Example: Mie calculation of Qs and µs

ECE532 Biomedical Optics ©1998 Steven L. Jacques, Scott A. Prahl Oregon Graduate Institute

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

• n_r = n_p/n_med = 1.5721/1.3316 = 1.1806
  
  
• x = 2a/(/n_med) = (2)(3.1415)(0.152)/(0.6328/1.3316) = 2.0097
  
  
• A = a² = (3.1415)(0.152)² = 0.0726 µm²
  
  
• _s = f_v/((4/3)a³) = (0.001)/((4/3)(3.1415)(0.152)³) = 0.0608 µm^-3

Run the Mie theory algorithm:

• Mie(n_r, x) ---> Q_s
  
  Mie(1.1806, 2.0097) ---> 0.1971

Calculate the scattering coefficient:

• _s = Q_sA = (0.1971)(0.0726) = 0.01431 µm²
  
  
• µ_s = _ss = (0.0608)(0.01431) = 0.0009723 µm^-1
  
  
• µ_s [cm^-1] = (µ_s [µm^-1])(10⁴ [µm/cm]) = 9.723 cm^-1