On generalization of exponential ray transform in tomography

A generalization of the operator of exponential ray transform, which values are the initial data for the problem of emission computer tomography, is suggested. The generalization is based on physical facts lying at a foundation of photometry and wave optics, and is realized towards three directions. Namely, an absorption becomes a complex-valued function, integral moments of source distributions with weight are considered, and a dependence of sources on time is introduced. Connections between exponential ray transforms of various orders are established and their differential equations are obtained. Uniqueness theorems for boundary-value and initial-boundary value problems for the derived equations are proved. Close connections of generalized exponential ray transforms with integral geometry of tensor fields and tomography problems are marked.