  In this work, the empirically derived dilution/correct factors of a sample
stripped-envelope, core-collapse supernovae (SE-SNe), including five SNe IIb,
four SNe Ib, six SNe Ic and two relativistic broad-lined type Ic supernovae
(SNe IcBL) are presented. The ultimate goal of this project is to derive
model-free distances to the host galaxy of one or more gamma-ray burst
supernova (GRB-SN), and to exploit their observed luminosity$-$decline
relationship by employing them as cosmological probes. In the first part of a
two-paper analysis, I present my method for deriving the dilution factors of
the SE-SN sample, which were chosen on the basis that
cosmological-model-independent distances exist to their host galaxies, and each
has a sufficient dataset that allows for host-subtracted, dereddened rest-frame
$BVI$ LCs to be constructed, and time-series spectra. A Planck function was fit
to the data to derive the blackbody radius and blackbody temperature as a
function of time, while the blueshifted velocity of either Si II $\lambda$6355
or Fe II $\lambda$5169 was used a proxy of the photospheric velocity, and hence
photospheric radius. The ratio of these empirically derived radii was taken as
the dilution/correct factor. I then compared the empirically derived dilution
factors with synthetic values obtained from radiative transfer models
calculated for SE-SNe arising from binary systems. It is seen that the
empirical dilution factors of the SNe Ic and GRB-SNe, the latter which were
derived based on luminosity distances calculated from their spectroscopic
redshift, are very similar. It is found that the dilution factors of the two
relativistic SN IcBL are very different to those of the GRB-SNe, meaning that
these engine-driven events may arise from fundamentally different progenitor
systems.
