Shape measurements and strain distribution measurements are important for analyzing the behavior of a rotating tire. Recently, a two-dimensional phase analysis method using phase-shifting moiré patterns, which are generated computationally from a two-dimensional grating image, was proposed. This method is well suited to the dynamic shape and strain measurement because the phase can be accurately obtained from a two-dimensional grating image. We show that it is possible to analyze the strain distribution and shape measurements of a moving object using a grating pattern attached to the surface of the specimen, and a dynamic shape and strain measurement system using the sampling moiré method is developed in this paper. The principle of the method and the experimental results of the method when applied to a rotating object are shown.
We present a new single-shot 3-D shape measurement method using a digital micromirror device (DMD) camera and fringe projection. In optics of the DMD camera, individual DMD mirrors operate as controllable high-speed shutters for corresponding charge-coupled device (CCD) pixels. Therefore, four phase-shifted images can be recorded within one frame of the CCD camera by integrated phase-shifting methods using correlations. To obtain 3-D information of the object, an easy and accurate phase-to-3-D calibration method is performed. The principle and hardware are presented. The experimental results under dynamic conditions show that 3-D shape information can be analyzed from only a single image.
Recently the authors developed sampling moiré method which analyzes the phase distribution of one image of a moiré
fringe pattern. The captured image is analyzed by performing easy image processing, i.e., thinning-out and linear interpolation, to obtain the multiple phase-shifted moiré patterns. Then, the phase distribution of the moiré pattern can be calculated using phase-shifting technique. The accuracy of the phase analysis is high because the phase is analyzed with a phase-shifting method. The accuracy is checked using simulation and experiment by changing several factors. An application of the sampling moiré method applied to deflection measurement of a metal cantilever beam is performed. The average error of the deflection measurement is less than 1/500 of the grating pitch.
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 this paper, we proposed a calibration method with a reference plane to analyze strain distribution using three spherical
waves in independent directions. The relationship between the phase difference and displacement for each pixel are
determined for one beam using a reference plane. When this measurement is performed for each of three beams, the
sensitivity matrix for each pixel can be obtained independently. We also proposed a phase analysis method using Fourier
transform for a wave composed by three waves. Three spherical waves are irradiated onto the reference plane or an
object simultaneously. The principle and the experimental results of strain measurement are shown.
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.
We propose an evaluation method for the reliability of the analyzed phase in a phase-shifting method using a Fourier transform (PSM/FT) for shape measurement by fringe projection method. In PSM/FT, since the initial phase information is determined only from 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, experimental noise can almost be eliminated. The phase reliability evaluation value using a 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 than the first frequency of the Fourier spectrum. PREV/FT is useful to merge data when we change the measurement condition for shape measurement. We apply the PREV/FT to eliminate the halation effect on a metallic object. Shape measurement of an aluminum specimen that is a rotational body produced by a lathe is performed as an experiment. The results show that the halation effect is eliminated successfully by selecting the highest PREV/FT.
This paper is a revision of a paper presented at the SPIE conference on Algorithms and Systems for Optical Processing V, Jul. 2001, San Diego, California. The paper presented there appears (unrefereed) in SPIE Proceedings Vol. 4471.
An encrypted digital holographic data reconstruction method with data compression is proposed. We show that the number of quantization levels of the digital hologram can be reduced. By computer simulations, we confirm that the method is especially useful for binary images. For gray-scale images, we propose a bit plane decomposition method. By this method, we show that both high reconstructed image quality and a high compression ratio can be achieved.
We previously developed a DMD(Digital Micro-mirror Device) reflection-type CCD camera that we call 'DMD camera' and we applied the DMD camera to shape measurement. In this former method, the integral values at a point are obtained by the averaging with the surrounding 9 pixels. This method, therefore, causes a problem that errors are caused by misalignment between the CCD pixel and the DMD pixel. In this paper, we propose a method to improve the algorithm to obtain the phase of a projected grating by phase-shifting method using correlation. The transferred on/off pattern to the DMD are modified and the integral values at a point are obtained by the averaging with the vertical 4 pixels. The accuracy of the shape measurement is improved using the proposed method. The principle, an experimental result, and a comparison of the accuracy between the former method and the proposed method are shown.
We previously proposed the integrated phase-shifting method for real-time shape measurement using grating projection method. However, the measurement range in this technique is not so wide, since phase-unwrapping has not been made. In this study, a grating synthesized two cosinusoidal waves of which the frequencies differ from each other, was used in order to perform unwrapping. If the frequencies are 3 and 4, in order to analyze frequencies and phases, the minimum sampling number of phase-shifted images is 8 according to the Whittaker-Shannon sampling theorem. We propose a new unwrapping method using only 5 phase-shifted images. The phase values are obtained from the aliased frequency components of the Fourier spectrum of the grating. The theory is shown and the effectiveness is confirmed by experiment.
