  In this paper, we study association schemes on the anisotropic points of
classical polar spaces. Our main result concerns non-degenerate elliptic and
hyperbolic quadrics in PG$(n,q)$ with $q$ odd. We define relations on the
anisotropic points of such a quadric that depend on the type of line spanned by
the points and whether or not they are of the same "quadratic type". This
yields an imprimitive $5$-class association scheme. We calculate the matrices
of eigenvalues and dual eigenvalues of this scheme.
  We also use this result, together with similar results from the literature
concerning other classical polar spaces, to exactly calculate the spectrum of
orthogonality graphs on the anisotropic points of non-degenerate quadrics in
odd characteristic and of non-degenerate Hermitian varieties. As a byproduct,
we obtain a $3$-class association scheme on the anisotropic points of
non-degenerate Hermitian varieties, where the relation containing two points
depends on the type of line spanned by these points, and whether or not they
are orthogonal.
