Toru Matui

Accurate pixel-to-pixel correspondence adjustment in a digital micromirror device camera by using the phase-shifting moiré method

A camera based on the digital micromirror device (DMD) technology has been previously developed. In this optical system, the correspondence of each mirror of the DMD to each pixel of the CCD cannot readily be done since the pixel sizes of the DMD and the CCD are very small. An accurate pixel-to-pixel correspondence adjustment in the DMD camera by means of the phase-shifting moiré method is proposed. To perform high accurate adjustment of the optical system, the phase distribution of a moiré fringe pattern is analyzed when the CCD pixels and the DMD mirrors have a mismatch and/or misalignment with each other. This technique does not need a complicated setting or complex image processing to generate the moiré fringe pattern, and it needs only one captured image. In the adjustment experiment, the proposed method provided very accurate adjustment whose error was less than 1/25 pixel. An experiment of phase analysis to demonstrate the usefulness was performed.

Development of real-time shape measurement system using whole-space tabulation method

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.

Simultaneous Measurement of Out-of-Plane and In-Plane Displacements by Phase-Shifting Digital Holographic Interferometry

In this paper, we apply phase-shifting digital holographic interferometry to simultaneous measurement for out-of-plane and in-plane displacements by employing two beam illuminations for an object. Phase-shifted holograms before and after displacements of the object using each of two beams are recorded by a CCD camera, separately. The complex amplitude at each pixel of the CCD plane is analyzed from the holograms taken with phase-shifting. The complex amplitude of he object is reconstructed from the complex amplitude distribution on the CCD plane using the Fresnel diffraction integral. Each directional phase difference distribution is obtained by calculating the phases before and after deformation for each directional beam. The phase distribution for out-of-plane displacements is obtained by calculating the sum of the two phase difference distributions. The phase distribution for in-plane displacements is obtained by calculating the difference of the two phase difference distributions. The phase values provide accurate displacement distribution information. Actually, when the object deforms in both out-of-plane and in-plane directions, it is possible to analyze the displacement distribution in each direction. The theory and an experiment are shown.

Three-dimensional Displacement Analysis by Windowed Phase-shifting Digital Holographic Interferometry

Digital holography is useful to reconstruct three-dimensional shapes of objects. The reconstruction process of the objects is fast and accurate because the reconstruction is performed by computer calculation without developing photographic plate. Phase-shifting digital holographic interferometry is possible to measure shape and displacement of objects quantitatively. The authors developed windowed phase-shifting digital holographic interferometry (WPSDHI) which provides very accurate results by decreasing the effect of speckle noise.

Real-Time Shape Measurement by Unwrapping Method Using Aliasing

We previously proposed a real-time shape measurement method using two-component synthesis grating projection. In the method, phase unwrapping of the projected grating is performed by using aliasing of the Fourier spectrum of the grating images. It requires only 5 images obtained for one-cycle phase-shifting. Each phase in the two-component can be extracted from only 5 phase-shifted grating images. In this paper, we propose a real-time shape measurement system. The theory, the algorithm for the analysis and the experimental results are shown.

Effect of weight in averaging of phases on accuracy in windowed digital holographic interferometry for pico-meter displacement measurement (Invited Paper)

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.

Application of Three-Dimensional Displacement and Strain Distribution Measurement by Windowed Phase-Shifting Digital Holographic Interferometry

In order to measure 3D displacement components and surface strain distributions of objects, three systems for digital holographic interferometry were developed. In this study, these three systems are introduced and the applications to measurement of 3D displacement components and surface strain distributions of cantilevers are shown.

Development of Phase Shifting Device Using the Deflection of a Cantilever for Digital Holography

Phase-shifting digital holography can be used for displacement measurement instead of strain gauge. Our research group is developing the measurement equipment for phase-shifting digital holography. Generally, in the measurement equipment, piezo stages are used as phaseshifting devices. But the piezo stage is expensive. Cheaper and smaller phase-shifting device is required in order to put the measurement equipment into practical use. In this paper, we, therefore, propose a phase-shifting device using the deflection of a cantilever and we verify whether this phase-shifting device can be usedfor digital holography.

Omnidirectional shape measurement using reliability evaluation value in Fourier transform

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.

Phase-Shifting Method with Unknown Intervals in Phase-Shifting Digital Holography

Displacement measurement can be performed with high accuracy using phase-shifting method. In phase-shifting method, it is often used four steps of phase-shifting for one cycle. In conventional method, to measure the displacement of an object by an interferometer, the phase of a reference beam should be shifted by every π/2 in the four-step phase-shifting. In this paper, a phase-shifting method with unknown intervals is proposed. This method does not need to shift a phase by every π/2. It can detect an intensity distribution and a phase distribution from five fringe images with equal intervals even if the phase-shift amount is unknown. Using this method, we propose a displacement measurement of phase-shifting digital holographic interferometry using spherical wave as reference wave.