  We study the inverse problem in Optical Tomography of determining the optical
properties of a medium $\Omega\subset\mathbb{R}^n$, with $n\geq 3$, under the
so-called diffusion approximation. We consider the time-harmonic case where
$\Omega$ is probed with an input field that is modulated with a fixed harmonic
frequency $\omega=\frac{k}{c}$, where $c$ is the speed of light and $k$ is the
wave number. Under suitable conditions that include a range of variability for
$k$, we prove a result of H\"older stability of the derivatives of the
absorption coefficient $\mu_a$ of any order at the boundary $\partial\Omega$ in
terms of the measurements, in the case when the scattering coefficient $\mu_s$
is assumed to be known. The stability estimates rely on the construction of
singular solutions of the underlying forward elliptic system, which extend
results obtained in J. Differential Equations 84 (2): 252-272 for the single
elliptic equation.
