= Scalar resonant Friedel-pair intensity difference
{title2=$I_+-I_-=4ab''\operatorname{Im}(AB^*)$}
For positional <structure factors> $A,B$, a real scattering factor $a$, and a complex factor $b+ib''$, the amplitudes are $F_+=aA+(b+ib'')B$ and $F_-=aA^*+(b+ib'')B^*$. Expanding their squared moduli gives the displayed difference. Resonance and lack of inversion allow a difference but do not force one: proportional positional sums with a real proportionality factor give zero.
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