An improved method of optical tooling for the determination of angular alignment of randomly oriented multicomponent systems is described. The method was developed for alignment of the Orbiting Astronomical Observatory. A test object is mounted on a precision rotary table and viewed in autocollimation by a first-order theodolite. Azimuth and elevation readings from subject mirrors and relay mirrors, and azimuth readings from a dihedral mirror reference system are transformed into test object coordinates of roll, pitch, and yaw by a computer program. The program uses matrix optics methods. Errors are discussed.