The procedure of calculation of the spectral line shape in optical spectra of rare-earth ions in crystals with the inclusion of random deformations of an elastically anisotropic crystal lattice caused by point defects is developed. The distribution function of components of the random strain tensor in the case of a low defect concentration is obtained as the generalized six-dimensional Lorentz distribution. The distribution function parameters are represented by the integral functional of the strain tensor components on a sphere of unit radius containing an isotropic point defect in its center. The numerical calculations of the strain tensors induced by point defects and the parameters of the distribution functions of random strains in LiLuF_4 and LaAlO_3 crystals have been performed. The calculated envelope with the doublet structure corresponding to the Γ_2(^3 H _4) → Γ_34(^3 H _5) singlet–doublet transition in the absorption spectrum of Pr^3+ ions in the LiLuF_4 crystal agrees well with the data of the measurements.

The results of investigations of Er3+ ions at an optical transition with a telecommunication wavelength (λ~1530 nm) in a YPO4 crystal by using photon echo and high-resolution laser spectroscopy in magnetic fields up to 4 T are presented. The maximum coherence time (T2) was 113 μs in a magnetic field of 4 T when it is oriented along the optical axis c of the crystal. The main sources of decoherence are discussed.