Predicting backscatter along the dorsal, ventral, or lateral surfaces of a fish at any spatial orientation requires an accurate representation of the animal's morphometry in three dimensions. Below is a cylindrical representation of a 107 mm Namibian pilchard (Sardinops ocellatus) body and swimbladder from data used in KRM backscatter models.
The swimbladder is tilted approximately 8o posterior relative to the sagittal axis of the fish. Axes units are in mm, cylinder lengths are 10 mm for the fish body and 2 mm for the swimbladder. Radiographs are digitized at 1 mm when compiling data for KRM models. Since radiographs are dorsal and lateral view planes of the animal, we elliptically interpolate points between the two planes at 15o intervals to calculate backscatter for specified roll aspects.
Backscatter amplitudes are calculated for 360o of tilt, yaw, and roll over a range of frequencies to produce a three-dimensional backscatter matrix. The graphic portrayal of a backscatter volume is called the 'backscatter ambit' of a fish at a specified frequency.
The graph above is the backscatter ambit of a 107 mm pilchard at 120 kHz. Amplitude is measured by distance from the origin and by color where blue is low and red is high. Backscatter predictions are resolved at 15o in the tilt plane and 15o in the roll plane. Orientation of the fish matches that of the wireframe figure above.
Visualization of the backscatter ambit graphically depicts the effects of tilt and roll on echo amplitude. Maximum amplitude occurs at approximately 92o which corresponds to a head down tilt of 8o and puts the swimbladder orthogonal to the incident wave front. Backscatter from the head on or tail on orientation is significantly less than dorsal or lateral orientations. The lateral symmetry observed in the ambit is due to the use of dorsal cylinder widths when representing the fish body and swimbladder.
The ability to predict backscatter in three dimensions has many applications. The increased availability of broadband, multi-frequency, multibeam, and sector-scanning sonars provides a new suite of tools for aquatic researchers. These tools increase the amount of information collected relative to scientific echosounders by increasing the frequency range or the number of perspectives (i.e. beams) used to view an aquatic environment. The combination of backscatter models with enhanced frequency or volume measurements improves the estimation, measurement, and visualization of fish aggregation backscatter; the behavior of individuals within aggregations; acoustic shadowing; abundance and biomass estimates; and contributes to the acoustic classification and identification of fish species.
Models may also be used to create computer animations of data collection as target backscatter changes through time. These applications are useful in simulating echograms from individual fish as well as large schools.