by Steven Jacques

1. Measure the diffusely reflected light from the sample

The diffusely reflected light, M, from surface of a 500-ml beaker of 10% Intralipid irradiated with normal incident light. Measure diffusely reflected light, Mstd, from a diffuse reflectance standard, Rstd, (Labsphere Inc. , NH, USA) using the same measurement geometry. Calculate the diffuse reflectance, R = (M/Mstd)Rstd.

2. Calculate the scattering to absorption ratio

To find the ratio N',

N' = μs'/μa

The Adding-Doubling method can be used to accurately characterize N' = function(R). Flock et al. used a function derived from the Adding-Doubling method to relate R to the reduced albedo, a'

a'= μs'/(μa' + μs').

Then N' = a'/(1 - a'). An approximate expression for N' is:

N' = A2/(3(-ln(R))2) - 1.

The factor A is approximately 7 or 8 for most tissues, but increases at high R values. The factor A also depends on the refractive index of the medium. For more on this approximate expression, see the NewsEtc. article.

3. Add a known amount of absorption

Add a small volume of absorber (India ink) to the Intralipid such that the reflectance, Rwith ink, is significantly reduced, perhaps to about 50%. Measurement of Rwith ink is made as above for the original Intralipid without ink. The amount of added absorption due to added ink to the Intralipid is known:

aink = (μaink_stock)(ink volume added)/(volume of Intralipid + ink volume added)

where μaink_stock is the absorption of the ink stock.

4. Calculate the scattering to absorption ratio with ink present

Determine N'with ink based on Rwith ink, as was done for N' above.

Because N'with ink/N' = μa/(μa + dμaink), the absorption of the Intralipid WITHOUT ink is calculated:

μa = dμainkN'with ink/(N' - N'with ink)

5. Calculate the reduced scattering coefficient

Measure the on-axis, narrow solid angle transmission, T = exp(-(μs + μa)L), through a cuvette with various dilution fractions (f) of the 10% Intralipid stock. The pathlength of the cuvette is L [cm]. Determine the scattering coefficient of the original 10% Intralipid:

μs = (-ln(T)/L)/f - μa

for each dilution f. The value of μa is about 0.01 cm-1 in this wavelength range has little effect on the value of μs. All the values of μs should be in agreement until too high concentrations of Intralipid are tested and multiple scattering causes the apparent μs to decrease.

6. Calculate the anisotropy, g = 1 - μs'/(μs - μa).

In summary, measurements of R, Rwith ink, and T yield μa, μs, and g, and the lumped term μs' = μs(1-g).