Refractivity from clutter (RFC) consists in inferring the lower atmospheric conditions from the clutter measured by a coastal or shipborne radar. A data processing tool based on an inverse or optimisation method is required. However, RFC cannot be used to retrieve all the atmospheric conditions. For some refractivity conditions, the modification of the electromagnetic wave behavior in the low troposphere is not detectable on the radar clutter return. In this paper, analytic conditions are given for trilinear atmospheric ducts to be retrievable by an RFC system. The study is based on a ray approach, and the results are validated through numerical simulations. It is finally extended to any piecewise linear profile. In the context of decision analysis, an RFC system user should know which ducts can be detected.Index Terms-Atmospheric duct, inverse problem, ray tracing, refractivity from clutter (RFC).