## Contents

- uBorn
- uScattROI
- uScattROI and uBorn are similar in case of small wavelengths

    init;

    % k: wave number
    % k = 5;
    k = 250;

    seti.k = k;

    seti.contrast = 'corner2D';
    seti = setData(seti);
    qROI = seti.qROIexact;

    uIncROI = seti.dSInc.*seti.incField(:,1); % incident field of first transmitter (1, ..., seti.incNb)

## uBorn

    % Solution 1:
    % Define factor k^2 in the volume potential operator V.
    V  = @(x) seti.k^2.*helmholtz2Dr2r(x, seti); % volume potential operator V: L^2(ROI) -> L^2(ROI)
    QU = @(x) qROI .* x;
    uBorn1 = V(QU(uIncROI));

    % Solution 2:
    % As solution 1, but V and QU are defined in intOpsFuncs.
    % [V, ~, ~, ~, ~, QU, ~, ~, ~] = intOpsFuncs(qROI, seti);
    % uBorn2 = V(QU(uIncROI));

    % Solution 3:
    % uBorn3 = seti.k^2.*helmholtz2Dr2r(qROI.*uIncROI, seti);

    % Test:
    % norm(uBorn1-uBorn2)
    % norm(uBorn2-uBorn3)

## uScattROI

    % Solution 1a:
    % uScattROI1 = solveLippmannSchwinger(@(x) V(QU(x)), V(QU(uIncROI)), seti);

    % Solution 1b:
    uScattROI1 = solveLippmannSchwinger(@(x) V(qROI.*x), V(qROI.*uIncROI), seti);

    % Solution 2:
    % [~, uScattROI2] = simo(qROI,uIncROI,seti);

    % Test:
    % norm(uScattROI1-uScattROI2)

## uScattROI and uBorn are similar in case of small wavelengths

    rel = norm(uBorn1-uScattROI1)/norm(uScattROI1);
    fprintf('  Wave number: %g\n',seti.k);
    fprintf('  Relative error: %g\n',rel');

figure(1); f1 = imagesc(real(seti.G(qROI))); colorbar; axis xy; % predefined contrast set(gca,'FontSize',20); axis square; print(1,'-depsc','pi3born1.eps'); figure(2); f2 = imagesc(real(seti.G(uIncROI))); colorbar; axis xy; % incident field set(gca,'FontSize',20); axis square; print(2,'-depsc','pi3born2.eps'); figure(3); f3 = imagesc(real(seti.G(uBorn1))); colorbar; axis xy; % Born approximation of scattered field set(gca,'FontSize',20); axis square; print(3,'-depsc','pi3born3.eps'); figure(4); f4 = imagesc(real(seti.G(uScattROI1))); colorbar; axis xy; % Scattered field (by solving Lippmann Schwinger eq.) set(gca,'FontSize',20); axis square; print(4,'-depsc','pi3born4.eps');