  We characterise the relation between the gas and dust content of the
interstellar medium towards young stellar objects in the Orion Nebula Cluster.
X-ray observations provide estimates of the absorbing equivalent hydrogen
column density N_H based on spectral fits. Near-infrared extinction values are
calculated from intrinsic and observed colour magnitudes (J-H) and (H-K_s) as
given by the VISTA Orion A survey. A linear fit of the correlation between
column density and extinction values A_V yields an estimate of the N_H/A_V
ratio. We investigate systematic uncertainties of the results by describing and
(if possible) quantifying the influence of circumstellar material and the
adopted extinction law, X-ray models, and elemental abundances on the N_H/A_V
ratio. Assuming a Galactic extinction law with R_V=3.1 and solar abundances by
Anders & Grevesse (1989), we deduce an N_H/A_V ratio of (1.39 +- 0.14) x 10^21
cm^-2 mag^-1 for Class III sources in the Orion Nebula Cluster where the given
error does not include systematic uncertainties. This ratio is consistent with
similar studies in other star-forming regions and approximately 31% lower than
the Galactic value. We find no obvious trends in the spatial distribution of
N_H/A_V ratios. Changes in the assumed extinction law and elemental abundances
are demonstrated to have a relevant impact on deduced A_V and N_H values,
respectively. Large systematic uncertainties associated with metal abundances
in the Orion Nebula Cluster represent the primary limitation for the deduction
of a definitive N_H/A_V ratio and the physical interpretation of these results.
