Cartesian-coordinate-system approach of the coordinate measuring machine(CMM) design suffers the parallax error that is caused by the Abbe's offset existing between the probe and measurement axes that are not geometrically perfect. The achievable volumetric uncertainty of the orthogonal type CMM is ultimately limited by this parallax error and is in the range of few micrometers in a working volume of about half a cubic meter at best. One attempt made in recent years is the so-called multilateration, which aims to reduce the parallax error by taking non-orthogonal parallel-mechanism structure wherein measurement axes are directly connected to the probe to minimize Abbe's offset. This multilateration determines the three-dimensional xyz-coordinate of the probe by solving inverse kinematics of measured diagonal distances of the probe from several fixed points. As a scheme of the multilateration, the volumetric interferometer was proposed which directly measure the xyz-coordinate without attaching either rotating joints or retro-reflectors to the probe. However the volumetric interferometer has difficulties that the measurment speed is limited by CCD & characteristics of PZT, the non-linearity errors of CCD & PZT limits the measurement capacity and the system is sensitive to noises of other frequencies.
To cope with difficulties of the volumetric interferometer, here in this paper, we proposed the heterodyne technique as a phase extraction method. The technique enables us to load the distance information not on intensity but on frequency. The volumetric interferometry using heterodyne technique generates two spherical wavefronts of different frequencies from the probe. The emanated wavefronts interfere with each other within the working volume, while a two-dimensional photodetector array fixed on the machine frame captures the resulting interferometric field. Phase information is then obtained by heterodyne technique and fitted to a geometric model of the multilateration, from which the xyz-coordinate of the probe are determined so as to minimize least square errors. A prototype demonstrates that the proposed interferometer is capable of measuring the xyz-coordinate of the probe with a repeatability of less than ±1.056㎛(±2σ) with phase measuring speed upto 1 kHz.
