  The paper presents an extension and a refinement of our previous work on the
extraction of the doubly virtual forward Compton scattering amplitude on the
lattice by using the background field technique, Phys. Rev. D 95, 031502 (2017)
(arXiv:1610.05545). The zero frequency limit for the periodic background field
is discussed, in which the well-known result is reproduced. Further, an upper
limit for the magnitude of the external field is established for which the
perturbative treatment is still possible. Finally, the framework is set for the
evaluation of the finite-volume corrections allowing for the analysis of
upcoming lattice results.
