  We present our investigation into the impact of wavefront errors on high
accuracy astrometry using Fourier Optics. MICADO, the upcoming near-IR imaging
instrument for the Extremely Large Telescope, will offer capabilities for
relative astrometry with an accuracy of 50 micro arcseconds ({\mu}as). Due to
the large size of the point spread function (PSF) compared to the astrometric
requirement, the detailed shape and position of the PSF on the detector must be
well understood. Furthermore, because the atmospheric dispersion corrector of
MICADO is a moving component within an otherwise mostly static instrument, it
might not be sufficient to perform a simple pre-observation calibration.
Therefore, we have built a Fourier Optics framework, allowing us to evaluate
the small changes in the centroid position of the PSF as a function of
wavefront error. For a complete evaluation, we model both the low order surface
form errors, using Zernike polynomials, and the mid- and high-spatial
frequencies, using Power Spectral Density analysis. The described work will
then make it possible, performing full diffractive beam propagation, to assess
the expected astrometric performance of MICADO.
