Abstract: Cryogenic testing of the James Webb Space Telescope (JWST) included center-of-curvature metrology of the 18-segment primary mirror (PM). The Center-of-Curvature Optical Assembly (COCOA) consisted of a multiple-wavelength interferometer, a reflective null, coarse and fine alignment systems, and two displacement measuring interferometer systems. The COCOA enabled alignment and phasing of the segments from millimeter-level errors down to the nanometer level. This paper describes the COCOA, the t…