A Fourier domain model for estimating astrometry errors due to static and quasi-static optical surface errors

Context. The wavefront aberrations due to optical surface errors in adaptive optics systems and science instruments can be a significant error source for high precision astrometry. Aims. This report derives formulas for evaluating these errors which may be useful in developing astrometry error budgets and optical surface quality specifications. Methods. A Fourier domain approach is used, and the errors on each optical surface are modeled as "phase screens" with stationary statistics at one or several conjugate ranges from the optical system pupil. Three classes of error are considered: (i) errors in initially calibrating the effects of static surface errors; (ii) the effects of beam translation, or "wander," across optical surfaces due to (for example) instrument boresighting error; and (iii) quasistatic surface errors which change from one observation to the next. Results. For each of these effects, we develop formulas describing the position estimation errors in a single observation of a science field, as well as the differential error between two separate observations. Sample numerical results are presented for the three classes of error, including some sample computations for the Thirty Meter Telescope and the NFIRAOS first-light adaptive optics system.