Modified Beer-Lambert Model
This calculator uses a modified Beer-Lambert model with geometric beam spreading:
I(z) = (P / (π × r(z)²)) × exp(-µeff × z)
- r(z) = r₀ + z × tan(θ) accounts for the expanding cone of light
- µeff = √(3 × µa × (µa + µs')) is the effective attenuation coefficient
- θ = arcsin(NA / n_tissue) is the half-angle of the fiber's acceptance cone
This is a standard approximation used in optogenetics literature (Aravanis et al. 2007, Yizhar et al. 2011).