# 2D Ultrasonic Antenna System for Imaging in Liquid Sodium
## 4 Experimental FMC/TFM Images Performed in Water and Associated Simulations with CIVA
### Computation Time Improvement  
The other axis for improvement is the computation time of the images. Three options are currently under investigation.  
The first option is to use massive GPU (Graphic Processing Unit) parallelization. As the TFM, Hadamard, or PWI algorithms consist in a large number of operations (summations of amplitudes at a given time of flights for shot and receiving elements), they can be quite parallelized on a CPU (Central Processing Unit) or a GPU. In order to avoid poor scaling effects due to concurrent memory accesses, parallelization has been done on pixels and very good improvements in computation time have been obtained on both CPU and GPU architectures [9].  
Figure 9: Comparison between (**a**) TFM, (**b**) Hadamard coding, and (**c**) Plane Wave Imaging (PWI) images obtained in a High-Density Polyethylene (HDPE) component for a 64-element, 5-MHz probe. The case is of a side-drilled hole (diameter of 2 mm) at a 25-mm depth. The amplification gain and voltage excitation are the same for the three acquisitions process. Attenuation of HDPE in the bandwidth is comprised between 0.4 and 1.4 dB/mm. Signal-to-Noise Ratios (SNR) are respectively 9 dB, 15 dB, and 18 dB [8].  
The second option, which can be used with any method and with parallelization, is to develop an \"adaptive\" grid in the imaged area. Here, the principle is to start the imaging process with a loose grid, then to detect the high-amplitude regions, and to iteratively refine the grid around those regions [10]. In our configuration that is purely three-dimensional, a 3D grid is needed. Work is ongoing to develop it, and at the moment, we can illustrate it only with a 2D configuration. Figure 10 shows 2D TFM images obtained on a set of simulated data for two side-drilled holes in a steel specimen imaged with 64 elements and a 2-MHz probe. It can be noted that, in this case, the same image quality is achieved by the adaptive grid with only 16% of the number of pixels used in the original case (area of \(45\times 40\) mm with a regular step of 0.4 mm).  
The last option is to use frequency domain (f-k) methods. These methods are well known to greatly reduce computation times. In particular, the methods developed by [PERSON] and [PERSON] has been adapted to NDE cases and to plane wave imaging [11]. It has been shown that f-k methods greatly reduce the algorithm complexity (number of operations) compared to the classical PWI (cf. Figure 11) and, thus, the computation time. The result presented Figure 11 was obtained in pulse-echo mode, and the work to extend it to our antenna system, with separate transmission and reception, is ongoing.  
Figure 10: Adaptive grid: (**a**) TFM image obtained using (**b**) a regular and very fine grid and (**c**) TFM image obtained using (**d**) an adaptive grid. The number of pixels in Figure 10d represents 16% of the total number of points in Figure 10b.  
Furthermore, it is important to note that our configuration presents two advantages regarding the computation time of the images that strongly depends on the time required to compute time of flight between the elements and the points of the imaged area. The first one is the absence of interface between the elements of the antennas and the inspected area, and the second one is that the propagation occurs in a fluid medium (case of the sodium at inspection temperature), where only longitudinal waves exist. Indeed, the time-of-flight computation requires knowledge of the wave path between the transmitting element and the focusing point. This path is much easier and thus faster to compute when there is no interface as there is no refraction of the waves. Imaging the large area of the antenna field of vision is made possible thanks to these advantages combined with the implementation of the methods to decrease the image's computation time.