This same method can also be used to find the fundamental mode size of a stable optical resonator.
Given the initial beam parameter, qi, one can use the ray transfer matrix of an optical system,
This is no longer true if those planes do not coincide with the principal direction of the surface on which the beam impinges; that case is called general astigmatism.
[3] Formulas for an incidence angle θi were derived in Massey and Siegman's 1969 paper.
With this matrix and by making qi = qf, a quadratic is formed as: Solving this equation gives the beam parameter for the chosen starting position in the cavity, and by propagating, the beam parameter for any other location in the cavity can be found.