  Inspired by a recent study of Iancu, Mueller and Triantafyllopoulos [1] and
earlier papers by Golec-Biernat and Wusthoff [2,3], we propose semi-inclusive
diffractive deep inelastic scattering (SIDDIS) to investigate the gluon
tomography in the nucleon and nuclei at small-$x$. The relevant diffractive
quark and gluon parton distribution functions (DPDF) can be computed in terms
of the color dipole S-matrices in the fundamental and adjoint representations,
respectively. Novel correlations from the gluon tomography in the dipole
S-matrix can be experimentally studied through the DPDFs in these processes at
the future electron-ion collider (EIC).
