|
ECE532 Biomedical Optics
© 1998
Steven L. Jacques, Scott A. Prahl
Oregon Graduate Institute |
Example: Mie calculation of Qs and µs
Consider the scattering of a HeNe laser beam by 0.304-µm-dia. nonabsorbing polystyrene spheres in water at a concentration of 0.1% volume fraction:
np = 1.5721 | particle refractive index
|
nmed = 1.3316 | medium refractive index
|
a = 0.152 µm, | particle radius
|
= 0.6328 µm | wavelength in vacuo
|
fv = 0.001 | volume fraction of particles in medium
|
Calculate the following parameters:
refractive index mismatch ratio, size parameter, geometrical cross-sectional area, and number density
- nr = np/nmed = 1.5721/1.3316 = 1.1806
- x = 2πa/(/nmed) = (2)(3.1415)(0.152)/(0.6328/1.3316) = 2.0097
- A = πa2 = (3.1415)(0.152)2 = 0.0726 µm2
- ρs = fv/((4/3)πa3) = (0.001)/((4/3)(3.1415)(0.152)3) = 0.0608 µm-3
Run the Mie theory algorithm:
- Mie(nr, x) ---> Qs
Mie(1.1806, 2.0097) ---> 0.1971
Calculate the scattering coefficient:
- σs = QsA = (0.1971)(0.0726) = 0.01431 µm2
- µs = ρsσs = (0.0608)(0.01431) = 0.0009723 µm-1
- µs [cm-1] = (µs [µm-1])(104 [µm/cm]) = 9.723 cm-1
next |
Mie theory |
Optical Properties