## 2 Materials and Methods
### Experimental Implementation
#### 2.3.3 Imaging Phantoms  
Four imaging phantoms were used to characterize our 3-D scanner. The phantoms were totally submerged (Figure 3), maintained fixed compared to the water tank, and centered in the imaged volume (Figure 1c).  
The first phantom (Ph1) contained 200-\(\upmu\)m-diameter polyethylene microspheres (BKPMS 180-212 um, Cospheric, Santa, Barbara, CA, USA) embedded in agar gel. The agar gel was prepared with agar powder 2% \(w/v\) (A1296, Sigma Aldrich, St. Louis, MO, USA) in water, and it was molded in 26.5-mm-diameter cylindrical mold. The microspheres had a significant acoustic contrast relative to the embedding medium (on the order of 40 dB). They were randomly, but sparely, distributed over the entire cross section of the cylinder, and could thus be identified individually. Ph1 was placed so that all microspheres had approximately the same y-coordinate, i.e., they all were within a plane perpendicular to the rotation axis. Ph1 was used to validate that the field of view can be adjusted by setting the translation range L (Figure 1c). Moreover, Ph1 enabled us to study the 3-D spatial resolution and its spatial homogeneity.  
The second phantom (Ph2) was prepared with agar powder (2% \(w/v\)) and 1% \(w/v\) cellulose powder (Sigmacell cellulose Type 20) in water. Cellulose particles (20 \(\upmu\)m) act as ultrasound scatterers to mimic the scattering properties of biological tissues for US imaging. The gel was molded in the cylindrical mold with three cylindrical solid inclusions of 5 mm in diameter and of the same length as the mold. The inclusions were removed when the gel was solidified. Thereby, Ph2 contained three cylindrical holes arranged along the vertices of an equilateral triangle centered on the phantom axis. The center-to-center distance between adjacent holes was about 9 mm. The holes were filled with water and Ph2 was placed with the axes of the cylinders aligned with the rotation axis (y-axis). The holes were far enough from each other to be considered as isolated anechoic regions embedded in a speckle-generating medium. They were used to measure the image contrast and its spatial homogeneity.  
Two other phantoms were made of 0.36-mm-diameter polyester threads. The threads were verified to be acoustically scattering; however, the contrast with agar gel was found to be poor. To obtain a higher contrast, the threads were simply placed in water: a non-scattering medium for 5-MHz ultrasound waves.  
The third phantom (Ph3) was composed of four threads parallel to each other and oriented along the rotation axis (y-axis). Three of the threads were arranged along the vertices of an equilateral triangle of 9-mm side length. The fourth thread was at the center of the triangle. Ph3 allowed us to obtain an estimate of line spread function at four positions with a large dynamic range and to derive a contrast metric, named the cystic resolution. The similar spatial arrangement between Ph2 and Ph3 allowed comparison of contrast measurements made with two suitable metrics (see Section 2.5).  
For the last phantom (Ph4), a 3-D net was formed with knots between 12 threads. The net was a complex structure comprised of a thin, homogeneous scattering material. Because the threads were dyed in black, the ultrasound image of Ph4 can be easily compared with optical pictures. Ph4 allowed us to study the ability to image a complex shape with multiple orientations.