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%---------------------------------------------------------------
% PROGRAM: NRI
% AUTHOR: Andri M. Gretarsson
% DATE: 8/5/03
%
%
% SYNTAX: z=NwetonRingsI([w1,w2,R1,R2,P1,P2,lambda,deltaphi],r);
%
% Returns the intensity of a set of Newton's rings as a function
% of the radial coordinate R. (See e.g. Fundamentals of Physical Optics
% by Jenkins and White, 1st ed. Section 4.4). The Newton's rings are
% generated by the interference of two coaxial beams with different radii
% of curvature and/or width.
%
% w1 = 1/e field amplitude radius of the 1st of the interfering beams
% w2 = 1/e field amplitude radius of the 2nd of the interfering beams
% R1 = Radius of curvature of the phasefront of the 1st of the interfering beams
% R2 = Radius of curvature of the phasefront of the 2nd of the interfering beams
% P1 = Radius of curvature of the phasefront of the 2nd of the interfering beams
% P2 = Radius of curvature of the phasefront of the 2nd of the interfering beams
% lambda = Radius of curvature of the phasefront of the 2nd of the interfering beams
% deltaphi = Radius of curvature of the phasefront of the 2nd of the interfering beams
% z(k) = Intensity of the interference pattern at radiusr(k).
%
% If x and y are not vectors but matrixes generated by
% the matlab function meshgrid, then the output variable z
% is a matrix rather than a vector. The matrix form allows
% the function to have a plane as it's domain rather than
% a curve. To generate a plane domain one uses meshgrid.
%
% EXAMPLE: thetaoffset=20*pi/180;
% rseed=[0:0.01:sqrt(0.3)].^2;
% thetaseed=[0:1:360]*pi/180;
% [theta,r]=meshgrid(thetaseed,rseed);
% [x,y]=pol2cart(theta,r);
% h=pcolor(x,y,NewtonRingsI([0.01,100,2e3,1e99,1,1,1.024e-6,thetaoffset],r));
% colormap('bone');
% set(h,'EdgeColor','none');
% set(h,'FaceColor','interp');
% set(gca,'Visible','off');
% set(gcf,'Color','black');
% axis square
% shg;
%
% Last updated: 8/5/03 by AMG
%
%---------------------------------------------------------------
%% SYNTAX: z=NewtonRingsI([w1,w2,R1,R2,P1,P2,lambda,deltaphi],r);
%---------------------------------------------------------------
function z=NewtonRingsI(params,r)
w1=params(1);
w2=params(2);
R1=params(3);
R2=params(4);
P1=params(5);
P2=params(6);
lambda=params(7);
deltaphi=params(8);
a=1/2/R1-1/2/R2;
z = exp(-r.^2/w1).*exp(-r.^2/w2).*...
( sin( (a/2/lambda)* r.^2 - deltaphi) ).^2 + abs(P1-P2);
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