About a correlation function

I saw a equation in a research artical which is C(Δt)=<I(t)·I(t+Δt)> / (<I(t)>·<I(t+Δt)>) - 1. where I(t) is the signal intensity value at the time t, and I(t+Δt) is the signal intensity value at time t+Δt. Note that I is a vector. <...> represents the average over t. I don't understand why this function can indicate the correlation between the I(t) and I(t+Δt) , especially why must -1 in the equation.