function result = mie_2(m, x, xmax)

% Low-frequency approximation of Mie Efficiencies for given 
% complex refractive-index ratio m=m'+im" 
% and size parameter x=k0*a, k0= wave number in ambient medium,  
% a=sphere radius using the complex Mie Coefficients an and bn 
% for n=1 to 2, p. 131 in Bohren and Huffman (1983) BEWI:TDD122.
% Result is m', m", x, efficiencies for extinction (qext), 
% scattering (qsca), absorption (qabs), backscattering (qb), 
% asymmetry parameter asy=<costeta> and qratio=qb/qsca.
% Uses the function "mieab_2" for the Mie Coefficients.
% C. Mätzler, May 2002.

if x==0
    result=[0 0 0 0 0 1.5];
elseif x>xmax,
    result=[NaN, NaN, NaN, NaN, NaN, NaN];
else,
    nmax=2;
    n1=nmax-1;
    n=(1:nmax);cn=2*n+1; c1n=n.*(n+2)./(n+1); c2n=cn./n./(n+1);
    x2=x*x;
    f=mieab_2(m,x);
    anp=(real(f(1,:))); anpp=(imag(f(1,:)));
    bnp=(real(f(2,:))); bnpp=(imag(f(2,:)));
    g1(1:4,nmax)=[0; 0; 0; 0];
    g1(1,1:n1)=anp(2:nmax);
    g1(2,1:n1)=anpp(2:nmax);
    g1(3,1:n1)=bnp(2:nmax);
    g1(4,1:n1)=bnpp(2:nmax);   
    dn=cn.*(anp+bnp);
    q=sum(dn);
    qext=2*q/x2;
    en=cn.*(anp.*anp+anpp.*anpp+bnp.*bnp+bnpp.*bnpp);
    q=sum(en);
    qsca=2*q/x2;
    qabs=qext-qsca;
    fn=(f(1,:)-f(2,:)).*cn;
    gn=(-1).^n;
    f(3,:)=fn.*gn;
    q=sum(f(3,:));
    qb=q*q'/x2;
    asy1=c1n.*(anp.*g1(1,:)+anpp.*g1(2,:)+bnp.*g1(3,:)+bnpp.*g1(4,:));
    asy2=c2n.*(anp.*bnp+anpp.*bnpp);
    asy=4/x2*sum(asy1+asy2)/qsca;
    qratio=qb/qsca;
    result=[qext qsca qabs qb asy qratio];
end;