Research On The Key Technologies Of The Spherical Grating Interferometer For Surface Measurement

Large range, high resolution and high precision surface measurement technique is an important research field of metrology. Especially with development of nano-science and technology, the resolution of instruments raised to nano-scale has bacome a reality demand. At the same time, measurement for engineering surface requires instruments with greater range. Those are challenge to existing sensor technique and measurement methods.After analyzing the development in this field in the recent years, a new kind of grating interferometer called spherical grating interferometer is proposed, which is a new technique for surface measurement. These key problems, such as theory of the spherical grating interferometric sensor, optical path configuration of the grating interferometer, high resolution electronic system, calibration method on the non-liner characteristics of the sensor, surface separation technologies, were researched. Solving these problems can help to build a new system of surface measurement and analysis.(1) The complex amplitude transmissivity function of spherical grating is given. In Fresnel diffraction and Fraunhofer diffraction using spherical sinusoidal phase grating, the distribution of the complex amplitude and light intensity of diffraction light are analyzed and compared with that using plane sinusoidal phase grating based on the theory of scalar diffraction. The result of the distributions of the light intensity using the two instruments in the Matlab simulation is the same as that in experiment.(2) A new optical path configuration used in grating interferometer is proposed in order to reduce the sensitivity of the interference fringe to the disturbing shifts and tilts of scale due to additional motion of the grating. Use the cat's-eye retroreflector to reflect the first diffraction light to the grating to generate the second diffraction light, then the interference fringe can be generated using the second diffraction light. This new method is not much less sensitive to the additional movement of the grating. This new method is analyzed in theory and it has been proved to be able to improve the quality of the interfere fringe in the experiment. (3) The ROM subdivision circuit system is developed which has high subdivision multiple and high frequency response. This circuit is based on high-speed A/D and CPLD and also has the function of preventing counting error. Then the subdivision error is analyzed. The influence of the zero offset, unequal amplitude of two channels, quadrature phase shift, odd harmonics and even harmonics on subdivision precision are also investigated. A real-time subdivision error compensation algorithm is developed, this algorithm can compensate on the subdivision error caused by zero offset, unequal amplitude of two channels and quadrature phase shift. The three above errors can be totally compensated in no more than three grating signal periods. The influence on the algorithm from harmonics is analyzed and developed. Through experiments the effect of this algorithm is proved. The advantage of this algorithm is simple, requiring little memory, easy to be real time processed.(4) The large-range surface measuring sensor has a problem of non-liner which leads signal distortion because of lever and finite ball tip radius.After analyzing several calibration technologies and methods, we used the standard ball to calibrate the sensor and build a calibration model of the transmission characteristic of the sensor. Then we got the solution using the least squares fitting method. The result showed that when the radius of the standard ball is 80.029mm, the residual form error is no more than 2μm after calibration, relative error is 0.0025%. When the radius of the standard ball is 12.5086mm, the residual form error is no more than 0.5μm after calibration, relative error is 0.004%.(5) A new approximate mathematic model of Gaussian filter is proposed on the basis of central limit theorem. The amplitude deviation is approximate to 0.25% when 8 approximate filter cascaded. A fast algorithm of Gaussian filtering is given to separate the surface roughness, waviness and form deviation. This algorithm can be also used in 3-D surface measurement. Depending on the separability of the 2-D Gaussian filter, a 2-D Gaussian filter is separated into two 1-D Gaussian filter. The realization of the 2-D Gaussian filter is predigested and the filtering efficiency is improved in 3-D surface measurement.The result of the experiment showed that the theories, technologies and methods are correct which is affording a stable foundation to developing a new instrument for surface measurement.