Statistical isotropy is often assumed in cosmology and should be tested rigorously against observational data .
We construct simple quadratic estimators to reconstruct asymmetry in the primordial power spectrum from CMB temperature and polarization data and verify their accuracy using simulations with quadrupole power asymmetry .
We show that the Planck mission , with its millions of signal-dominated modes of the temperature anisotropy , should be able to constrain the amplitude of any spherical multipole of a scale-invariant quadrupole asymmetry at the 0.01 level ( 2 \sigma ) .
Almost independent constraints can be obtained from polarization at the 0.03 level after four full-sky surveys , providing an important consistency test .
If the amplitude of the asymmetry is large enough , constraining its scale-dependence should become possible .
In scale-free quadrupole models with 1 % asymmetry , consistent with the current limits from WMAP temperature data ( after correction for beam asymmetries ) , Planck should constrain the spectral index q of power-law departures from asymmetry to \Delta q = 0.3 .
Finally , we show how to constrain models with axisymmetry in the same framework .
For scale-free quadrupole models , Planck should constrain the direction of the asymmetry to a 1 \sigma accuracy of about 2 degrees using one year of temperature data .