## 4 Discussion
The steered angles were chosen to ensure uncorrelated transmitted wave vectors. As a consequence, the coherent summation over all the steered angles during the reconstruction process reinforced coherent echoes and reduced incoherent noise, which led to image contrast enhancement. The proposed rotate-translate scanning scheme is novel for 3-D US imaging. Furthermore, since both PA and US imaging use the same detector, acquisition parameters optimized for one imaging modality can be applied directly to the other. We benefited from previous innovations in rotate-translate PA tomography such as continuous scanning [27] that showed a reduction in the scan duration. We further reduced the scan duration by more fully assessing the needs in terms of angular sampling. Two main improvements were made to angular scanning. (1) The angular spacing was chosen based on the elevation focusing of the array and (2) a spatial density taper was applied. The smallest angular period considered here, \(\Delta\alpha_{3}\), is three times larger than the angular period in [20]: \(\lambda_{\text{c}}/F=0.7^{\circ}\). Therefore, the optimization of the angular spacing reduced the number of tomographic positions by at least a factor of 3. Additionally, the spatial density taper reduced the number of tomographic positions by about 40% and reduced side lobes of the PSF in the elevation plane without any additional amplitude apodization. Indeed, strong side lobes were expected at \(\pm 45^{\circ}\) with no apodization, but due to the spatial density taper used here they were not stronger at \(45^{\circ}\) than at \(0^{\circ}\) (Figure 8b). Finally, the total number of tomographic positions was thus reduced by at least by a factor of 5 (80% decrease) relative to the number previously reported in [20]. Three different angular periods, \(\Delta\alpha_{1}\approx 8^{\circ}\), \(\Delta\alpha_{2}\approx 4^{\circ}\), and \(\Delta\alpha_{3}\approx 2^{\circ}\), were tested. The number of tomographic positions and the scan duration increased by a factor of 2 when the angular period was divided by 2 (Table 1). Metrics were computed to evaluate the impact of the angular sampling period on the image quality. We found that \(\Delta\alpha_{1}\) led to a significant degradation of the FWHM resolution along the x-axis compared to \(\Delta\alpha_{2}\) and \(\Delta\alpha_{3}\). Therefore, \(\Delta\alpha_{1}\) was determined to be too loose to prevent side lobes from degrading the main lobe of the PSF. The cystic resolution and the contrast on the edge of an anechoic region were also improved with the decreasing angular period. For the angular sampling, \(\Delta\alpha_{2}\), we performed acquisitions in straight transmit mode and in steered transmit mode. Interestingly, both contrast measurements improved with the addition of steered angles, while the angular sampling was the same. We can explain this result by the enhanced spatial averaging of the \"diffraction noise\" when steered transmits were performed. Moreover, the contrast parameters (\(Cc\) and C0) were found to be similar with the angular sampling \(\Delta\alpha_{2}\) in steered transmit and with \(\Delta\alpha_{3}\) in straight transmit. The steered transmit did not modify the acquisition duration but did substantially increase the size of the data set, while the scan duration at \(\Delta\alpha_{2}\) was half that at \(\Delta\alpha_{3}\). Therefore, a gain in the image quality can effectively be made without compromising the acquisition duration by the addition of a steered transmit. A systematic evaluation of the contrast for different numbers of steered angles was beyond the scope of this paper but is of great interest for our rotate-translate system and will be considered in future studies. The angular periods, \(\Delta\alpha_{2}\) and \(\Delta\alpha_{3}\), will also be implemented in PA tomography.