387 research outputs found
A reflection approach to the broken ray transform
We reduce the broken ray transform on some Riemannian manifolds (with
corners) to the geodesic ray transform on another manifold, which is obtained
from the original one by reflection. We give examples of this idea and present
injectivity results for the broken ray transform using corresponding earlier
results for the geodesic ray transform. Examples of manifolds where the broken
ray transform is injective include Euclidean cones and parts of the spheres
. In addition, we introduce the periodic broken ray transform and use the
reflection argument to produce examples of manifolds where it is injective. We
also give counterexamples to both periodic and nonperiodic cases. The broken
ray transform arises in Calder\'on's problem with partial data, and we give
implications of our results for this application.Comment: 29 pages, 6 figures; final versio
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