  A new algorithm to perform coherent mode decomposition of the undulator
radiation is proposed. It is based in separating the horizontal and vertical
directions, reducing the problem by working with one-dimension wavefronts. The
validity conditions of this approximation are discussed. Simulations require
low computer resources, and run interactively in a laptop. We study the
focusing with lenses of the radiation emitted by an undulator in a
fourth-generation storage ring (EBS-ESRF). Results are compared against
multiple optics packages implementing a variety of methods for dealing with
partial coherence: full 2D coherent mode decomposition, Monte-Carlo combination
of wavefronts from electrons entering the undulator with different initial
conditions, and hybrid ray-tracing correcting geometrical optics with wave
optics.
