Comparison of the definitions for azimuthal orientation of ±m-paired Zernike polynomials. The angular orientation of the Zernike polynomials $Z_n^{\pm m}$ is illustrated for different choices of θ₀ (black arrow: common definition ${\theta }_0^{\mathrm{lp}}$; white arrow: proposed new definition ${\theta }_0^{\mathrm{fp}}$). Left: tertiary astigmatism $Z_6^{\pm 2}$ with peaks at same azimuthal orientation. Middle: primary coma $Z_3^{\pm 1}$, where π = 180° has to be added. Right: secondary trefoil $Z_5^{\pm 3}$, where π/3 = 60° must be subtracted.