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, M_{std}, from a diffuse reflectance standard, R_{std}, (Labsphere Inc. , NH, USA) using the same measurement geometry. Calculate the diffuse reflectance, R = (M/M_{std})R_{std}.

#### 2. Calculate the scattering to absorption ratio

To find the ratio N',

N' = μ_{s}'/μ_{a}

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'= μ_{s}'/(μ_{a}' + μ_{s}').

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

N' = A^{2}/(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, R_{with ink}, is significantly reduced, perhaps to about 50%. Measurement of R_{with 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:

dμ_{a}^{ink} = (μ_{a}^{ink_stock})(ink volume added)/(volume of Intralipid + ink volume added)

where μ_{a}^{ink_stock} is the absorption of the ink stock.

#### 4. Calculate the scattering to absorption ratio with ink present

Determine N'_{with ink} based on R_{with ink}, as was done for N' above.

Because N'_{with ink}/N' = μ_{a}/(μ_{a} + dμ_{a}^{ink}), the absorption of the Intralipid WITHOUT ink is calculated:

μ_{a} = dμ_{a}^{ink}N'_{with ink}/(N' - N'_{with ink})

#### 5. Calculate the reduced scattering coefficient

Measure the on-axis, narrow solid angle transmission, T =
exp(-(μ_{s} + μ_{a})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:

μ_{s} = (-ln(T)/L)/f - μ_{a}

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

#### 6. Calculate the anisotropy, g = 1 - μ_{s}'/(μ_{s} - μ_{a}).

In summary, measurements of R, R_{with ink}, and T yield μ_{a}, μ_{s}, and g, and the lumped term μ_{s}' = μ_{s}(1-g).