This implementation accompanies the article "On the eigenmodes of periodic orbits for multiple scattering problems in 2D", D. Huybrechs and P. Opsomer, submitted. We compute and validate a Taylor approximation of the equilibrium phase of the density in ray tracing. We initially exploit symmetry in the case of two circular scatterers, but also provide an explicit algorithm for an arbitrary number of general 2D obstacles. The coefficients, as well as the time to compute them, are independent of the wavenumber and of the incident wave.