How to Implement Beamforming in Ultrasound Diffraction Tomography

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SUMMARY

This discussion focuses on implementing beamforming in ultrasound diffraction tomography using a BentRay based Time of Flight approach. The experimental setup involves a circular transducer array that collects acoustic time-domain signals, which are then transformed into frequency domain components using FFT. The calculation of the beamforming value I_BF(z) at each pixel requires a double integral involving the Green's function and the scattered wavefield, leading to challenges in accurately computing the integral due to discrete receiver positions. Suggestions include using simplified sources for testing and improving the accuracy of the integral calculations.

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  • Understanding of ultrasound diffraction tomography principles
  • Familiarity with BentRay based Time of Flight methods
  • Proficiency in Fast Fourier Transform (FFT) techniques
  • Knowledge of Green's functions in wave propagation
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TL;DR
Confronted with coding problems in ultrasound diffraction tomography. Please tell me how to perform the correct coding to achieve 2D imaging.
I'm currently working on an ultrasound diffraction tomography algorithm that incorporates a BentRay based Time of Flight approach. In the experimental setup, a circular transducer array is deployed around the region of interest, with each sensor actuated sequentially to collect acoustic time-domain signals. This setup allows us to acquire time-domain signals for all transmitter-receiver combinations, then use FFT to extract frequency domain components.

A critical step in image reconstruction involves calculating the beamforming value I_BF(z) at each pixel, where z=(z_x,z_y) defines the pixel position in the 2D plane. According to equation (13) from my reference material, this requires a double integral over both source and receiver coordinates in the plane, where Gw(x,z) represents the Green's function. However, ψs(x,y) represents the scattered wavefield, which we can only measure at discrete receiver positions. This limitation has led to confusion about how to compute the integral accurately.

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Currently, my approach to calculate I_BF(z) is as follows:
Code: 
I_BF = zeros(Nx, Ny);
for i = 1:Nsrc
    for j = 1:Nrec
        for ipos = 1:Nx
            % Calculate psi_s(i, j)
            for jpos = 1:Ny
                Gw_src = Gw(xx(ipos), yy(jpos), xsrc(i), ysrc(i));
                Gw_rec = Gw(xx(ipos), yy(jpos), xrec(j), yrec(j));
                I_BF(ipos, jpos) = I_BF(ipos, jpos) + psi_s(i, j) / (Gw_src * Gw_rec);
            end
        end
    end
end
I am aware that this method does not account for the scattered field at points not located at the transducer locations. My questions are:

What are the potential pitfalls of my current method?

How can I improve my code to more accurately perform the necessary integrals, considering the limitations of the measured scattered field?

Thank you!
 
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I think it unlikely anyone will do your work here. May I suggest using simplified sources and shapes to run black box tests on the software. These should be situations for which analytical solutions can be obtained. Learning these techniques on simpler systems will also educate your skills. Its a win-win situation !!
 
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