## Appendix B  
In Appendix B, we explain the theoretical basis for choosing the angular sampling periods \(\Delta\alpha\) for the rotate-translate scan. The translation period for the rotate-translate scan was set to \(\Delta I=H\), as discussed in Section 2.2. Additionally, we justified the translation sampling period chosen for the benchmark translation-only scan.  
For the rotate-translate scan, the angular sampling problem was related to two different configurations: sampling for a circular ring array [22] and linear sampling with finite size transducers [24]. First, [PERSON] et al. [22] derived a spatial sampling criterion for imaging objects within a circular array comprised of point transducers deployed over the entire circular aperture. In such a case, the angular sampling period \(\Delta\alpha\) depends on the maximal radial dimension \(r\) of the imaged object and should be adjusted so that \(\Delta\alpha<\lambda_{\mathrm{c}}/(2\times r)\) to reject grating lobes outside of the imaged area. The wavelength \(\lambda_{\mathrm{c}}\) is the wavelength at the center frequency of the transducer. There was no fixed center of rotation in the coordinate system (O, \(\mathbf{e_{v}}\), \(\mathbf{e_{y}}\), \(\mathbf{e_{z}}\)) in our synthetic rotation array; however, we may consider that the rotation occurs around each point in the imaged area and, due to the amplitude masks in the reconstruction process, \(r\) could be replaced by \(d_{\mathrm{u}}=0.6\times\lambda_{\mathrm{c}}\)\(\times\) f-number. In this case, the sampling criterion would be \(\Delta\alpha<1/(1.2\times\) f-number). This solution is independent of \(\lambda_{\mathrm{c}}\). Second, [PERSON] et al. [24] noted that the finite size of a transducer element acts as a low-pass spatial filter reducing the Nyquist-Shannon frequency compared to point detectors. For a synthetic planar array comprised of disk transducers of radius \(a\), [PERSON] et al. showed that an analysis in the spatial Fourier space leads to a sampling frequency equal to \(a/4\), as opposed to the sampling frequency of \(\lambda_{\mathrm{c}}\) / 2 that would be required for point detectors [24]. We applied similar reasoning. The angular aperture of the transducer was \([-\beta,\,\beta]\) with \(\beta=\mathrm{atan}(D/(2\times F))\approx 1/(2\times\) f-number) (Figure 1a). Therefore, in the Fourier space, the maximum angular frequency could be considered to be equal to \(1/(2.\beta)\). Thus, the minimum angular sampling frequency could be set to \(1/\beta\), and \(\Delta\alpha\leq\beta\). This solution is also independent of \(\lambda_{\mathrm{c}}\) and it is more restrictive than the criterion based on the circular array. However, in order to be sure to discard any aliasing effects, the maximum angular frequency can be considered as equal to \(1/\beta\) or \(2/\beta\). These frequencies lead to angular sampling periods equal to \(\Delta\alpha=\beta/2\) and \(\Delta\alpha=\beta/4\), respectively.  
For the scans using only a translation, we applied the criterion based on the analysis developed for linear sampling with finite-size transducers [24]. For our focused transducer, we considered that the transducer could be modeled as a segment of length \(H\) located at the focus where \(H\) is the two-way FWHM of the ultrasound beam. Therefore, an appropriate sampling period for translation is \(\Delta I=H/8\)[24].