A new kind of surface-measuring machine has been developed under government contract at Itek Optical Systems, a Division of Itek Corporation, to assist in the fabrication of large, highly aspheric optical elements. The machine uses four steerable distance-measuring interferometers at the corners of a tetrahedron to measure the positions of a retroreflective target placed at various locations against the surface being measured. Using four interferometers gives redundant information so that, from a set of measurement data, the dimensions of the machine as well as the coordinates of the measurement points can be determined. The machine is, therefore, self-calibrating and does not require a structure made to high accuracy. A wood-structured prototype of this machine was made whose key components are a simple form of air bearing steering mirror, a wide-angle cat's eye retroreflector used as the movable target, and tracking sensors and servos to provide automatic tracking of the cat's eye by the four laser beams. The data are taken and analyzed by computer. The output is given in terms of error relative to an equation of the desired surface. In tests of this machine, measurements of a 0.7 m diameter mirror blank have been made with an accuracy on the order of 0.2µm rms.