A study of first-order Talbot resonators is presented. The general conditions for Talbot effect in ABCD systems are determined. These conditions are applied to the computation of the diffraction overlapping coefficients between array Gaussian emitters in a general first-order Talbot resonator. Relations on the ray-transfer matrix to generate the symmetric and the totally antisymmetric supermodes of the array are derived. These relations generalize the free-space, round-trip lengths of 1/2 and 1/4 of the Talbot distance. A new type of resonator based on a plano-convex gradient-index rod is proposed.