Side maximum of a finite-width double-slit pattern ($I(X)\propto {\mathrm{sinc}}^2(\pi wX/(\lambda L)){\cos }^2(\pi dX/(\lambda L))$)

The maxima of the full two-slit intensity need not lie at maxima of its cosine-squared interference factor, because the single-slit envelope has a nonzero slope. Differentiating its logarithm gives $[\pi w/(\lambda L)](\cot u-1/u)=[\pi d/(\lambda L)]\tan v$, where $u=\pi wX/(\lambda L)$ and $v=\pi dX/(\lambda L)$. Solving this equation in the appropriate fringe gives the true maximum. The usual fringe-center estimate is useful when the envelope varies slowly across a fringe.