We study a particular broken ray transform on the Euclidean unit square and establish injectivity and stability for C_0~2 perturbations of a vanishing absorption parameter σ ≡ 0. Given an open subset E of the boundary, we measure the attenuation of all broken rays starting and ending at E with the standard optical reflection rule applied to ?ΩE. Using the analytic microlocal approach of Frigyik et al. for the X-ray transform on generic families of curves, we show injectivity via a path unfolding argument under suitable conditions on the available broken rays. Then we show that with a suitable decomposition of the measurement operator via smooth cutoff functions, the associated normal operator is a classical pseudo differential operator of order ?1, which leads to the desired result.
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