Relativistic effects on the imaging by a rotating optical system

Context. High accuracy astrometric instruments like Gaia aiming at an accuracy of 1 microarcsecond cannot be considered as point-like observers in the framework of relativistic modelling of observable quantities. Aims. Special-relativistic effects on the imaging by a non-point-like arbitrarily moving optical instrument are discussed. Methods. A special-relativistic reflection law for a mirror of arbitrary shape and motion is derived in the limit of geometrical optics. The aberration patterns are computed with ray tracing using a full pecial-relativistic model for two simple rotating optical instrument. Results. It was found that the effect of special-relativistic reflection law on the photocenters of aberration patterns of an optical system rotating with a moderate angular velocity of $60 \arcsec/{\rm s}$ may be at the level of 1 microarcsecond if the system involves mirrors significantly inclined relative to the optical axis. Conclusions. Special-relativistic optical modelling of the future astrometric instrument is generally speaking indispensable if a level of a few microarcseconds is envisaged.