Introduction Lyman-$\alpha$ emitters and their intensity map are powerful probes of the large-scale structure. Given typically very high optical depths, scatterings with neutral hydrogen have a non-negligible impact on the observed distribution of Lyman-$\alpha$ photons. To study this in detail, we run a suit of radiative transfer (RT) simulations on the Illustris simulation and investigate two possible distortion effects arising from RT in real space as well as in redshift space for the two-point correlation function.