# Modelling Sensor Directivity In 3D Example

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.

## Defining a large element detector

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

```% define a large area detector
sz = 16;        % [grid points]
sensor.mask = zeros(Nx, Ny, Nz);
sensor.mask(Nx/2 + 1, (Ny/2 - sz/2 + 1):(Ny/2 + sz/2 + 1), (Nz/2 - sz/2 + 1):(Nz/2 + sz/2 + 1)) = 1;
```

## 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
radius = 20;    % [grid points]
points = 11;
circle = makeCartCircle(radius * dx, points, [0, 0], pi);
circle = [circle; zeros(1, points)];

% find the binary sensor mask most closely corresponding to the cartesian
% 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;   % [Hz]
source_mag = 1;         % [Pa]
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);
```

## 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.

```% run a simulation for each of these sources to see the effect that the
% angle from the detector has on the measured signal
for source_loop = 1:points

% 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 grid point 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. 