When the para and perp polarization magnitudes are not equal, as happened during commissioning when the beam was presumably hitting the frames more during one diamond orientation, the experimental asymmetry picks up a dP*cos(2phi)**2 term. If very high statistics are available, it may be necessary to include this additional term to get a good fit probability.
Slowly drifting instrumental asymmetries can be measured using the sum of para and perp yields. However, when dP is not zero there will of course be a small (and easily correctable) bleed-through from the Sigma asymmetry proportional to dP*Sigma*cos(2phi).