  We develop the eikonal perturbation theory to describe the strong-field
ionization by finite laser pulses. This approach in the first order with
respect to the binding potential (the so-called generalized eikonal
approximation) avoids a singularity at the potential center. Thus, in contrast
to the ordinary eikonal approximation, it allows to treat rescattering
phenomena in terms of quantum trajectories. We demonstrate how the first Born
approximation and its domain of validity follow from eikonal perturbation
theory. Using this approach, we study the coherent diffraction patterns in
photoelectron energy spectra and their modifications induced by the interaction
of photoelectrons with the atomic potential. Along with these first results, we
discuss the prospects of using the generalized eikonal approximation to study
strong-field ionization from multi-centered atomic systems and to study other
strong-field phenomena.
