k-Wave Toolbox

Modelling Sensor Directivity in 3D Example

Overview

This example demonstrates how the sensitivity of a large single element detector varies with the angular position of a point-like source. It is a 3D version of the Modelling Sensor Directivity in 2D example.

• open the file in the MATLAB Editor
• run the file in MATLAB

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Defining a large element detector

The sensor is defined as a large area detector in the shape of a rectangle.

% define a large area detector 
sensor.mask = zeros(Nx, Ny, Nz);
sensor.mask(Nx/2+1, (Ny/2-9):(Ny/2+11),(Nz/2-9):(Nz/2+11)) = 1;

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Defining a collection of point sources

Equi-spaced point sources are then defined at a fixed distance from the centre of the detector face. To do this, the Cartesian coordinates of the points are calculated using makeCartCircle. A binary source mask corresponding to these Cartesian points is then calculated using cart2grid. The indices of the matrix elements for which the binary mask is equal to 1 (the source points) are found using find.

% define equally spaced point sources lying on a circle centred at the
% centre of the detector face 
Nangles = 11;
circle = makeCartCircle(25*dx, Nangles, [0, 0], pi);
circle = [circle; zeros(1, Nangles)];

% find the binary sensor mask most closely corresponding to the cartesian
% points coordinates from makeCartCircle
circle3D = cart2grid(kgrid, circle);

% find the indices of the sources in the binary source mask
source_positions = find(circle3D == 1);

A time varying pressure source is defined to drive the point sources.

% define a time varying sinusoidal source
source_freq = 0.25e6;
source_mag = 1;
source.p = source_mag*sin(2*pi*source_freq*kgrid.t_array);

% filter the source to remove high frequencies not supported by the grid
source.p = filterTimeSeries(kgrid, medium, source.p);

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Running simulations for each point source

For each point source, a new binary source mask is defined, and the simulation is run. When each simulation has finished, the returned sensor data is summed together to mimic a single large detector.

for source_loop = 1:length(source_positions)
    
    % select a point source
    source.p_mask = zeros(Nx,Ny,Nz);
    source.p_mask(source_positions(source_loop)) = 1;

    % create a display mask to display the transducer
    display_mask = source.p_mask + sensor.mask;

    % run the simulation
    input_args = {'PMLSize', 10, 'DisplayMask', display_mask, 'PlotScale', [-0.2 0.2], 'PlotFreq', 50,  'DataCast', 'single'};
    sensor_data = kspaceFirstOrder3D(kgrid, medium, source, sensor, input_args{:});

    % average the data recorded for each pixel to simulate the measured signal
    % from a large aperture, single element, detector
    single_element_data(:,source_loop) = sum(sum(sensor_data,1),1);

end

The maxima of the time series, one per source position, are plotted below as a function of the angle between the detector plane and a line joining the point source and the centre of the detector face. The directionality introduced by the large size of the detector is clearly seen.

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Modelling Sensor Directivity in 2D

Sensor Element Directivity in 2D

© 2009-2014 Bradley Treeby and Ben Cox.