Definition: Optical density (or Absorbance) is defined as the (decadic) logarithm of the ratio of incident to transmitted radiant power through a (non-scattering) sample. This quantity is used, e.g., in spectrophotometry to characterize a dissolved chromophore in a non-scattering solution or an optical filter. Absorbance is defined as:
I_{d}I_d
I_{0}I_0
T = e^{-mu_a d} = 10^{-epsilon cd}
mu_a
epsilon
A = epsilon cd = frac{mu_a d}{log_e 10}mu_a = log_e 10 cdot epsilon c = 2.2303 epsilon c$
In fNIRS, optical density (OD) is sometimes used as a synonym for (decadic) attenuation (termed A as well). In this context, attenuation is relevant instead of absorbance since it also includes the effect of light scattering.
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References: https://doi.org/10.1117%2F1.NPh.8.1.012101
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