An encryption method of a 3-D object based on the phase modulation of an object wave is proposed. The phase of the object wave is modulated by a virtual optical random phase mask using a digital holographic technique. The keys of an encryption step are both a phase distribution and a position of the virtual optical phase mask. If either of them is not correct, we cannot decrypt the 3-D object. Owing to a characteristic of a hologram, we can see some parallax of a reconstructed 3-D object. Experimental results are presented to confirm the proposed method.
Shape and deformation measurement by moiré topography or interferometry are introduced. By using the integrated phase shifting method proposed by the authors, shape measurements of various objects such as a hand with cell phone and a human face are performed in real-time. The integrated phase-shifting method can analyze the phase information of a projected grating on the object or an interferometric fringe pattern. The phase analysis provides the accurate shape of the object. The object is recorded by an NTSC-TV-CCD camera at 30 frames/second. The analyzed shape or flatness distribution is simultaneously displayed as a moving image of computer graphics. The analyzed shape is observed from any direction directed by a computer mouse in real-time.
KEYWORDS: Digital holography, Phase shifts, Holographic interferometry, Semiconductor lasers, Holograms, Holography, Near field diffraction, Denoising, Charge-coupled devices, 3D image reconstruction
Deformation measurement of a cantilever based on digital holographic interferometry is presented. The digital holograms of the cantilever before and after deformation are obtained by use of phase-shifting technique. By using the phase-shifting digital holography, the object wave information without zeroth order diffraction wave can be extracted. The phase difference of the reconstructed cantilever before and after deformation is obtained numerically using discrete Fresnel diffraction integral. Owing to the numerical analysis, the deformation of the cantilever can be obtained with high resolution of nanometer dimensions. The optical experimental results are shown to confirm our proposed method. Furthermore, we propose a mechanical movement free double-exposure method in phase-shifting digital holography using a laser diode.
An encrypted optical storage based on a joint transform correlator architecture by using a photorefractive material is presented. A key code designed by optimized algorithm so that its Fourier transform has a uniform amplitude distribution and a random phase distribution is introduced. Original two-dimensional data and the key code are placed side by side at the input plane. Both of them are stored in a photorefractive material as a joint power spectrum. The retrieval of the original data can be achieved with the same key code. We can record multiple two-dimensional data in a same crystal by angular multiplexing. Furthermore we can record by key code multiplexing because another designed key code can produce another independent phase distribution. We demonstrate the concept of the optical data storage system by computer simulations.
Grating projection methods have been often used for non- contacting shape measurement. An image of equal-height contours of an object can be obtained in real-time using moire topography. We have developed the phase-shifting scanning moire method for real-time shape measurement with high resolution. But there is a problem that the measuring error becomes larger when the object is moving speedily because several images are captured while shifting the grating phase. In this paper, we propose a phase- shifting scanning moire method using a DMD, which can obtain an image of equal-height contours within a frame time. The direction of a ray reflected at each mirror of a DMD can be selected quickly. For this purpose, we developed a DMD reflection-type CCD camera called as 'DMD camera'. The camera works as a camera whose each pixel has a shutter. The structure and an experimental result to confirm the algorithm to obtain a contour image using het DMD camera are shown.
It is possible to measure the 3D shape of an object using grid projection methods. Moire topography which is a kind of grid projection methods can obtain the contour lines of the measured object in real-time. The authors developed a real-time shape measurement system based on the Moire topography. In order to perform quantitative and real-time shape measurement, we developed the integrated phase shifting method. However, the obtained distribution is wrapped in the range of -(pi) to (pi) . Therefore, a real-time phase unwrapping process is required. The present paper proposes a new unwrapping method using a composite rectangular grid which si composed of two rectangular waves of different pitches. The composite rectangular grid is projected onto an object. Each phase distribution of the two waves can be separated and calculated using the integrated phase-shifting method. The unwrapped phase distribution is produced from the two different phase distributions.
To analyze fringe patterns, frequency and phase analysis of fringes becomes popular. It provides accurate results and automated processing. In this paper, the theories of the frequency and phase analysis methods using Fourier transform, Gabor transform, wavelet transform are introduced for shape analysis using gratin projection method, strain analysis using gratin method or iso chromatics and iso clinics analysis using photooelasticity. The applications of these methods are also described.
A digital holographic data reconstruction method with data compression is proposed. We show the number of quantization level of a digital hologram can be reduced. By computer simulations it is confirmed that the method is especially useful for binary images. For gray scale images, we propose a bit plane decomposition method. By this method, we show both high reconstructed image quality and a high compression ratio can be achieved. This method is applicable to both a normal digital hologram and an encrypted digital hologram.
To analyze fringe patterns, frequency and phase analysis of fringes becomes popular. It provides accurate results and automated processing. In this paper, the theories of the frequency and phase domain methods such as the Fourier transform method, the wavelet transform method and the phase-shifting method are proposed for photoelastic fringe pattern analysis. The applications of these methods are described.
