FRINGES Generates synthetic fringe patterns
by Chuck DiMarzio Northeastern University May 2009
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Contents
Equation
Coordinates
xx=(-1:0.01:1); [x1,y1]=meshgrid(xx,xx); % x,y rectangular coordinates rsq=x1.^2+y1.^2; % r = radial coordinate
Parameters
lambda=632.8; % wavelength in nm bumpheight=2*lambda; % Represents a bump on a mirror smallbumpheight=lambda/5; % bumpwidth=0.3; % width of the bump in x1,y1 bumpcenter=[0.15,0.4]; % % Delta is twice the bumpheight because the light reflects from the mirror % and thus the path length change is twice the change in the surface % position. The bump has a Gaussian shape. % relrad=((x1-bumpcenter(1)).^2+(y1-bumpcenter(2)).^2)/(bumpwidth/2).^2;
Optical Path Length for a bump and a small bump
Delta_bump=2*bumpheight*exp(-relrad); Delta_smallbump=2*smallbumpheight*exp(-relrad);
Reference Wave at z=0, t = 0
Eref=zeros(size(x1));
Eref(rsq<1)=1; % Plane wave in circular aperture
Tilted plane-wave signal, with tilt coefficient a1
a1=8*lambda/2; Esigflat=exp(1i*2*pi/lambda*a1*x1); % % E = Eref+Esigflat; I = (abs(E)).^2; fig1=figure;imagesc(xx,xx,I);axis image;colormap(flipud(gray));axis off;

Tilted plane--wave signal with bumps
Esig=Esigflat.*exp(1i*2*pi/lambda*Delta_bump); E = Eref+Esig; I = (abs(E)).^2; fig2=figure;imagesc(xx,xx,I);axis image;colormap(flipud(gray));axis off; Esig=Esigflat.*exp(1i*2*pi/lambda*Delta_smallbump); E = Eref+Esig; I = (abs(E)).^2; fig3=figure;imagesc(xx,xx,I);axis image;colormap(flipud(gray));axis off;


Curved, spherical signal wavefront
b1=4*lambda; Esigsph=exp(1i*2*pi/lambda*b1*rsq); E = Eref+Esigsph; I = (abs(E)).^2; fig4=figure;imagesc(xx,xx,I);axis image;colormap(flipud(gray));axis off;

Curved signal wave with bumps
Esig=Esigsph.*exp(1i*2*pi/lambda*Delta_bump); E = Eref+Esig; I = (abs(E)).^2; fig5=figure;imagesc(xx,xx,I);axis image;colormap(flipud(gray));axis off; Esig=Esigsph.*exp(1i*2*pi/lambda*Delta_smallbump); E = Eref+Esig; I = (abs(E)).^2; fig6=figure;imagesc(xx,xx,I);axis image;colormap(flipud(gray));axis off;

