Measuring Interpreting and Translating Electron Quasiparticle Phonon Interactions on the Surfaces of the Topological Insulators Bismuth Selenide and Bismuth Telluride Introduction Properties of Bi2Se3 and Bi2Te3 Helium atom surface scattering (HASS) Experimental Apparatus and Technique Pseudocharge phonon model HASS results from the surface of Bi2Se3 and Bi2Te3 Translating between electron and phonon perspectives Conclusion and future directions Appendices. The thesis presents experimental and theoretical results about the surface dynamics and the surface Dirac fermion (DF) spectral function of the strong topological insulators Bi2Te3 and Bi2Se3. The experimental results reveal the presence of a strong Kohn anomaly in the measured surface phonon dispersion of a low lying optical mode and the absence of surface Rayleigh acoustic phonons. Fitting the experimental data to theoretical models employing phonon Matsubara functions allowed the extraction of the matrix elements of the coupling Hamiltonian and the modifications to the surface phonon propagator that are encoded in the phonon self energy. This allowed for the first time calculation of phonon mode specific DF coupling λν(q) from experimental data with average coupling significantly higher than typical values for metals underscoring the strong coupling between optical surface phonons and surface DFs in topological insulators. Finally to connect to experimental results obtained from photoemission spectroscopies an electronic (DF) Matsubara function was constructed using the determined electron phonon matrix elements and the optical phonon dispersion. This allowed calculation of the DF spectral function and density of states allowing for comparison with photoemission and scanning tunneling spectroscopies. The results set the necessary energy resolution and extraction methodology for calculating λ from the DF perspective.