We derive the weak value deflection given in an article by Dixon et al. [P. B. Dixon et al. Phys. Rev. Lett. 102 173601 (2009)] both quantum mechanically and classically, including diffraction effects. This article is meant to cover some of the mathematical details omitted in that article owing to space constraints.
J. C. Howell, D. J. Starling, P. B. Dixon, P. K. Vudyasetu, and A. N. Jordan, Interferometric Weak Value Deflections: Quantum and Classical Treatments, Phys. Rev. A 81(3), 033813. https://doi.org/10.1103/PhysRevA.81.033813
American Physical Society