经典Mie理论中的散射系数的另外一种计算
H&B书中经典Mie散射和吸收系数有两种表示方式,一种是29号整理的表示,还有一种常见的表示方式:
式1
两种表示的中间关系式为:
式2
与Bessel函数的关系为:
式3
递推关系式为:
式4
1951年,Aden引入对数微分算法
将Mie散射系数表示为:
式5
式5中Dn的迭代算法表示为:
在matlab中的函数代码可表示为:
function result = Mie_ab(m,x)
% Computes a matrix of Mie Coefficients, an, bn,
% of orders n=1 to nmax, for given complex refractive-index
% ratio m=m'+im' and size parameter x=k0*a where k0= wave number in ambient
% medium for spheres of radius a;
% Eq. (4.88) of Bohren and Huffman (1983), BEWI:TDD122
% using the recurrence relation (4.89) for Dn on p. 127 and
% starting conditions as described in Appendix A.
z=m.*x;
nmax=round(2+x+4*x.^(1/3));
nmx=round(max(nmax,abs(z))+16);
n=(1:nmax); nu = (n+0.5);
sx=sqrt(0.5*pi*x);
px=sx.*besselj(nu,x);
p1x=[sin(x), px(1:nmax-1)];
chx=-sx.*bessely(nu,x);
ch1x=[cos(x), chx(1:nmax-1)];%fai n-1阶
gsx=px-i*chx;
gs1x=p1x-i*ch1x;%y n-1阶
dnx(nmx)=0+0i;
for j=nmx:-1:2 % Computation of Dn(z) according to (4.89) of B+H (1983)
dnx(j-1)=j./z-1/(dnx(j)+j./z);
end;
dn=dnx(n); % Dn(z), n=1 to nmax
da=dn./m+n./x;
db=m.*dn+n./x;
an=(da.*px-p1x)./(da.*gsx-gs1x);
bn=(db.*px-p1x)./(db.*gsx-gs1x);
result=[an; bn];
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No common goal, no common cause to coorperate.
道不同,不相为谋。
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