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mie_beamefficiency

PURPOSE ^

Cumulative power (corresponds to the beam efficiency in antenna theory)

SYNOPSIS ^

function result = mie_beamefficiency(m, x, tetalim, nsteps)

DESCRIPTION ^

 Cumulative power (corresponds to the beam efficiency in antenna theory) 
 scattered within a maximum scattering angle (variable from 0 to pi) for
 Mie Scattering (with and without diffraction peak) with
 complex refractive-index ratio m=m'+im", size parameters x=k0*a, 
 according to Bohren and Huffman (1983) BEWI:TDD122
 INPUT: 
 m, x: as usual
 tetalim: maximum angle to be considered, in radians
 nsteps: number of angles to be considered
 C. M�zler, June 2003, revised April, 2004.

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

DOWNLOAD ^

mie_beamefficiency.m

SOURCE CODE ^

0001 function result = mie_beamefficiency(m, x, tetalim, nsteps)
0002 
0003 % Cumulative power (corresponds to the beam efficiency in antenna theory)
0004 % scattered within a maximum scattering angle (variable from 0 to pi) for
0005 % Mie Scattering (with and without diffraction peak) with
0006 % complex refractive-index ratio m=m'+im", size parameters x=k0*a,
0007 % according to Bohren and Huffman (1983) BEWI:TDD122
0008 % INPUT:
0009 % m, x: as usual
0010 % tetalim: maximum angle to be considered, in radians
0011 % nsteps: number of angles to be considered
0012 % C. M�zler, June 2003, revised April, 2004.
0013 
0014 dteta=tetalim/nsteps;
0015 xmin=dteta/pi;
0016 m1=real(m); m2=imag(m);
0017 nx=(1:nsteps); 
0018 teta=(nx-0.5).*dteta;
0019 u=cos(teta); xs=x.*sqrt(1-u.*u);
0020     for j = 1:nsteps, 
0021 % Computation of diffraction pattern S according to BH, p. 110
0022         if abs(xs(j))<0.0001
0023             S(j)=x*x*0.25*(1+u(j));            % avoiding division by zero
0024         else
0025             S(j)=x*x*0.5*(1+u(j)).*besselj(1,xs(j))./xs(j);    
0026         end;
0027         a(:,j)=Mie_S12(m,x,u(j));
0028         b(:,j)=a(:,j)-S(j); % Subtraction of diffaction peak
0029         
0030         SL(j)= real(a(1,j)'*a(1,j))/(pi*x^2);   % with diffraction
0031         SR(j)= real(a(2,j)'*a(2,j))/(pi*x^2);
0032         SLb(j)= real(b(1,j)'*b(1,j))/(pi*x^2);  % without diffraction
0033         SRb(j)= real(b(2,j)'*b(2,j))/(pi*x^2);  
0034     end;
0035 st=2*pi*sin(teta);
0036 SSL=st.*SL;
0037 SSR=st.*SR;
0038 SSLb=st.*SLb;
0039 SSRb=st.*SRb;
0040 tetad=teta*180/pi;
0041 Q=mie(m,x);
0042 Qsca=Q(2);
0043 z=0.5*dteta*cumsum(SSL+SSR)/Qsca;
0044 zb=0.5*dteta*cumsum(SSLb+SSRb)/Qsca;
0045 semilogx(tetad/180,z,'r-',tetad/180,zb,'k--'),
0046 title(sprintf('Cumulative Fraction of Scattered Power: m=%g+%gi, x=%g',m1,m2,x)),
0047 xlabel('Maximum Scattering Angle/180�'),
0048 axis([xmin, tetalim/pi, 0, 1.1]);
0049 result=[teta; SSL; SSR; SSLb; SSRb; z; zb]';

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