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An analytical method to compute the scattering of spherically and hemispherically stratified lens antennas is described. The expansion of any real source on spherical wave functions is detailed and validated by comparison to commercial software simulations and measurements at both 50 GHz and 77 GHz. A mode matching technique (MMT) based on spherical wave functions is first used to analyze the scattering by spherically stratified lens antennas. The far field patterns and directivity obtained are in excellent agreement with commercial software simulations and measurements for a six-shell Luneburg lens at 6 GHz. This MMT is then extended to hemispherically stratified lens antenna analysis. Its validation is also carried out by comparisons to both commercial software and measurements for a three-shell half Maxwell fish-eye lens fed by an open-ended waveguide at W-band. The expansion on spherical modes gives direct access to the field everywhere. To highlight the progressive focusing effect of inhomogeneous lens antennas, the electric field is mapped in terms of magnitude and phase in the neighborhood of the entire structure. One of the originalities of this work is the quantification of the reaction created by the scatterer on the feed. Narrowing the scatterer to a stratified lens does not affect the generality of the presented procedure. While providing controlled accuracy, the MMT tremendously reduces both computation time and memory load in comparison to commercial software.