Tensor fluctuations are transverse-traceless perturbations to the metric, which can be viewed as gravitational waves. A plane gravitational wave perturbation represents a quadrupolar ``stretching'' of space in the plane of the perturbation (see Fig. 7). As the wave passes or its amplitude changes, a circle of test particles in the plane is distorted into an ellipse whose semi-major axis semi-minor axis as the spatial phase changes from crest trough (see Fig. 7, yellow ellipses). Heuristically, the accompanying stretching of the wavelength of photons produces a quadrupolar temperature variation with an pattern
in the coordinates defined by .
Thomson scattering again produces a polarization pattern from the quadrupole anisotropy. At the equator, the quadrupole pattern intersects the tangent ( ) plane with hot and cold lobes rotating in and out of the direction with the azimuthal angle . The polarization pattern is therefore purely Q with a dependence. At the pole, the quadrupole lobes lie completely in the polarization plane and produces the maximal polarization unlike the scalar and vector cases. The full pattern,
is shown in Fig. 8 (real part). Note that Q and U are present in nearly equal amounts for the tensors.