  A multi-slit interference experiment, with which-way detectors, in the
presence of environment induced decoherence, is theoretically analyzed. The
effect of environment is modeled via a coupling to a bath of harmonic
oscillators. Through an exact analysis, an expression for $\mathcal{C}$, a
recently introduced measure of coherence, of the particle at the detecting
screen is obtained as a function of the parameters of the environment. It is
argued that the effect of decoherence can be quantified using the measured
coherence value which lies between zero and one. For the specific case of two
slits, it is shown that the decoherence time can be obtained from the measured
value of the coherence, $\mathcal{C}$, thus providing a novel way to quantify
the effect of decoherence via direct measurement of quantum coherence. This
would be of significant value in many current studies that seek to exploit
quantum superpositions for quantum information applications and scalable
quantum computation.
