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Drag the teal surface or the point target; drag elsewhere to orbit, scroll to zoom. The track's motion is drawn five times larger than it is.
Swipe sideways to orbit.

The surface of focus

A synthetic aperture sonar draws the seabed on a chosen image surface, and anything standing off that surface is displaced. Whenever the vehicle's path is not straight it is blurred as well: a point target 5 m above the surface is drawn about 2.5 m nearer the track and, under chop, loses about 9 dB of peak.

Tour

Above the surface
Drawn nearer the track
Along-track shift
Synthetic aperture
Peak loss
80 % energy width

Controls

Point target height
Vehicle motion
Sound speed assumed
Aperture used

SAS image of the patch

loading

8 m × 8 m, along-track up, range 12 to 20 m to the right · × where the point stands · ○ where it is drawn

Point target, 1.2 m

−400 dB

Along-track cut

Range cut

Method

Simulation and image formation

The sonar is the array described throughout this site: 36 receivers 30 mm long at 300 kHz with 60 kHz of bandwidth, on a track 10 m above a flat sand bed. It advances 34 phase-center spacings per ping, so that consecutive pings share two phase centers; a phase center is the midpoint between the transmitter and a receiver. The seabed is simulated with ApertureLab's point-scatterer engine at 20,000 scatterers per square meter, with the objects as meshes and their acoustic shadows cast by the simulator. The vehicle sways and heaves sinusoidally, the heave about half the sway at 1.3 times its frequency, and the beamformer is always given the true path.

Every image is a time-domain back-projection on a 1.25 cm pixel grid with no glint suppression, formed on a flat surface at the height and with the sound speed that the controls set. Images are shown through the dataset's display chain with one fixed brightness scale per aperture, so that a blurred point is drawn dimmer than a focused one. 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 numbers in the readout are measured on that response.

The steps that lead up to a synthetic aperture are described on Why synthetic aperture?, and the full imaging chain, including micronavigation, on Image formation. On a circular track the image surface becomes a true plane of focus, a case described on The plane of focus in circular SAS. The effect of faults in the sonar's own hardware on the same scene is shown on Hardware faults.

The point-target panel is 1.2 m on a side, along-track up and range to the right, and is centered on where the point's energy landed. It is in decibels against a perfectly focused point; its cuts run through the brightest pixel, with the dashed line at −3 dB. Slow swell is 5 cm of sway over a 20 m wavelength and chop 15 cm over 6 m. The images were computed ahead of time for every combination of the controls, 792 in all.

The format of this page follows Ryan Sael's interactive explainer of a camera lens's plane of focus.