diff --git a/src/figure_2_2.m b/src/figure_2_2.m index 1b300f0352f716b7edf7e0608e9dd0535a01c7d6..6865455a3ada74439f06d16f8465c1d220bcae98 100644 --- a/src/figure_2_2.m +++ b/src/figure_2_2.m @@ -10,42 +10,49 @@ sampling.nd = M; % number of illumination directions, i.e. number of columns sampling.xhat = (0:sampling.nxhat-1)'/sampling.nxhat*2*pi; % detector positions sampling.d = (0:sampling.nd-1)/sampling.nd*2*pi; % illumination directions -q = 2; +q = [-.5,2]; parkite = [1.5 .65 4 8 45 1]; -[Fkite, ~, ~] = evaluateFarfieldNystrom({'kite'}, parkite, q, k, sampling.nxhat, 0); +parnut = [1 .5 8 2 105 1]; zkite = [4;8]; +znut = [8;2]; Rkite = [2.2]; +Rnut = [1.1]; + +%% + +[Fkitenut] = evaluateFarfieldSecondOrder(k, sampling, {'kite', 'nut'}, [parkite; parnut], [11], q); %% s = [50 50 550 550]; figure('Renderer', 'painters', 'Position', s) -N = 13; +N1 = 13; +N2 = 7; -FFkite = 1/M^2*fftshift(fft2(translOp(Fkite, sampling, zkite, zkite, k))); -FFkite = [FFkite, FFkite(:,1)]; -FFkite = [FFkite; FFkite(1,:)]; -FFkite = flipud(FFkite); - -imagesc((-32:32),(-32:32),abs(FFkite(M/2+1-32:M/2+1+32,M/2+1-32:M/2+1+32))) -set(gca,'ColorScale','log') -cx = caxis; -caxis([10^(-3) cx(2)]) +FFkitenut = 1/M^2*fftshift(fft2(translOp(Fkitenut, sampling, znut, zkite, k))); % VERTAUSCHT +FFkitenut = [FFkitenut, FFkitenut(:,1)]; +FFkitenut = [FFkitenut; FFkitenut(1,:)]; +FFkitenut = flipud(FFkitenut); +imagesc((-32:32),(-32:32),abs(FFkitenut(M/2+1-32:M/2+1+32,M/2+1-32:M/2+1+32))) hold on -x1 = [-N:N,N*ones(1,2*N-1),N:-1:-N,-N*ones(1,2*N)]; -x2 = [-N*ones(1,2*N+1),-N+1:N-1,N*ones(1,2*N+1),N-1:-1:-N]; +x1 = [-N2:N2,N2*ones(1,2*N1-1),N2:-1:-N2,-N2*ones(1,2*N1)]; +x2 = [-N1*ones(1,2*N2+1),-N1+1:N1-1,N1*ones(1,2*N2+1),N1-1:-1:-N1]; hold on -plot(x1,x2,'--k', 'LineWidth', 1.5) +plot(x2,x1,'--k', 'LineWidth', 1.5) % VERTAUSCHT load('MyCMap.mat') cmp = CMap; colormap(cmp); +set(gca,'ColorScale','log') +cx = caxis; +caxis([10^(-3) cx(2)]) + set(gca,'XTick',[-30 -20 -10 0 10 20 30]); set(gca,'YTick',[-30 -20 -10 0 10 20 30]); @@ -56,36 +63,56 @@ ylabel('$n$', 'Interpreter', 'LaTex', 'Fontsize', 21) axis square + colorbar -title('Expansion coefficients $(|a_{m,n}|)_{m,n}$', 'Interpreter', 'Latex') -set(gca,'Fontsize',15) +title('Expansion coefficients $(|a_{m,n}^{(2)}|)_{m,n}$', 'Interpreter', 'Latex') +set(gca,'Fontsize',21) set(gca,'YDir','normal') -print ../figures/figure_exp_coeff.eps -depsc + +print ../figures/figure_exp_coeff_kiteandnut.eps -depsc %% +s = [50 50 550 550]; figure('Renderer', 'painters', 'Position', s) d = (0:100)/100*2*pi; [x_kite,~,~,~] = kurve(100, 'kite', parkite); x_kite = [x_kite;x_kite(1,:)]; + +[x_nut,~,~,~] = kurve(100, 'nut', parnut); +x_nut = [x_nut;x_nut(1,:)]; + plot(x_kite(:,1),x_kite(:,2),'LineWidth', 1.5, 'Color', 'blue') hold on +plot(x_nut(:,1),x_nut(:,2),'LineWidth', 1.5, 'Color', 'blue') +hold on + plot(Rkite*cos(d)+zkite(1) ,Rkite*sin(d)+zkite(2),'LineStyle', '--', 'LineWidth', 1, 'Color', 'black') hold on scatter(zkite(1),zkite(2),100,'Marker','+','LineWidth', 1,'MarkerEdgeColor', 'black') -title('Scatterer $D$ and ball $B_R(c)$', 'Interpreter', 'Latex') +plot(Rnut*cos(d)+znut(1) ,Rnut*sin(d)+znut(2),'LineStyle', '--', 'LineWidth', 1, 'Color', 'black') +hold on +scatter(znut(1),znut(2),100,'Marker','+','LineWidth', 1,'MarkerEdgeColor', 'black') + +title('Scatterers $D_j$ and balls $B_{R_j}(c_j)$, $j=1,2$', 'Interpreter', 'Latex') + +text(4.15,8.35,'$D_1$','Color','blue','FontSize',22, 'Interpreter','latex') +text(7.6,2.45,'$D_2$','Color','blue','FontSize',22, 'Interpreter','latex') axis([0 11 0 11]) grid on ax = gca; ax.FontSize = 22; +xticks([0,2,4,6,8,10]) +yticks([0,2,4,6,8,10]) + xlabel('$x_1$', 'Interpreter', 'LaTex', 'Fontsize', 22) ylabel('$x_2$', 'Interpreter', 'LaTex', 'Fontsize', 22) -print ../figures/figure_geometry.eps -depsc \ No newline at end of file +print ../figures/figure_geometry_kiteandnut.eps -depsc \ No newline at end of file