DAS3 Delay-And-Sum of volume (3-D) signals

DAS3 beamforms the RF or I/Q volume signals.

Contents

Syntax

BFSIG = DAS3(SIG,X,Y,Z,DELAYS,PARAM) beamforms the RF or I/Q signals stored in the array SIG, and returns the beamformed signals BFSIG. The signals are beamformed at the points specified by X, Y and Z.

TRY IT! Enter das3 in the command window for an example.

SIG must be a 2-D array. The first dimension (i.e. each column) corresponds to a single RF or I/Q signal over (fast-) time, with the COLUMN #n corresponding to the ELEMENT #n of PARAM.elements.

DELAYS are the transmit time delays (in s). The number of elements in DELAYS must be the number of elements in the array (which is equal to size(SIG,2)). If a sub-aperture was used during transmission, use DELAYS(i) = NaN if element # i of the linear array was off.

PARAM is a structure that contains the parameter values required for DAS beamforming (see below for details).

Note: SIG must be complex when beamforming I/Q data (i.e. SIG = complex(I,Q) = I + 1i*Q).

Note: DASMTX3

DAS3 calls DASMTX3. DASMTX3 creates a DAS matrix.

If you need to beamform a large series of ultrasound signals acquired with a same probe and a same transmit sequence, DASMTX3 is recommended. BEWARE, however. DASMTX3 can generate tall sparse DAS matrices when beamforming large volume data! Consider chunking your datasets.

DAS3 chunks the input data (X,Y,Z) automatically to avoid using too large matrices.

Other syntaxes

DAS3(SIG,X,Y,Z,PARAM) uses DELAYS = param.TXdelay.

DAS3(...,METHOD) specifies the interpolation method. The available methods are decribed in NOTE #3 below.

[M,PARAM] = DAS3(...) also returns the structure PARAM with the default values.

The structure PARAM

PARAM is a structure that contains the following fields:

Passive imaging

PARAM.passive: must be true for passive imaging (i.e. no transmit). The default is false.

Notes

Conventional axes are used:

The X-axis is PARALLEL to the transducer. The Z-axis is PERPENDICULAR to the transducer and points downward (Z = 0 at the level of the transducer, Z increases as depth increases). The Y-axis is such that the coordinates are right-handed. These axes are represented in the following figure.

DAS3 uses a standard delay-and-sum. Phase rotations are included if I/Q (complex) signals are beamformed.

By default DAS3 uses a linear interpolation. To specify the interpolation method, use DAS3(...,METHOD), with METHOD being:

The linear interpolation (it is a 2-point method) returns a matrix twice denser than the nearest-neighbor interpolation. It is 3, 4, 5, 6 times denser for 'quadratic', 'lanczos3', '5points', 'lanczos5', respectively (they are 3-to-6-point methods).

Example: Two-way PSF for a focused wave by a 32x32 matrix array

This example shows how to simulate RF signals then beamform I/Q signals

Create a 3-MHz matrix array with 32x32 elements.

param = [];
param.fc = 3e6;
param.bandwidth = 70;
param.width = 250e-6;
param.height = 250e-6;

Specify the x- and y-coordinates of the elements.

pitch = 300e-6; % pitch (in m)
[xe,ye] = meshgrid(((1:32)-16.5)*pitch);
param.elements = [xe(:).'; ye(:).'];

Use TXDELAY3 to calculate the transmit delays for a focused wave.

x0 = 0; y0 = 0; z0 = 3e-2;
txdel = txdelay3(x0,y0,z0,param);

Plot the transducer with VIEWXDCR.

p = viewxdcr(param);
p.FaceVertexCData = txdel(:)*1e9;
title('32\times32-element matrix array')
c = colorbar('SouthOutside');
c.Label.String = 'TX delays (ns)';

Calculate the pressure field with PFIELD3.

n = 24;
[xi,yi,zi] = meshgrid(linspace(-5e-3,5e-3,n),linspace(-5e-3,5e-3,n),...
    linspace(0,6e-2,4*n));
RP = pfield3(xi,yi,zi,txdel,param);

Have a look at the RMS pressure field.

figure
slice(xi*1e2,yi*1e2,zi*1e2,RP,0,0,3)
set(gca,'zdir','reverse')
zlabel('[mm]')
shading flat
axis equal
colormap([1-hot;hot])
hold on
plot3(xe(:)*1e2,ye(:)*1e2,0*xe(:),'.')
title('Focused field by the 32{\times}32 matrix array')

Simulate RF signals by using SIMUS3.

[RF,param] = simus3(x0,y0,z0,1,txdel,param);

Demodulate the RF signals with RF2IQ.

IQ = rf2iq(RF,param);

Create a 3-D grid for beamforming.

lambda = 1540/param.fc;
[xi,yi,zi] = meshgrid(-2e-2:lambda:2e-2,-2e-2:lambda:2e-2,...
    2.5e-2:lambda/2:3.2e-2);

Beamform the I/Q signals with DAS3.

IQb = das3(IQ,xi,yi,zi,txdel,param);

Obtain the log-envelope.

env = abs(IQb);
I = 20*log10(env/max(env(:)));

Display the two-way PSF.

figure
I(1:round(size(I,1)/2),1:round(size(I,2)/2),:) = NaN;
for k = [-40:10:-10 -5 -1]
    isosurface(xi*1e2,yi*1e2,zi*1e2,I,k)
end
view(-60,40)
colormap([1-hot;hot])
c = colorbar;
c.Label.String = 'dB';
box on, grid on
zlabel('[cm]')
title('PSF at the focal point [dB]')

See also

cite, das, dasmtx3, simus3, txdelay3

References

About the author

Damien Garcia, Eng., Ph.D.
INSERM researcher
Creatis, University of Lyon, France

websites: BioméCardio, MUST

Date modified

Published with MATLAB® R2022a