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Rayleigh Scattering
Rayleigh scattering origniates in the random positioning
of small, isotropic inhomogeneities. Because of the
random positioning, the phase of the ultrasound signals
may add constructively or destructively, or somewhere
in-between. It can be shown that such a system has
a SNR of 1.91.
In order to simulate this effect, we create the following
Matlab/Octave code.
function sig=usound(Nscat);
t=linspace(0,2*pi,200); t(1)=[];
sig= zeros(size(t));
for i=1:Nscat;
sig= sig+sin(t + 2*pi*rand);
end
endfunction
for Nscat= [1,2,3,5,10,30,100,300,1000];
s= zeros(1,10000);
for n=1:10000;
s(n)= mean(abs(usound(Nscat)));
end
disp([ Nscat, mean(s), std(s), mean(s)/std(s)]);
end
Output
| Nscat |
Mean |
Std |
SNR |
| 1 | 0.64 | 0.0000059 | 108650 |
| 2 | 0.80 | 0.39 | 2.03920 |
| 3 | 1.00 | 0.46 | 2.19039 |
| 5 | 1.28 | 0.63 | 2.01837 |
| 10 | 1.79 | 0.91 | 1.95932 |
| 30 | 3.11 | 1.61 | 1.9385 |
| 100 | 5.63 | 2.93 | 1.9206 |
| 300 | 9.76 | 5.14 | 1.8997 |
| 1000 | 17.99 | 9.46 | 1.9025 |
Comments:
- The SNR at Nscat=1 should be ∞. The reason that
it isn't is because we are integrating over a discrete
approximation to the sin.
- Note how quickly the approximation is close to SNR=1.91.
Even with Nscat=2, the value is very close.
- I know that there are much more efficient ways to do this.
This is supposed to be a quick simulation to illustrate the
effect.
Last Updated:
$Date: 2004-03-23 14:05:22 -0500 (Tue, 23 Mar 2004) $
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Engineering