Broken ray transforms (BRTs) are typically considered to be reciprocal,
meaning that the transform is independent of the direction in which a photon
travels along a given broken ray. However, if the photon can change its energy
(or be absorbed and re-radiated at a different frequency) at the vertex of the
ray, then reciprocity is lost. In optics, non-reciprocal BRTs are applicable to
imaging problems with fluorescent contrast agents. In the case of x-ray imaging,
problems with single Compton scattering also give rise to non-reciprocal
BRTs. In this paper, we focus on tomographic optical fluorescence imaging
and show that, by reversing the path of a photon and using the non-reciprocity
of the data function, we can reconstruct simultaneously and independently
all optical properties of the medium (the intrinsic attenuation coefficients at
the excitation and the fluorescence frequency and the concentration of the
contrast agent). Our results are also applicable to inverting BRTs that arise
due to single Compton scattering.