# MATLAB: Plotting the product of two functions.

curve fitting

Hi,
I have plotted two offset Bessel functions of the first kind (blue and red dotted curves) – see figure below.
I would like to produce something similar to the black curve shown in the second attached figure below, but for the two curves I have plotted. Can someone please point me in the correct direction?
Thank you
lambda = 500e-6;                     % wavelength [m]D = 0.0001 ;                         % diameter D of the primary aperture [m]theta1 = -20:.01:20;                 % angular radius θ (as measured from the primary aperture) [Degrees]u1 = (pi/lambda)*D*theta1;theta2 = -20:.01:20;  u2 = (pi/lambda)*D*theta2;x1 = u1./pi +0.61;x2 = u2./pi -0.61;I01 = 1.0; I02 = 1.0;i1 = real((besselj(1,u1)./(u1)).^2);i2 = real((besselj(1,u2)./(u2)).^2);I1 = I01*(i1./max(i1));I2 = I02*(i2./max(i2));colormap('default')figure(1);%clf;hold on;plot(x1,I1,'b:','LineWidth',1.5);plot(x2,I2,'r:','LineWidth',1.5);hold off;grid on; set(gca,'FontSize',14);%axis([-4 4 0 1.05])xlabel('\theta (\lambda/D)', 'fontsize', 16);ylabel('Normalized Intensity', 'fontsize', 16);legend('Source 1','Source 2','fontsize', 10);legend;figure(2);clf;[X,Y]=meshgrid(-10:.1:10);%[X,Y]=meshgrid(x);R=sqrt(X.^2+Y.^2);z=(besselj(1,R)./R).^2;Z=z./max(max(z));surf(X,Y,Z,'EdgeColor','none');colorbarcamlight left;lighting phong;set(gca,'XTick',[], 'YTick', [], 'ZTick', [])

lambda = 500e-6;                     % wavelength [m]D = 0.0001 ;                         % diameter D of the primary aperture [m]theta1 = -20:.01:20;                 % angular radius θ (as measured from the primary aperture) [Degrees]u1 = (pi/lambda)*D*theta1;theta2 = -20:.01:20;  u2 = (pi/lambda)*D*theta2;x1 = u1./pi +0.8;x2 = u2./pi -0.8;I01 = 1.0; I02 = 0.5;  % <<==== changed this parameteri1 = real((besselj(1,u1)./(u1)).^2);i2 = real((besselj(1,u2)./(u2)).^2);I1 = I01*(i1./max(i1));I2 = I02*(i2./max(i2));% vvv Interpolated to make both vector equalx = unique([x1 x2]);I1_ = interp1(x1, I1, x);I2_ = interp1(x2, I2, x);colormap('default')figure(1);%clf;hold on;plot(x1,I1,'b:','LineWidth',1.5);plot(x2,I2,'r:','LineWidth',1.5);plot(x,I1_+I2_,'r:','LineWidth',1.5); % <<==== added this linehold off;grid on; set(gca,'FontSize',14);%axis([-4 4 0 1.05])xlabel('\theta (\lambda/D)', 'fontsize', 16);ylabel('Normalized Intensity', 'fontsize', 16);legend('Source 1','Source 2','fontsize', 10);legend;figure(2);clf;[X,Y]=meshgrid(-10:.1:10);%[X,Y]=meshgrid(x);R=sqrt(X.^2+Y.^2);z=(besselj(1,R)./R).^2;Z=z./max(max(z));surf(X,Y,Z,'EdgeColor','none');colorbarcamlight left;lighting phong;set(gca,'XTick',[], 'YTick', [], 'ZTick', [])