A synthetic aperture is built from echoes recorded at many positions along the track. Each position is a stave: one phase center of the HISAS 1030 array, 1.875 cm from the next. At 80 m range the beam reaches a point from 1,707 of them. Which staves are summed sets the image: how many sets the along-track resolution, and where they sit sets the angle from which the patch is seen.
SAS image of the patch
5 m × 5 m, drawn at its native 1.25 cm pixels; along-track up, in meters from the patch center; ground range 77.5 to 82.5 m to the right.
Readout
At the patch center, 80 m out on the seabed and about 82.5 m from the sonar. Range resolution is set by the 30 kHz bandwidth and does not change.
Cut through the sphere
Across the line of sight through the sphere, from the middle of the span, in dB against the full-aperture peak; dashed line −3 dB. For equal weights the −3 dB width is 0.886 times the resolution.
Tour
Pick a step, or drag the span yourself.
The slider is the 1,707 staves over 32 m of track, aft at the bottom, forward at the top. Drag a grip to move one end, the span or its handle to slide it, click the track to jump, or pick a Tour step; the arrow keys nudge one stave.
Method
The sonar is the Kongsberg HISAS 1030 as catalogued on Reference sonars: a 100 kHz carrier with 30 kHz of bandwidth and 32 contiguous receivers 3.75 cm long, so that its phase centers lie 1.875 cm apart. A stave on this page is one phase center. The real beam of a receiver of length D spans Rλ/D of track at range R, 32 m at 80 m, so the most staves any point at 80 m can use is N = 2Rλ/D² = 2 × 80 × 0.015 / 0.0375² = 1,707. Consecutive pings advance 30 phase-center spacings, so the last two receivers of one ping share their phase centers with the first two of the next; where two pairs fall on one stave the page uses the earlier ping's, as ApertureLab's beamformer does.
The track is straight and level and the water is still. The sonar flies at an assumed altitude of 20 m over a sand bed simulated with ApertureLab's point-scatterer engine at 20,000 scatterers per square meter. The four objects scatter as Kirchhoff facets, so each glint follows from the object's shape and the angle it is seen from, and their acoustic shadows are cast by the simulator. Smooth facets alone return only glints and edges, so each object also carries a diffuse surface layer for the roughness and fouling of a real surface. The layer scatters with the sand's own angular law about each face of the object and is 4 dB stronger per unit area than the sand at the same local grazing angle.
The range-compressed echo of every stave over the patch's range window is stored with the page, and the browser back-projects the selected staves onto a 1.25 cm grid with the carrier phase restored, as described on Why baseband?. Each image is therefore formed from the echoes for exactly the staves selected; when the span moves, only the staves that entered or left it are added or subtracted. For every stave, a tenth at broadside, the aft tenth and a single stave, the browser's image matches ApertureLab's own back-projection of the same ping and receiver pairs with a correlation above 0.99999 and a residual 45 dB or more below the image.
The readout gives the along-track resolution as λ / (2 (sin θ2 − sin θ1)), where θ1 and θ2 are the angles from the patch center to the ends of the span, and the range resolution as c / 2B. For equally weighted staves the −3 dB width of a point is 0.886 times the first. Measured on the sphere across the line of sight, the width follows that law to within about 1 percent for spans of up to 513 staves at broadside and to within 3 percent for spans squinted by up to 11 degrees. Over longer spans the elements' own beam pattern weakens the outermost staves and the width grows above the law: the full aperture measures 2.0 cm, against 1.7 cm for equal weights and 1.9 cm with that taper.
Images are shown through the dataset's display chain: the magnitude is compressed by a Schlick curve and mapped to the site's colormap, with one fixed brightness scale set by the full aperture. The median of the full-aperture image is drawn at 30 % of the color scale, and 30 times that median saturates, so a shorter aperture, which sums fewer echoes, is drawn dimmer. The cut through the sphere is formed at 2.5 mm spacing from the same staves as the image, and its −3 dB width is interpolated between those points.
The steps that lead up to a synthetic aperture are described on Why synthetic aperture?. Where an image is in focus, and how objects above the seabed are displaced and blurred, is shown on The surface of focus and, for a circular track, on The plane of focus in circular SAS.