A spectrophotometric apparatus (1) is proposed for determining optical parameters in a scattering medium (4) based on the measurement of attenuation of light propagating through said medium (4) by diffusion. To eliminate the detrimental effect of light being guided in an intermediate optical layer (25) between a surface (23) of the medium (4) and a contact surface (8) of the apparatus (1), either a multitude of optical barriers (4) may be formed in the contact surface (8) or the angular range over which light is emitted or received by the apparatus (1) may be limited by appropriate means (13). With both of these alternative approaches, light propagation in the intermediate layer (25) can be suppressed, leading to increased measurement accuracy. The invention is particularly beneficial for building an oximeter (1) with improved precision. Further aspects of the invention concern features for improving the applicability of the apparatus (1) on curved surfaces (23) such as the strongly curved skulls of neonates (c.f. Fig. 2).
