Diffractive Microlensing III: Astrometric Signatures

Gravitational lensing is generally treated in the geometric optics limit; however, when the wavelength of the radiation approaches or exceeds the Schwarzschild radius of the lens, diffraction becomes important. Although the magnification generated by diffractive gravitational lensing is well understood, the astrometric signatures of diffractive microlensing are first derived in this paper along with a simple closed-form bound for the astrometric shift. This simple bound yields the maximal shifts for substellar lenses in solar neighbourhood observed at 20~GHz, accessible to high sensitivity, high angular resolution radio telescopes such as the proposed Square Kilometre Array (SKA).