  The fringe pattern that allows geometrical and orbital structure information
to be extracted from LIED spectra of symmetric molecules is shown to reflect a
symmetry conservation principle. We show that under a field polarization which
preserves certain symmetry elements of the molecule, the symmetry character of
the initial wave function is conserved during its time-evolution. We present a
symmetry analysis of a deviation from a perfect alignment by decomposing the
field into a major, symmetry-determining part, and a minor, symmetry breaking,
part. This decomposition leads to a corresponding factorization of the
time-evolution operator. The formalism is applied to the analysis of the
robustness of LIED readings and inversions with respect to deviations from a
perfect perpendicular and parallel alignment of a symmetric ABA triatomic
molecule. The results indicate a particularly strong stability of the type of
LIED spectra associated with the perpendicular alignment situation.
