  In my thesis, I present one particular example of the formalism capable of
describing the propagation of a family of light rays in a curved spacetime. It
is based on the resolvent operator of the geodesic deviation equation for null
geodesics which is known as the bilocal geodesic operator (BGO) formalism. The
BGO formalism generalizes the standard treatment of light ray bundles by
allowing observations extended in time or performed by a family of neighbouring
observers. Furthermore, it provides a more unified picture of relativistic
geometrical optics and imposes a number of consistency requirements between the
optical observables. The thesis begins with a brief introduction of the
transfer matrix and its relativistic versions known as the Jacobi propagators
and the bilocal geodesic operators. Then the basics of differential geometry
are reviewed, with an emphasis on the geometry of the tangent bundle and the
geodesic flow, which later provide the foundation for the BGO formalism. The
mathematical introduction is then followed by two articles about the
applications of the BGO formalism in the studies of optical distance measures
and the conclusion.
