolution between the output signal and the time-reversed input signal, shifted by a value . In other words, the optimal matched filter Ψ(n) is the time replica of the input signal, i.e. Ψ(n)=x(-n). As will be explained in the following sections, matched filter optimization is one of the key-points that has to be taken into account with the use of coded signals. Moreover, it can be demonstrated that the matched filter is the one that maximizes the SNR enhancement at the output of the PuC procedure [9].

The next section describes the main types of coded waveforms, where particular attention is given to the ones that have been exploited in this research work. A detailed mathematical analysis of the two mains PuC procedures is reported in section 2.3.