= Moiré fringe spacing formula
{title2=$D=1/|\mathbf g_1-\mathbf g_2|$}
Subtract the phases $2\pi\mathbf g_1\cdot\mathbf r$ and $2\pi\mathbf g_2\cdot\mathbf r$ of two projected periodic structures. Their relative phase repeats along the difference vector after distance $D=1/|\mathbf g_1-\mathbf g_2|$. For magnitudes $1/d_1$ and $1/d_2$ separated by angle $\theta$, this gives $D=d_1d_2/\sqrt{d_1^2+d_2^2-2d_1d_2\cos\theta}$. At zero rotation it reduces to $d_1d_2/|d_1-d_2|$; equal spacings give $d/[2|\sin(\theta/2)|]$. Finite specimen extent limits how many periods can be observed.
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