  Orbital tomography has recently been established as a technique to
reconstruct molecular orbitals directly from photoemission data using iterative
phase retrieval algorithms. In this work, we present a detailed description of
steps for processing of the photoemission data followed by an improved
iterative phase retrieval procedure and the interpretation of reconstructed
two-dimensional orbital distributions. We address the issue of background
subtraction by suggesting a signal restoration routine based on the
maximization of mutual information algorithm and solve the problem of finding
the geometrical center in the reconstruction by using a tight-centered object
support in a two-step phase retrieval procedure. The proposed image processing
and improved phase retrieval procedures are used to reconstruct the highest
occupied molecular orbital of pentacene on Ag(110), using photoemission data
only. The results of the reconstruction agree well with the density functional
theory simulation, modified to comply with the experimental conditions. By
comparison with photoelectron holography, we show that the reconstructed
two-dimensional orbital distribution can be interpreted as a superposition of
the in-focus orbital distribution evaluated at the z = 0 plane and out-of-focus
distributions evaluated at other z = const planes. Three-dimensional molecular
orbital distributions could thus be reconstructed directly from two-dimensional
photoemission data, provided the axial resolution of the imaging system is high
enough.
