Formulae and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential

For the Schrödinger equation at fixed energy with a potential supported in a bounded domain we give formulae and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential. For the case of zero background potential these results were obtained in (Novikov 1988 Multidimensional inverse spectral problem for the equation -Δψ + (v(x) - Eu(x))ψ = 0 Funkt. Anal. Ego Pril. 22 (4) 11-22).