The broken ray transform in n dimensions with flat reflecting boundary

We study the broken ray transform on n-dimensional Euclidean domains where the reecting parts of the boundary are at and establish injectivity and stability under certain conditions. Given a subset E of the boundary ∂Ω such that ∂Ω\E is itself at (contained in a union of hyperplanes), we measure the attenuation of all broken rays starting and ending at E with the standard optical reection rule applied to ∂Ω\E. By localizing the measurement operator around broken rays which reflect off a flixed sequence of at hyperplanes, we can apply the analytic microlocal approach of Frigyik, Stefanov, and Uhlmann ([7]) for the ordinary ray transform by means of a local path unfolding. This generalizes the author's previous result in [9], although we can no longer treat reections from corner points. Similar to the result for the two dimensional square, we show that the normal operator is a classical pseudo differential operator of order –1 plus a smoothing term with (C^∞₀) Schwartz kernel.