Abstract: A biconic connector (40) includes two plugs (44-44) each of which terminates a single fiber optical cable (55) and each of which includes a truncated conically shaped end portion (50). The connector also includes an alignment sleeve having back-to-back conically shaped cavities each of which is adapted to receive an end portion of a plug. In order to minimize loss through the connection, it becomes important for the centroid of the cross-sectional area of a light beam in the end face of the plug to be coincident with the axis of revolution of the conically shaped surface of plug. This is accomplished by holding the plug in a fixture such that its end portion is exposed and the fixture adapted to be turned about an axis of rotation. Images of a light beam launched into the optical fiber are acquired in a plane through the end face of the plug.