## 2 Materials and Methods
### Characterization of the Imaging Performance
#### 2.5.2 The CyR  
The CyR was introduced by [PERSON] et al. [28] to evaluate the effects of side lobes and grating lobes of the point-spread function (PSF) on the contrast of ultrasound images. The CyR is expressed as the minimum detectable size of anechoic structures embedded in a speckle-generating background. Instead of evaluating the detection of anechoic cysts of various sizes, [PERSON] et al. [29] suggested using the image of the concentric PSF with a spherical void \(c\). The CyR is then defined as the size of the spherical void that produces a contrast above a given threshold. In 2-D, the cyst contrast \(Cc\) is computed [29] from the ratio of PSF energy outside the void relative to the total PSF energy:  
\[Cc_{dB}=10 log_{10}\left(\frac{\iint_{(x,z)\
eq c}{h^{2}(x,z,x_{0},z_{0})dxdz}}{ \iint{h^{2}(x,z,x_{0},z_{0})dxdz}}\right), \tag{5}\]  
where \(h(x,z,x_{0},z_{0})\) is the image of a point-like object centered at \((x_{0},z_{0})\), which stands for the PSF function.  
For 3-D imaging, [PERSON] et al. [13] suggested to use the line spread function (LSF) instead of the PSF to access the CyR because the LSF is easier to measure experimentally and has a larger dynamic range. In our case, we were interested in measuring the effect of the scan parameters on the image quality. Therefore, we wanted to evaluate the CyR in xz-planes (perpendicularly to the rotation axis), using the LSF in the y-direction (along the rotation axis). Phantom Ph3 allowed us to compute a robust estimate of the LSF with little background noise. The \(Cc\) contrast was computed using the slice at \(y=0\) (center of the array) and the two closest uncorrelated xz-slices located at \(y=\pm 0.86\)mm. Each slice was a disk of \(25\times\lambda_{\text{c}}\) diameter, which was a compromise between the need to encompass the entire spatial extent of the LSF and the need to avoid overlap between neighboring LSFs. To obtain a smooth \(Cc\) curve, the images were oversampled by a factor 2 in the xz-plane (\(yx=pz=36\) um). Because we expected anisotropy of the LSF, we extended the definition of the \(Cc\) and we proposed a sectorial cyst contrast.  
We can then introduce a general definition of \(Cc\) as:  
\[Cc_{dB}^{T}=10 log_{10}\left(\frac{E_{T}^{out}}{E_{T}^{tot}}\right), \tag{6}\]  
\[E_{T}^{out}=\sum_{ny=-1}^{1}\iint\limits_{(x,z)\in\{T\backslash c\}}{h^{2} \left(x,y,z,x_{0}^{y},z_{0}^{y}\right)dxdz}, \tag{7}\]  
\[E_{T}^{tot}=\sum_{ny=-1}^{1}\iint\limits_{(x,z)\in T}{h^{2}\left(x,y,z,x_{0}^{ y},z_{0}^{y}\right)dxdz}, \tag{8}\]  
where \(T\) is either the entire slice (Equation (6) is equivalent to (5) but for the LSF) or an angular sector of the slice (leading to sectorial contrast), \(c\) is the disk-shaped void, and \(T\backslash c\) is the set of elements of \(T\) but not in \(c\). The sectorial contrast was computed in angular sectors of \(\pi/10\). The \(h\left(x,z,y,x_{0}^{y},z_{0}^{y}\right)\) is the image of the LSF, at a given \(y\), and centered at \(\left(x_{0}^{y},z_{0}^{y}\right)\), the coordinates of maximum amplitude of this LSF image.  
Similarly to [PERSON] et al. [29], we defined CyR as the cyst radius that produces a contrast \(Cc_{dB}\) of \(-20\) dB. For the entire disk-shaped slice, this definition of CyR is called isotropic cystic resolution, iCyR, in the following. For a sector, the sectorial cyst resolution is called anisotropic cystic resolution, aCyR.