  MICADO, a near-infrared imager for the Extremely Large Telescope, is being
designed to deliver diffraction limited imaging and 50 micro arcsecond
(${\mu}$as) astrometric accuracy. MICADO employs an atmospheric dispersion
corrector (ADC) to keep the chromatic elongation of the point spread function
(PSF) under control. We must understand the dispersion and residuals after
correction to reach the optimum performance. Therefore, we identified several
sources of chromatic dispersion that need to be considered for the MICADO ADC.
First, we compared common models of atmospheric dispersion to investigate
whether these models remain suitable for MICADO. We showed that the
differential dispersion between common atmospheric models and integration over
the full atmosphere is less than 10 ${\mu}$as for most observations in H-band.
We then performed an error propagation analysis to understand the uncertainty
in the atmospheric dispersion as a function of atmospheric conditions. In
addition, we investigated the impact of photometric color on the astrometric
performance. While the differential refraction between stars within the same
field of view can be significant, the inclusion of an ADC rendered this effect
negligible. For MICADO specifically, we found that the current optomechanical
design dominates the residual dispersion budget of 0.4 milli arcseconds (mas),
with a contribution of 0.31 mas due to the positioning accuracy of the prisms
and up to 0.15 mas due to a mismatch between the dispersive properties of the
glass and the atmosphere. We found no showstoppers in the design of the MICADO
ADC for achieving 50 ${\mu}$as relative astrometric accuracy.
