  Helioseismology is the study of the solar interior using observations of
oscillations at the surface. It suffers from systematic errors, such as a
center-to-limb error in travel-time measurements. Understanding these errors
requires a good understanding of the nontrivial relationship between wave
displacement and helioseismic observables. The wave displacement causes
perturbations in the atmospheric thermodynamical quantities which perturb the
opacity, the optical depth, the source function, and the local ray geometry,
thus affecting the emergent intensity. We aim to establish the most complete
relationship up to now between the displacement and the intensity perturbation
by solving the radiative transfer problem in the atmosphere. We derive an
expression for the intensity perturbation caused by acoustic oscillations at
any point on the solar disk by applying the first-order perturbation theory. As
input, we consider adiabatic modes of oscillation of different degrees. The
background and the perturbed intensities are computed considering the main
sources of opacity in the continuum. We find that, for all modes, the
perturbations to the thermodynamical quantities are not sufficient to model the
intensity. In addition, the geometrical effects due to the displacement must be
taken into account as they lead to a difference in amplitude and a phase shift
between the temperature at the surface and intensity perturbations. The closer
to the limb, the larger the differences. This work presents improvements for
the computation of the intensity perturbations, in particular for high-degree
modes, and explains differences in intensity computations in earlier works. The
phase shifts and amplitude differences between the temperature and intensity
perturbations increase towards the limb. This should help to interpret some of
the systematic center-to-limb effects observed in local helioseismology.
