This work compares the reflection optical response of a homogeneous sample with natural optical activity with the Bragg reflection from an inhomogeneous system consisting of a periodic helicoidal structure. Examples of periodic helicoidal systems are cholesteric liquid crystals and the cuticle of some beetles. For transmitted light natural optical activity and Bragg reflection essentially lead to the same type of optical response, but there are fundamental differences on how they reflect circularly polarized light. The Mueller matrix symmetries for the two types of media are theoretically deduced and experimentally verified with ellipsometry measurements. (C) 2016 Elsevier B.V. All rights reserved.