Abstract: Ringel duality is a fundamental symmetry on Category O associated to a semisimple Lie algebra. It is realized by the so-called "Radon transform," which categorifies a basic multiplication operation on the finite-dimensional Hecke algebra. In this talk, we study the affine analogue of Ringel duality, realized by the affine Radon transform between sheaves on the thin and thick affine flag varieties. Our main tool is Bezrukavnikov's equivalence between two categorifications of the affine Hecke algebra associated to a reductive group, which can be thought of as a tamely ramified local geometric Langlands correspondence. By understanding how the affine Radon transform functor interacts with various t-structures which appear naturally in Bezrukavnikov's equivalence, we use this functor to prove a conjecture of Arkhipov-Bezrukavnikov concerning convolution-exact and tilting perverse sheaves which appears in one of the first installments in the series of papers which established Bezrukavnikov's equivalence.