  If the alpha effect plays a role in the generation of the Sun's magnetic
field, the field should show evidence of magnetic helicity of opposite signs at
large and small length scales. Measuring this faces two challenges: (i) in
weak-field regions, horizontal field measurements are unreliable because of the
pi ambiguity, and (ii) one needs a truly global approach to computing helicity
spectra in the case where one expects a sign reversal across the equator at all
wavenumbers. Here we develop such a method using spin-2 spherical harmonics to
decompose the linear polarization in terms of the parity-even and parity-odd E
and B polarizations, respectively. Using simple one- and two-dimensional
models, we show that the product of the spectral decompositions of E and B,
taken at spherical harmonic degrees that are shifted by one, can act as a proxy
of the global magnetic helicity with a sign that represents that in the
northern hemisphere. We then apply this method to the analysis of solar
synoptic vector magnetograms, from which we extract a pseudo-polarization
corresponding to a "pi-ambiguated" magnetic field, i.e., a magnetic field
vector that has no arrow. We find a negative sign of the global EB helicity
proxy at spherical harmonic degrees of around 6. This could indicate a positive
magnetic helicity at large length scales, but the spectrum fails to capture
clear evidence of the well-known negative magnetic helicity at smaller scales.
This method might also be applicable to stellar and Galactic polarization data.
