Photochromic switching of additively colored La, Ce, Gd, or Tb doped CaF2with linearly polarized UV light and subsequent thermal decay of other photochromic effects leads to a linear dichroism of the two major absorption bands, band 1 (∼4000 Å) and band 2 (∼6000 Å), of the thermally stable state. The dichroism is due to a net reorientation of an anisotropic center having a symmetry axis that can lie along any one of the four crystal directions. The photochromically active band, band 1, is shown to be due to an absorption dipole in the direction of the symmetry axis, while band 2 is due to two orthogonal absorption dipoles perpendicular to the symmetry axis. The direction of the symmetry axis and the character of the absorption bands suggest an center perturbed by a rare earth replacing a nearest neighbor Ca. A possibility remains, however, that the center is more complex.