Two linearly independent polarizations of a gravitational wave are illustrated by displaying their effect on a ring of free particles arrayed in a plane perpendicular to the direction of the wave. The figure shows the distortions in the original circle that the wave produces if it carries the + polarization or the x polarization. In general relativity there are only 2 independent polarizations. The ones shown here are orthogonal to each other and the polarizations are transverse to the direction of the wave.
The bottom of the panel shows the response of the laser interferometer to the passage of a gravitational wave.