We analyzed Deep Impact High Resolution Instrument (HRI) images acquired within the first seconds after collision of the Deep Impact impactor with the nucleus of comet 9P/Tempel 1. These images reveal an optically thick ejecta plume that casts a shadow on the surface of the nucleus. Using the 3D radiative transfer code HYPERION we simulated light scattering by the ejecta plume, taking into account multiple scattering of light from the ejecta, the surrounding nuclear surface and the actual observational geometry (including an updated plume orientation geometry that accounts for the latest 9P/Tempel 1 shape model). Our primary dust model parameters were the number density of particles, their size distribution and composition. We defined the composition through the density of an individual particle and the ratio of its material constituents, which we considered to be refractories, ice and voids. The results of our modeling indicate a dust/ice mass ratio for the ejecta particles of at least 1. To further constrain the parameters of the model, we checked for consistency between the ejecta mass resulting from our modeling with the ejecta mass estimated by the crater formation modeling. Constraining the particle size distribution by results of other studies of the Deep Impact ejecta, we find the number density of ejecta particles equal to ~10^4 particles/cm^3 at the base of the plume.