Fig 1.
Staring transducer array design for 3D PAT.
(a) A 3D CAD rendering of the plastic shell used to hold the transducers. (b) A 3D sketch of object space in relation to plastic shell. (c) Photograph of a custom-built transducer (left) and front face of the transducer (right). The red scale bar represents 1 cm. (d) Example of a photoacoustic pressure signal from a photoacoustic point source (~100 μm) averaged over 5 triggers acquired with one transducer at 40 MHz sampling rate. The amplitude represents the counts on the digital converter and ranges from ±2048 counts.
Fig 2.
System sensitivity and aliasing as a function of transducer count and sampling rate.
(a) System sensitivity maps of the xy-plane 3.5 mm below center (left column), center plane (middle column), and xy-plane 3.5 mm above center (right column) as a function of transducer count and sampling rate. Maps were normalized to peak system sensitivity per sampling rate. (b) System sensitivity maps showing last row of (a) (96 transducers) normalized to peak system sensitivity across sampling rates. (c) Aliasing maps for the center voxel as a function of transducer count and sampling rate. Planes correspond to those shown in (a). Maps were normalized to peak system sensitivity per sampling rate and per transducer count and then scaled to 20% max for display purposes. (d) Same as (c) but for aliasing for a voxel near the edge of object space.
Fig 3.
Figures-of-merit for system performance.
Figures-of-merit (clockwise from top left: RMSE, PSNR, MAE, and 3D-SSIM) averaged over object space and plotted as a function of transducer count and sampling rate (legend shown in panel (a)).
Fig 4.
Metric maps for system performance as a function of transducer count and sampling rate.
Metric maps for (a) RMSE, (b) MAE, and (c) 3D-SSIM displayed as a function of transducer count and sampling rate in the xy-plane 3.5 mm below center (left column), center plane (middle column), and xy-plane 3.5 mm above center (right column).
Fig 5.
System sensitivity and aliasing for the experimental transducer arrangement and uniform sampling arrangement.
(a) Transducer response profile to a PA point source (~100 μm) averaged over 64000 triggers acquired with one transducer at a 40 MHz sampling rate. The amplitude represents the counts on the digital-to-analog converter and has been normalized to the maximum sensitivity. (b) Point cloud representations of the experimental transducer arrangement (top) and uniform sampling arrangement (bottom). Darker shaded area represents exterior of shell closest to reader. Lighter shaded area represents interior surface of the shell. (c) Same as (b) from a side-view. (d) Normalized sensitivity maps for the two arrangements and scaled to 30% max sensitivity for display purposes. Aliasing maps for the center voxel (e) and a voxel along the left edge (f) shown for the two arrangements (experimental transducer arrangement in the top row and uniform sampling arrangement in the bottom row). Each arrangement was independently normalized and scaled to 10% max for display purposes. The image planes are 2 x 2 cm2 and correspond to every other xy-plane of object space (left to right corresponds to bottom (z = -2 cm) to top (z = 1.8 cm) planes at 2 mm step size).
Fig 6.
System sensitivity and aliasing as a function of array angular coverage.
(a) Point cloud representations of transducer arrays as a function of array angular coverage (top to bottom corresponds to 0° to 60°). Side views are shown in the right-hand column. (b) Normalized sensitivity maps (scaled to 30% max for display purposes) for each array coverage angle (top to bottom row corresponds to 0° to 60°). (c) Independently normalized aliasing maps (scaled to 10% max for display purposes) for the center voxel and left edge voxel (d) for each array coverage angle. Image planes correspond with those in Fig 5.
Fig 7.
System sensitivity and aliasing as a function of array radius.
(a) Normalized sensitivity maps (scaled to 30% max for display purposes) for each array radius (top to bottom corresponds to 37.5 mm to 87.5 mm, respectively, and Φ = 15°). (b) Independently normalized aliasing maps (scaled to 10% max for display purposes) for the center voxel and left edge voxel (c) for each array radius. Image planes correspond with those in Fig 5.
Fig 8.
Effects of transducer arrangement on system performance.
Metric maps for (a) RMSE, (b) PSNR, (c) MAE, and (d) 3D-SSIM displayed for both experimental transducer arrangement (top row) and uniform sampling arrangement (bottom row). (e)-(h) System performance figures of merit (RMSE, PSNR, MAE, and 3D-SSIM reading clockwise starting from top left panel) plotted as a function of cube contours for the two arrangements (legend shown in panel (e)).
Fig 9.
Effects of angular coverage on system performance.
Metric maps for (a) RMSE, (b) PSNR, (c) MAE, and (d) 3D-SSIM displayed as a function of array angular coverage (top to bottom corresponds to 0° to 60°). (e)-(h) System performance figures of merit (RMSE, PSNR, MAE, and 3D-SSIM reading clockwise starting from top left panel) plotted as a function of cube contours with varying array angular coverage (legend shown in panel (e)).
Fig 10.
Effects of array radius on system performance.
Metric maps for (a) RMSE, (b) PSNR, (c) MAE, and (d) 3D-SSIM displayed as a function of array radius (top to bottom corresponds to 37.5 mm to 87.5 mm). (e)-(h) System performance figures of merit (RMSE, PSNR, MAE, and 3D-SSIM reading clockwise starting from top left panel) plotted as a function of cube contours with varying array radius (legend shown in panel (e)).