We reduce boundary determination of an unknown function and its normal
derivatives from the (possibly weighted and attenuated) broken ray data to the
injectivity of certain geodesic ray transforms on the boundary. For
determination of the values of the function itself we obtain the usual geodesic
ray transform, but for derivatives this transform has to be weighted by powers
of the second fundamental form. The problem studied here is related to
Calder\'on's problem with partial data.Comment: 23 pages, 1 figure; final versio
