| Date 06/09/2010 |
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| Script S5_2_11.m | |||
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%==============================================
%A five-slit grating %============================================== % %distance between the slits in mm d=0.1; %parameter ks ks=2*pi/d; % %================================================== %The Fourier synthesis of square wave of five slits %================================================== % %N integer odd numbers are defined between 1 and 2N-1 N=4000; i=linspace(0,N-1,N); p=2*i+1; % pmax=length(p) %M values of x are defined between -d/2 and d/2 M=56; x=linspace(-d/2,d/2,M); %g(x) is calculated in each x(j) point using N %harmonic waves in the Fourier synthesis %(see Sec.5.2.1) for j=1:M g(j)=0; for p=1:N arg1(p)=p*(pi/2); fatt1(p)=sin(arg1(p))/arg1(p); arg2(p)=p*ks*x(j); fatt2(p)=cos(arg2(p)); g(j)=g(j)+fatt1(p)*fatt2(p); end g(j)=0.5+g(j); end g; %the array containing the Fourier synthesis for the five slits g5=[g g g g g]; %corresponding abscissa x5 is defined e1=2.5*d; x5=linspace(-e1,e1,5*M); plot(x5,g5,'ro-'),grid on title('The Fourier synthesis of square wave of five slits') figure % %============================================== %The corresponding Fourier transform %============================================== % %lambda in mm lambda=0.5e-03; % %interval between -1.5° and 1.5° divided in NN parts NN=1001 tetag=linspace(-1.5,1.5,NN); teta=tetag*pi/180; %parameter k k=(2*pi/lambda)*sin(teta); %the G transform of g in NN points for j=1:NN gamma=k(j)*x5; coseno=cos(gamma); y5=g5.*coseno; G(j)=(1/pi)*trapz(x5,y5); end %relative value is used maxG=max(G) GG=G/maxG; plot(tetag,GG,'bd-'),grid on axis([-1.5 1.5 -0.2 1]) title('Fourier transform function of tetag') figure %corresponding relative intensity Ir GGs=conj(GG); Ir=GG.*GGs; plot(tetag,Ir,'r-'),grid on % axis([-650 650 -0.3 1]) title('Relative intensity function of tetag (using Fourier transform)') figure % %============================================== %Relative intensity %using Fraunhofer formulae %============================================== % %h is the width of each slit h=d/2; %calculus of the diffraction factor alfa=(h/2)*k; num1=sin(alfa); num1q=num1.*num1; alfa2=alfa.*alfa; %avoiding the warning divide by zero den1q=alfa2+(alfa2==0)*eps; %Ir1 intensity due to the diffraction Ir1=num1q./den1q; %calculus of the interference factor beta=(d/2)*k; num2=sin(5*beta); num2q=num2.*num2; den2=5*sin(beta); den22=den2.*den2; %avoiding the warning divide by zero den2q=den22+(den22==0)*eps; %Ir2 intensity due to the interference Ir2=num2q./den2q; %effective relative intensity IrF=Ir1.*Ir2; plot(tetag,IrF,'r-'),grid on % axis([-650 650 -0.3 1]) title('Relative intensity function of tetag (using Fraunhofer formulae)') %============================================== % |
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