This review on “wave optics in gravitational lensing” includes a derivation of the diffraction integral formula for the lensed wave amplitude using the path integral (§2), reduction of this formula to the geometric optics approximation in the short wavelength limit along with discussion on the condition that the wave effects become important (§3), examples of wave effects for a point-mass lens and the fold caustic (§4), and a numerical method of evaluating the diffraction integral (§5).
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Nakamura et al. (1999) studied this question.