## 4 Discussion  
We experimentally investigated the performance of a synthetic aperture rotate-translate approach for volumetric US imaging with a linear ultrasound array. In the elevation direction of the array, this approach demonstrated the synthesis of an angular aperture several times larger than the aperture provided by the native elevation focus of the array. The aperture was increased by a factor of 5 and a Hamming apodization was implemented. As a result, the elevation resolution was improved by a factor of 3 compared to a translate scanning approach. Moreover, the aperture synthesis in the elevation plane was obtained over a large area (the DSCA): An area of 4.5 cm\({}^{2}\) was covered here with a translation range of 3 cm. The elevation resolution was confirmed to be homogeneous in this area. Therefore, the rotate-translate scan was shown to yield superior image quality compared with a translation scan. To the best of our knowledge, this study is the first demonstration that 3-D ultrasound imaging can be performed with a rotate-translate scanning scheme combined with coherent compounding. A similar scanning approach had previously been proposed for photoacoustic (PA) tomography [20]. However, the ultrasound sources in PA imaging are the illuminated optical absorbers. For PA imaging the transducer is scanned to a  
Figure 10: Images of a 3-D net. (**a**) Optical picture of the top of phantom Ph4. A paper cylinder was inserted in the net to mask the lower part; (**b,d,e**) display of a volumetric image of Ph4 for a rotate-translate scan at \(\Delta\alpha_{2}\) with a steered transmit; (**b**) MAP image along z-axis of the top part of the volumetric image (part of the volume with z-coordinates smaller than the yellow dotted line in (**d**)); (**d**) MAP image along y-axis; (**e**) MAP image along x-axis of the left part of the volume (part of the volume with x-coordinates smaller than the green dotted line in (**d**)). The voxels outside of the DSCA were discarded for the MAP for (**b,e**); (**c,f**) display images extracted from the volumetric rendering of Ph4 for a translation-only scan; (**c**) MAP image along z-axis for the same volume as (**b**); (**f**) MAP image along x-axis for the same volume as (**e**); the color scale for (**b–f**) is between \(-\)30 and 0 dB. Knots are identified with numbers that serve as landmarks. Pink arrows indicate threads that appear discontinuous in the image for the translation-only scan and are better mapped with the rotate-translate scan. different orientation after each laser pulse to receive the ultrasound wavefield generated by absorbers in the medium. For US imaging, the ultrasound waves are both emitted and captured by the scanned US transducer array. As a consequence, the backscattered echoes from different orientations of the exciting US beam need to be recombined coherently to generate a high-quality image. This concept has been extensively used for plane-wave ultrasound imaging [8] and synthetic aperture imaging [31] with a fixed transducer array. However, in this case, the field of view and the accessible orientations are limited by the number and geometrical properties of the elements of the array. Coherent compounding was also recently shown for 2-D imaging using multiple transducer arrays with different orientations [32] or a rotation scan of an array [33]. Such approaches increase the angular aperture and the lateral resolution but the transducer arrays were always oriented within the same imaging plane. Similar results were obtained in 2-D PA imaging [34]. Here, we performed 3-D synthetic aperture scanning by applying coherent compounding from tomographic positions of the array with both different angular elevation orientations and different elevation spatial positions. Additionally, we combined the coherent summing of echoes obtained from different tomographic positions with the summing of echoes from beams electronically steered to different angles. For each steered angle, a data set with the same translation and angular sampling periods was recorded.