Image formation from raw sonar returns

The raw data from a sonar array are a complex time series per channel per ping, pressure against time, with no image in them. The image is constructed afterwards by estimating where the platform was when each return was recorded and summing the returns so that energy from the same patch of seabed arrives in phase. A platform position error of a fraction of a wavelength blurs the image.

Processing chain from raw cube to focused image

The pipeline runs in a fixed order, and each stage is checkable against the file's own recorded attributes rather than against an assumption made at the top.

Load the raw cube and check it against the physics the file declares: sound speed, sample rate, array geometry.

Zero-phase lowpass, then matched filtering, which compresses each long transmitted chirp into a sharp pulse and is where range resolution comes from.

Cross-ping time-varying gain, so returns from 90 m are comparable to returns from 10 m, and glint suppression for specular flashes that would otherwise dominate the dynamic range.

Eight-times range upsampling, so the back-projection can interpolate without quantizing delay.

Micronavigation, which measures where the platform actually went.

Time-domain back-projection on the GPU, producing a single-look complex image on a georeferenced grid.

Dynamic-range compression for viewing.

A left-to-right pipeline diagram titled How a SAS/SAR image is made. Raw I/Q time-series and navigation feed into filtering and pulse compression, then motion estimation by micronavigation, then image formation by back-projection, producing a single-look complex image, then post-processing for dynamic range, ending in a human-readable seafloor image. Each stage shows a small example of its data: I/Q traces, a compressed pulse, an estimated sway track, focusing arcs, complex speckle, a tone curve, and a real focused sonar image.

The same chain as a figure, from raw I/Q and navigation to a focused seafloor image, with each stage shown carrying its own data at that point in the chain. How a real echo on its carrier becomes the I/Q samples at the start of the chain is the subject of Why baseband?

Back-projection, wavenumber and real-aperture beamformers

Time-domain back-projection is the production path. It makes no assumption that the platform flew straight: it handles continuous motion, six-degree-of-freedom attitude, curved tracks, and circular collections, and because it is geometry-driven rather than band-specific it also focuses airborne radar.

Wavenumber (omega-k) processing is the exact inverse of the Fourier-wavefield forward model, so each serves as a consistency check on the other; it assumes stop-and-hop motion.

Real-aperture stacking forms conventional side-scan imagery, so one scene can be compared across both imaging regimes.

9.6 Mpx in 9.6 s

a 2400 by 4000 pixel image at 2.5 cm, against 134 s of collection time, or about fourteen times faster than the sonar collects the data

Track estimation from the echoes

Inertial navigation is not accurate enough to focus a synthetic aperture. At 300 kHz the wavelength is 5 mm, and the platform position has to be known to a small fraction of that over an aperture several meters long.

The track is therefore recovered from the data: every ping lays down a row of phase centers, the transmitter-receiver midpoints, spaced half a channel apart. The vehicle advances a whole number of those spacings between pings, two short of the array, so consecutive pings share two phase centers. The instrument the fidelity page measures has 36 phase centers per ping and advances 34 spacings, so the two fore-most centers of one ping are re-occupied by the two aft-most of the next. Those repeated centers observed the same patch of seabed from the same place, so comparing the phase of the two recordings measures how far the vehicle moved rather than how far it was commanded to. The per-pair delay estimates are then fitted into a per-ping sway and heave history, which the beamformer uses instead of the nominal line. The fit is a Huber-robust least squares, which keeps a handful of bad correlations from dragging the whole track.

Even a perfectly measured track leaves one error behind: it corrects the path exactly only for points on the surface being imaged. How motion then blurs objects that stand above that surface is shown interactively in The surface of focus. What a fault in the receivers or their electronics does to the same chain, from the raw ping to the image, is shown in Hardware faults. How a whole survey line images real terrain, and what that terrain hides, is shown in From bathymetry to SAS.

< 0.625 mm

fine delay error at 300 kHz, one eighth of a wavelength, asserted in the test suite at correlation above 0.9

The sound-speed slider on the walkthrough page introduces this kind of error deliberately and shows the resulting blur as it is applied.

Single-look complex product and display image

The beamformer's output is the single-look complex (SLC) image. Its phase is intact, so it supports coherent change detection, interferometry, and sub-aperture analysis, and it is the product intended for model training.

The display image is derived from the SLC image for human viewing: magnitude, an adaptive Schlick tone map that compresses the dynamic range into a displayable one, and a perceptual color map. The chain contains no logarithm, which matters when reproducing the display or comparing levels against it.

A circular-collection synthetic aperture sonar image: a bright ring around a dark disc with ripple structure crossing the center

A circular collection, 360 degrees around one point. Back-projection does not assume a straight track, so every facet of a target is resolved from at least one aspect.