A sonar that circles a patch of seabed sees it from every side, so the depth plane given to its beamformer becomes a true plane of focus. A point on the plane is sharp; a point target 3 m above it is drawn as a ring 0.7 m in radius and loses about 34 dB of peak.
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Across the depth planes
Ring radius (cm) against plane height (m)
Peak loss (dB) against plane height (m)
Dots: measured on the images for this point height, path and sound speed. Line: the ring the geometry predicts. Pick a dot to move the plane there.
Controls
SAS image of the patch
8 m × 8 m, north up · × where the point stands · ○ predicted ring
Point target response 4 m across
North-south cut dB, cm
East-west cut dB, cm
Method
The sonar is the site's standard array: 36 receivers 30 mm long at 300 kHz with 60 kHz of bandwidth. It is flown clockwise around a circle of 30 m radius, 8 m above a flat sand bed, looking inward, with consecutive pings sharing two phase centers. The seabed is simulated with ApertureLab's point-scatterer engine at 20,000 scatterers per square meter, with the wedge, truncated-cone and cylinder meshes of ApertureLab's dataset and a point target. Each image is a time-domain back-projection of all 370 pings on a 1.25 cm grid, formed on a flat plane at the height and with the sound speed that the controls set. The path error adds 5 mm of sway, and heave of about half that, over each 6 m of track to the path given to the beamformer. The point target stands 5 mm above its stated height, clear of the sand's relief, so the planes 1 and 2 cm either side of it are not quite symmetric about it.
The point target's own response is isolated by simulating each scene a second time without it and subtracting the two images; the subtraction is exact because the imaging chain is linear. The point-target panel and the readout are measured on that response, in decibels against a perfectly focused point, or against the point's own peak when Scale to own peak is ticked. The point-target panel is drawn at the image's 1.25 cm pixels and shows the smallest of 25 cm, 50 cm, 1 m, 2 m and 4 m that holds the response; the two cuts run north-south and east-west through the pixel where the point stands, over the same width. The charts under the readout plot, for every depth plane, the radius holding 80 % of the response's energy and its loss of peak, as measured on these images, against the ring the geometry predicts. The seabed image is scaled to its own median brightness so the rings stay visible; holding the compare button shows the image formed with the plane on the bed, the true sound speed and the true path. The straight-track counterpart is The surface of focus, and how the length and position of a straight synthetic aperture set the image is shown on Aperture length and position. The imaging chain is described on Image formation, and the effect of faults in the sonar's hardware on an image is shown on Hardware faults.