In this paper, a real-time shape measurement system using pixel-by-pixel calibration tables is developed. We proposed a shape measurement method using pixel-by-pixel calibration tables produced with multiple reference planes. In this method, all the relationships between the phase of the projected grating and the spatial coordinates can be obtained for each pixel. This method excludes a lens distortion and intensity errors of the projected grating in measurement results theoretically. Tabulation makes short-time measurement possible. The linearity of each pixel of a camera is also corrected using pixel-by-pixel calibration tables for linearity immediately after grabbing images.
In phase-shifting digital holographic interferometry for measuring the displacement distribution of an object, holograms and reconstructed images have speckle noise, and they cause large errors in the calculation of the displacement analysis. In order to reduce the effect of speckle noise and hence to increase the sensitivity of the measurement of the displacement, we previously proposed a method using windowed holograms. In this paper, we propose a new method for averaging the obtained phase-difference values. Many phase-difference values at a point of the reconstructed image obtained with different windows for a hologram are averaged with weights. In order to check the effect on accuracy, the number n of windows used for averaging is varied. The weight, which is the m'th power of the absolute value of the complex amplitude of the reconstructed object, is also varied. As a result, when n becomes larger, the standard deviation of the errors becomes smaller. When the power m is 2, the error becomes a minimum. The standard deviation of the errors in the case of a flat plate with 316-nm out-of-plane displacement is 88 pm when n=1024 and m=2.
DMD (Digital Micro-mirror Device) is a new device, which has hundreds of thousands of micro-mirrors in one chip. This paper presents results of the development of a camera system based on DMD technology for phase analysis and shape measurement that we call "DMD reflection-type CCD camera" or "DMD camera". Incorporation of DMD technology enables accurate control of the intensity reaching the imaging detector of a camera. In order to perform accurate pixel-to-pixel correspondence adjustment with high accuracy, we use a moire technique. In addition, we introduce a high-speed controllable DMD operation board and improve the software to control each DMD mirror with high-speed. As the results, each DMD mirror works as a high-speed controllable shutter for the corresponding CCD pixel. Furthermore, as an application using the DMD camera, we perform an experiment by "DMD-type integrated phase-shifting method using correlations," which can analyze the phase distributions of projected grating from one image taken by the DMD camera. These principles and experimental results in dynamic condition are shown.
Non-contacting shape measurement for 3-D objects is important in automated manufacturing, quality control of components, 3-D solid modeling, etc. Optical measurement of omnidirectional shape has been done by rotating an object and/or measuring it from different directions. We previously proposed a phase-shifting method using Fourier transform (PSM/FT) and a multi-reference-planes method (MRPM) to obtain geometric parameters without influence of lens distortions. Both a measured object and a reference object are simultaneously measured from different directions. All partial point-clouds can be merged into one global coordinate system by a transform matrix calculated from the reference column on a rotary stage. 360-deg 3-D shape can be measured using the above method.
In the PSM/FT, since the initial phase information is determined from only the first frequency of the Fourier spectrum of the phase-shifted intensity values at each point of an object and the frequency components higher than the first frequency almost depend on noise, almost experimental noise can eliminated. The phase reliability evaluation value using Fourier transform (PREV/FT) is, therefore, defined as the ratio of the first frequency component of the Fourier spectrum to the average of the frequency components higher then the first frequency of the Fourier spectrum. The PREV/FT is useful to merge data when measurement conditions are changed. In this paper, we propose a method that all partial data can be merged into global coordinates using the PREV/FT on overlapped areas and omnidirectional shape measurement is achieved.
In phase-shifting digital holographic interferometry for measuring a displacement distribution of an object, holograms and reconstructed images have speckle noise and they provide large error in the calculation of displacement analysis. In order to decrease the effect of speckle noise, we previously proposed a new method using windowed holograms. In this paper, we propose a new averaging method of the obtained phase-difference values. Many phase-difference values at a point obtained by different windows for a hologram are averaged by considering the weight for each phase value. The weight is changed as the m-th power of the absolute amplitude of the complex amplitude of the reconstructed object. As the result, when the number n of the windowed holograms becomes larger, the standard deviation of the error becomes smaller. When the power m is 2, the error becomes the minimum. The standard deviation of the errors in the case of a flat plate with 316 nano-meter out-of-plane displacement is 88 pico-meter when n=1024 and m=2.
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