A straight-track synthetic aperture sonar has no true plane of focus: The surface of focus shows how it draws a point at the wrong height in the wrong place but still sharp, and blurs it only when the vehicle moves off its line. Circular synthetic aperture sonar (CSAS), in which the vehicle circles a patch of seabed and views it from every direction, behaves differently, and the difference matters to anyone who processes or interprets its imagery: the depth plane the beamformer is given becomes a real plane of focus, sharp on the plane and ruinously soft off it.
The scene below is the same patch and the same objects as on the straight-track page, a wedge, a truncated cone, a cylinder and a point target, seen from a 60 m diameter orbit. The teal sheet is the depth plane; drag it up and down, or set the point target's height. Every image was made by ApertureLab's own simulator and beamformer, and the controls step through the settings those images were computed for.
Point target image
North-south cut, dB against offset in cm
East-west cut, dB against offset in cm
Controls
Point target
8 m × 8 m at the centre of the orbit, north up, east to the right. × where the point target stands · ○ the ring the geometry predicts
This is the whole patch, beamformed onto the same plane with the same settings: sand at 20,000 scatterers per square metre, the wedge, truncated-cone and cylinder meshes of ApertureLab's dataset, and the point target. Seen from every side, each object is outlined all the way round.
Each image is shown with its own brightness scale, because a defocused circular image gathers more energy near the centre of the orbit than a focused one; the point-target panel keeps one fixed reference and carries the quantitative loss.
1 of 3
On a straight track, every point at the same closest range produces the same range history, so a point above the seabed is laid over toward the track but stays sharp. On a circle there is no single direction to lay it over toward. Each part of the orbit lays the point over toward itself, by the same distance, so the aperture as a whole draws it in every direction at once: as a ring centred on where it stands, with a radius equal to its layover.
Only points on the depth plane escape this, because only for them does every direction agree. A point target 3 m above the plane is drawn as a ring about 0.7 m in radius and keeps only a small fraction of its peak.
2 of 3
Raise the depth plane to the point target's 3 m and it focuses to a dot again, while the seabed, now 3 m below the plane, dissolves into rings and the objects become arcs. Lowered beneath the bed, the plane does the same to the seabed from the other side. This is a lens focused at one distance, as sharp a plane of focus as any camera has, and it is why circular imagery is formed on a measured surface of the seabed rather than on a flat plane.
3 of 3
If the beamformer assumes 1530 m/s in water that carries sound at 1500 m/s, every range comes out 2 percent long. On a straight track that mostly stretches the image; on a circle each direction pushes the point away from itself by the same amount, which is another ring, and the point on the bed defocuses as a raised point does.
How the figures are made
The sonar is the site's standard array, 36 receivers 30 mm long at 300 kHz with 60 kHz of bandwidth, flown clockwise round a circle of 30 m radius, 8 m above a flat sand bed, looking inward, with consecutive pings sharing two phase centres. The seabed is simulated with ApertureLab's point-scatterer engine at 20,000 scatterers per square metre, the objects as meshes with their shadows cast by the simulator. The orbit is a perfect circle.
Every image is a time-domain back-projection of all 370 pings, formed on a flat plane at the height the control sets, with the sound speed the control sets. The point target's own response is isolated by simulating each scene a second time without it and subtracting the two images, which is exact because the imaging chain is linear; the point-target panel and the readout are measured on that response.
For the straight-track counterpart, see The surface of focus; for the imaging chain, see Image formation.