= Microlensing optical depth
{title2=$\tau=\int n_l\pi R_E^2\,dD_l$}
The <microlensing optical depth> is the probability, when small, that a source lies within one <Einstein radius> of a foreground lens. For point lenses and compact-object <mass density> $\rho_l$ in nearby Euclidean geometry,
$$
\tau=\frac{4\pi G}{c^2}\int_0^{D_s}\rho_l(D_l)\frac{D_l(D_s-D_l)}{D_s}\,dD_l.
$$
The individual lens mass cancels because $n_l=\rho_l/m$ and $R_E^2\propto m$. Detection efficiencies and event durations still depend on individual masses and survey cadence.
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