We previously proposed the integrated phase-shifting method for the grating projection method using a Ronchi grating to display the height distribution of an object in real-time. The method uses a correlation between a grating brightness with a rectangular distribution and a rectangular function. The brightness of the phase-shifted fringe pattern is integrated on a CCD sensor of a camera during one exposure time and the integrated values are recorded. The theory uses the integration of the brightness at each pixel point during one exposure-time. In the present study, this method is extended to fringe pattern analysis with a cosinusoidal brightness distribution. A theory of the phase-shifting method for high-speed phase shifting is proposed. By integrating the brightness during one exposure time, the equation is modified to obtain accurate phase values. The analyzed phase values from continuous four images immediately before the last exposure time are obtained at very exposure time, i.e. every 1/30 seconds. The application to small displacement analysis of a cantilever and a micro- accelerometer are shown.
Phase distribution analysis of deformed gratings in moire method and grating projection method provides accurate shape of specimen. We previously proposed the phase-shifting method using correlation with a rectangular function. The phase analysis uses many images during phase shifting of the projected grating. In this paper, we propose a new real-time phase analysis method, that is, the integrated phase- shifting method using four images of phase-shifted grating patterns with a rectangular brightness distribution. The theory and some applications to shape measurement are shown.
A phase-shifting scanning moire method and a phase-difference scanning moire method are developed by the authors. They provide smooth equal-height contours and equal-displacement contours, respectively, in real-time. A phase-shifting method using correlation with rectangular is also developed. It uses the correlation of the rectangular brightness of a projected grid and two rectangular functions to determine a phase. It can provide accurate phase distributions in real-time.
Automatic non-contacting shape measurement using grid projection methods is often used as monitoring system for protection against disaster. Both high accurate phase analysis of grids and high accurate geometric parameters of the optical system are necessary for accurate shape measurement. We have been proposing the phase shifting method using Fourier transform (PSM/FT) and a method to obtain geometric parameters without influence of lens aberrations. The PSM/FT is most insensitive to noise in phase-shifting methods. In the case of a cylindrical object, a contour map is directly obtained by projecting a grid to the object and gathering the images taken by a line sensor with rotating the object. The phase of the contour map is shifted with shifting the projected grid phase. The shape can be obtained with high accuracy using the above method. In this paper, the principle of the method and an application are shown.
The interference fringes obtained by optical methods such as holographic interterometry and Twyman-Green interferometry are analyzed using image processing. To perform accurate and automated analysis, phase analysis methods have been recently developed. The Fourer transform moire and grid methods (FTMGM) and the phase-stepping method (PSM) are popular techniques to analyze phase distribution. However the FTMGM has noticeable error at the edges of the image if the data at both edges are not continuous. The PSM has large error if the brightness has noise. A new phase analysis method is proposed to erase these errors. This method can be performed using 3-D image processing. A 3-D (x,y,α) image is formed of many sequential phase-shifted 2-D (x,y) images, where a is the shifted phase value. By performing the a-directional Fourier transform on this 3-D image, the accurate phase distribution of the fringe pattern is obtained. An example applied to Twyman-Green interferometry is shown.
The Fourier transform moiré and grid method, which we previously presented, is extended to analyze strain distributions from the image of a fringe pattern with carrier fringes obtained by moiré interferometry. The characteristics of the carrier fringes and the procedure of obtaining strain distributions are explained in the spatial frequency domain. The fringe pattern without carrier fringes is obtained from the fringe pattern with carrier fringes by extracting the first harmonic of the spectrum of the fringe pattern with carrier fringes and shifting it. The strain distribution is obtained by analyzing the phase of the image obtained from the inverse Fourier transform of the shifted first harmonic. Strain distributions of a composite material with a wavy ply under compressive loading are analyzed.
The Fourier transform moiré and grid method (FTMGM) which we have previously presented is extended to analyze strain distribution from the image of a fringe pattern with carrier fringes obtained by moiré interferometry. The characteristics of the carrier fringes are explained in the frequency domain. The fringe pattern without carrier fringes is obtained from the fringe pattern with carrier fringes by extracting the first harmonic of the spectrum of the fringe pattern with carrier fringes and shifting it. The strain distribution is obtained by analyzing the phase of the image obtained from the inverse Fourier transform of the shifted first harmonic. Strain analysis of composites under compressive loading are shown.
The Fourier Transform Moiré and Grid Method(FTMGM) is a method for measuring displacement and strain by using Fourier transform of a grating image. In this paper, we will present a new method and a system to analyze displacement distribution of the track, which are signal recorded by a video cassette recorder(VCR) and a digital audio tape recorder(DAT), by using the FTMGM. Using this method, we can obtain a two-dimensional distribution of the displacement amount from linear state of the track recorded on a magnetic tape. Therefore, by using this track displacement information, it is possible to clarify the timewize variation state of the displacement and to remove the factors of worsening the track linearity. It is available for a high density recording on a magnetic tape.
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