Relativistic effects on imaging by a rotating optical system^*

¹ Departament d'Astronomia i Meteorologia, Universitat de Barcelona, Av. Diagonal 647, 08028 Barcelona, Spain
² Lohrmann Observatory, Dresden Technical University, Mommsenstr. 13, 01062 Dresden, Germany

Received: 7 October 2005
Accepted: 29 September 2006

Abstract

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 special-relativistic model for two simple rotating optical instruments.

Results.The effect of special-relativistic reflection law on the photocenters of the aberration patterns of an optical system rotating with a moderate angular velocity of 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 future astrometric instruments is indispensable if a level of a few microarcseconds is envisaged.