  The cross-sections of diffractive double hadron photo- or electroproduction
with large $p_T$, on a nucleon or a nucleus, are calculated to NLO accuracy. A
hybrid formalism mixing collinear factorization and high energy small-$x$
factorization, more precisely the shockwave formalism for the latter, is used
to derive the results. The cancellation of divergences is explicitly shown, and
the finite parts of the NLO differential cross-sections are found. We work in
arbitrary kinematics such that both photoproduction and leptoproduction are
considered. The results are therefore usable, to detect saturation effects, at
both the future EIC or already at LHC, using Ultra Peripheral Collisions.
