 Reversing one slit at an array minimum

Let a coherent array of identical narrow slits have total far-field complex amplitude zero at a chosen direction. Reversing one slit's phase by $\pi$ changes its amplitude from $a_j$ to $-a_j$, so the new total is $-2a_j$. Its intensity is four times the single-slit intensity, independent of which slit was changed. For $N$ equally spaced slits, adjacent phase step $2\pi m/N$ gives such a zero when $m$ is not a multiple of $N$. A finite slit envelope multiplies the common intensity factor.