  We study the task of coherence filtration under strictly incoherent
operations in this paper. The aim of this task is to transform a given state
$\rho$ into another one $\rho^\prime$ whose fidelity with the maximally
coherent state is maximal by using stochastic strictly incoherent operations.
We find that the maximal fidelity between $\rho^\prime$ and the maximally
coherent state is given by a multiple of the $\Delta$ robustness of coherence
$R(\rho\|\Delta\rho):=\min\{\uplambda|\rho\leq\uplambda\Delta\rho\}$, which
provides $R(\rho\|\Delta\rho)$ an operational interpretation. Finally, we
provide a coherence measure based on the task of coherence filtration.
