# Methods for Grating Lobe Suppression in Ultrasound Plane Wave Imaging
## 3 Results and Discussion
Consequently, the GL level increases with \(\hat{d}_{\alpha}\) in section B of Figure 4a. In section C of Figure 4a, the first GL has the same magnitude (0 dB) as the main lobe because the number of PWs passing through each point are the same over all of region C. Note that the GL can be suppressed below \(-6\) dB if \(\hat{d}_{\alpha}<1\), as in Figure 4a. The method using a non-uniform angle set was verified by the CW Tx beam pattern and PSF image simulations using the same PW sets used in Figure 3. Figure 5a shows the CW Tx beam patterns using the PW angle sets presented in the left panels of Figure 3a-c, from top to bottom. Since a finite-length transducer is used, regions where not all of the PWs pass through exist. In Figure 5a, region A and B indicate the region where none of the PWs pass and the region where more than one of the PWs propagate, respectively. The GL levels decrease in regions A and B; it is noteworthy that the GL at \(x\) = 25.6 mm in Figure 3c is greatly suppressed in the bottom left panel of Figure 5 when considering the finite aperture. The effect of GL reduction using the non-uniform angle set was also assessed with the 2D PSF images shown in Figure 5b. In the top and middle panels of Figure 5b, artifacts due to the first GL are observed, though the GL artifacts were reduced because of the Rx beamforming. The GL artifacts in the middle panel are located further from the point target than those in the top panel as the uniform PW set 2 has a smaller angular interval than that of the PW set 1 (\(d_{\alpha,1}=0.069\) vs. \(d_{\alpha,2}=0.046\)). Figure 4: Magnitude of the first GL normalized by that of main lobe when the GL is located in regions A, B, and C. (**a**) Magnitude of the first GL in a simulated Tx beam pattern versus \(\hat{d}_{\alpha}\). (**b**) Region where none of (region A), more than one of (region B), and all of (region C) the collimated beam areas of PWs overlap. (**c**) Simulated beam patterns when using \(\hat{d}_{\alpha}\) (marked with star, cross, and triangle in a (from left to right panels)). The gray dash-dot line indicates the theoretical first GL position, \(x_{\text{GL},1}\), of each beam pattern. When the non-uniform angle set is employed (bottom panel in Figure 5b), it is clearly observed that the GLs are successfully suppressed compared to those from the uniform PW sets. The proposed non-uniform angle is very easy to design as it is composed of two uniform angle sets with different angle intervals. However, there must be ways to discover other types of non-uniform PW angle distributions or to design an optimal PW angle set for a given imaging specification and the system requirements. One such approach might be to find a specific PW angle distribution that produces GLs where they can be further suppressed by the receive beam pattern, which may also have to be properly (or deliberately) designed. It is also worth noting that a deep neural network can be applied to find a method for the compressed sampling of PW angles [16]. In future studies, we should also consider ways to maintain or improve other important image qualities with a smaller number of PWs for fast imaging. The proposed methods in this paper can be combined with adaptive beamforming and sidelobe reduction techniques [9; 10; 11; 12; 13; 14] that have recently been developed to improve the spatial and contrast resolutions of PW imaging. In addition, encoded PWs can be transmitted and compounded for a higher signal-to-noise ratio using Chirp, Barker code, or the Hadamard matrix [5; 17; 18].