© 2020, © 2020 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group. We study the inverse problem in Optical Tomography of determining the optical properties of a medium (Formula presented.), with (Formula presented.), under the so-called diffusion approximation. We consider the time-harmonic case where ¿ is probed with an input field that is modulated with a fixed harmonic frequency (Formula presented.), where c is the speed of light and k is the wave number. We prove a result of Lipschitz stability of the absorption coefficient (Formula presented.) at the boundary (Formula presented.) in terms of the measurements in the case when the scattering coefficient (Formula presented.) is assumed to be known and k belongs to certain intervals depending on some a-priori bounds on (Formula presented.), (Formula presented.).