## 3 Pulse-Compression-Based Phased Array Setup and Imaging Procedures  
The implementation of the PuC in PA ultrasonic testing requires a hardware system capable of generating an independent arbitrary waveform for each transmitting element, even with long duration. This is to generate the desired coded excitation, as well as for applying both variable time and phase shift delays to each channel (beamforming) and amplitude modulation among the elements (apodization) [9]. Moreover, to fully exploit the PuC features, the time-bandwidth product of the coded signal should be the largest possible, so the signal generation and acquisition system should have a flat operating bandwidth, at least constant over the bandwidth of the transducer. For this purpose, a specific hardware system was designed and realized by X-Phase s.r.l. (Sesto Fiorentino, Italy) for driving a pair of 16 linear array transducers in pitch-catch mode. The system contains 16 arbitrary waveform generators based on a 500 MS/s Delta-sigma modulator and 16 ADC with 12-bit resolution. Each generator can transmit a coded signal up to 100 ms duration with a maximum amplitude of 158 Vp-p. The maximum length of the acquired signals can be up to 500 ms with a constant sampling rate of 50 Mbps. This depends on the on-board memory. The overall PuC-based measurement setup consists of:  
* The hardware system for signal generation and acquisition;
* A desktop computer where the code for PuC is generated, including all the signal manipulation processes required for the UT image reconstruction (time delay laws, apodization, etc. );A pair of 16-element linear array transducers working in pitch-catch configuration. The PuC-based measurement setup is illustrated in Figure 1, where the transmitting and receiving array transducers are placed adjacent to each other, so as to maintain a measurement configuration which is as close as possible to the standard pulse-echo setup. In order to construct the ultrasonic images of the sample, the transmitted beam of the array transducer is manipulated (steered and focused, etc.) by applying the time delays law to the generated chirp signals of each element before the transmission, in full analogy with the standard pulse-echo PA testing [9]. On the other hand, in reception, the acoustic beam is manipulated by applying time delays to the acquired signal after the PuC process. Note that for the linearity of the overall processing, the outcome is the identical if the time delays were applied before the PuC process [38]. Other beam manipulation techniques such as apodization work exactly in the same manner for pulsed or chirp excitations. Two types of PA imaging procedures were adopted in this work. 1. Sector and focused scan imaging: in this method, the full aperture of the array transducer is exploited where the UT beam is focused at a specific depth and steered by applying time delays to both the transmitted and received signals at the array elements. A 2D image of the sample is reconstructed by sweeping the sound beam of the array transducer through a discrete set of directions within the sample [8]. 2. The total focusing method (TFM): the method is typically used when a better resolution and sensitivity is required, especially for the detection of smaller defects. The image is reconstructed from the post-processing of FMC data. FMC is an information matrix obtained by exciting a single transmitting element at a time while the echo from the sample is captured through all the receiving elements of the array, and the process is repeated for all the transmitting elements [15; 16]. Thus, the matrix consists of \(N_{Tx}\times N_{Rx}\) A-scan signals where \(N_{Tx}\) is the number of transmitting elements and \(N_{Rx}\) that of receiving elements. Henceforth, we assume \(N_{Tx}=N_{Rx}=16\) in the case of the PuC-PA custom system, and \(N_{Tx}=N_{Rx}=43\) for the pulse-echo system.