Study On Point-diffraction Interferometry Based On Fourier Transform

Since 1960s the industry producing has developed a lot. After the sprang up of machine tools, engines, aviation and spaceflight, cars, and electronic industry, the developing and producing of many different complex parts need advanced checking techniques and instruments, which accelerated the birth of coordinate measuring machine(CMM) which embodiments 3-D measure technique. In the past years with the fast improving and developing of machine manufacture techniques, numerical control techniques, numerical optimization theories, program software developing environment and optic information techniques, the coordinate measuring machine has developed quickly and become more perfect.Nowadays. Coordinate measuring machine (CMM) was used in more and more areas. The CMMs have a higher measure precision which equipped with optical interferometer. However, the Abbe systemic error would be produced in measurement process because of the Abbe offsets. Currently, a volumetric interferometer (point diffraction interferometer) was presented. It has been specially designed to improve the measurement accuracy of the three-dimensional coordinate metrology by reducing excessive Abbe offsets. The interferometer is composed of two main parts: one is a three-dimensionally movable target and the other is a stationary two-dimensional array of photo-detectors. The target made of point diffraction sources emanates two spherical wavefronts, of which interference intensity is monitored by the photo-detectors. Applying phase shifting allows the phases of the photo-detectors to be precisely obtained, and the measured phases are fitted to a geometric model of multilateration so as to determine the xyz-location of the target by minimizing least square errors. This article emphasizes on point-diffraction interferometry.1. We present a point-diffraction interferometry based on Fourier transform instead of the phase-shifting point-diffraction interferometry. It is a measurement method following the diffraction and interference theory of the point light source. The phase message of interference pattern was obtained by the Fourier transform pattern analysis method. And the xyz-coordinates of the two point diffraction sources were calculated by the modified Newton method based on the BFGS algorithm.2. The Point-diffraction Interferometry based on phase-shifting algorithm is analyzed particularly. The best condition for the nonlinear nonrestraint optimization question and iteration termination rule are introduced. Moreover, several common linear search method and descending algorithm are introduced, the corresponding algorithm are given in the paper. According to different adapting characteristics, we find out the optimization algorithm suitable for the experiment, and the algorithm flow chart is given.3. The experiments Point-diffraction Interferometry of based on phase-shifting algorithm and that on FTP is simulated in the instances with and without random disturbing noises are simulated. It was proved in this article that the point-diffraction interferometry based on Fourier transform could reduce the effect of the random noise on measurement effectively by computer simulate experiment. Therefore, this method is valuable in the actual measure environment with random noise.