A new method for measuring atmospheric refraction angles is presented, with in-orbit measurements demonstrating a precision of +/-0.02 arcsec (+/-0.1 mu rad). Key advantages of the method are the following: (1) Simultaneous observation of two celestial points during occultation (i.e., top and bottom edges of the solar image) eliminates error from instrument attitude uncertainty. (2) The refraction angle is primarily a normalized difference measurement, causing only scale error, not absolute error. (3) A large number of detector pixels are used in the edge location by fitting to a known edge shape. The resulting refraction angle measurements allow temperature sounding up to the lower mesosphere. (C) 2009 Optical Society of America