A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

A self-scanned 1024 element photodiode array and minicomputer are used to measure the phase (wavefront) in the interference pattern of an interferometer to lambda/100. The photodiode array samples intensities over a 32 x 32 matrix in the interference pattern as the length of the reference arm is varied piezoelectrically. Using these data the minicomputer synchronously detects the phase at each of the 1024 points by a Fourier series method and displays the wavefront in contour and perspective plot on a storage oscilloscope in less than 1 min (Bruning et al. Paper WE16, OSA Annual Meeting, Oct. 1972). The array of intensities is sampled and averaged many times in a random fashion so that the effects of air turbulence, vibrations, and thermal drifts are minimized. Very significant is the fact that wavefront errors in the interferometer are easily determined and may be automatically subtracted from current or subsequent wavefrots. Various programs supporting the measurement system include software for determining the aperture boundary, sum and difference of wavefronts, removal or insertion of tilt and focus errors, and routines for spatial manipulation of wavefronts. FFT programs transform wavefront data into point spread function and modulus and phase of the optical transfer function of lenses. Display programs plot these functions in contour and perspective. The system has been designed to optimize the collection of data to give higher than usual accuracy in measuring the individual elements and final performance of assembled diffraction limited optical systems, and furthermore, the short loop time of a few minutes makes the system an attractive alternative to constraints imposed by test glasses in the optical shop.

Digital wavefront measuring interferometer for testing optical surfaces and lenses

Measuring accurate displacement distributions for large-scale structures is an important issue and a very challenging task. Recently, a simple and accurate phase measurement technique called sampling moire method [Exp Mech 50–4:501–508, (2010)] has been developed for small-displacement distribution measurements. In this method, the phase distribution of moire fringes can be analyzed from a single grating image by simultaneously performing down-sampling image processing and intensity-interpolation to generate multiple phase-shifted moire fringe images. In addition, the phase of the original grating can also be obtained from the phase of the moire fringe by adding the phase of the sampling grating. In this study, the measurement accuracy of the sampling moire method was analyzed through computer simulations and a displacement measurement experiment. Four factors of the sampling moire method were investigated, including the sampling pitch, the order of the intensity-interpolation, random noise, and the form of grating. The results show that determining the optimal sampling pitch is an important factor for obtaining better results but it is not critical. In addition, a practical application of the sampling moire method is presented that involves a deflection measurement on a 10-meter-long crane. The experimental results demonstrate that submillimeter deflections of the crane can be successfully detected.

Accuracy of the Sampling Moiré Method and its Application to Deflection Measurements of Large-Scale Structures

Parallel computing in experimental mechanics and optical measurement: A review

Review of real-time three-dimensional shape measurement techniques

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 moire 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 moire 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

Dynamic shape and strain measurements of rotating tire using a sampling moiré method

High-speed 3D shape measurement by one pitch phase analysis method using brightness values in small square area of single-shot image

Moire method is a useful method to measure deformation and strain distribution of structures. Moire fringe patterns are analyzed quantitatively and speedy by image processing using a computer. In this paper, the theory of moire method and sampling moire method is introduced. Since the sampling moire method is useful to analyze phases of a moire fringe and a grating from one image of a grating pattern, it is possible to analyze dynamic deformation accurately. Some applications of the sampling moire method to displacement measurement of a beam, and shape and strain measurement of a rubber structure are shown.

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Displacement and Strain Distribution Measurement by Sampling Moire Method

Three-dimensional shape measurement is used in various fields such as robotics and inspection of industry production. It is requested to measure shape with high speed and high accuracy. It is also requested to make the system compact and low-cost. It is, however, difficult to satisfy these requests simultaneously for 3D shape measurement. In order to measure shape in real-time, Kato et al. proposed a method using phase-shifting electronic moire pattern (Kato et al., 1997). The authors developed integrated phase-shifting method for real-time shape measurement by a grating projection method using phase-shifting (Morimoto et al., 1999, Fujigaki & Morimoto, 2003). However, they showed only the phase distribution of the contour lines.

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Shape Measurement by Phase-Stepping Method Using Multi-Line LEDs

Equipments for 3D shape measurement with compact and low-cost are required in wide industrial fields. We proposed Shape Measurement by a light source stepping method to realize the requirement. The method is one of the grating projection methods. In this method, multiple point light sources and a ronchi grating are used as a grating projector. Phase-shifting is performed with switching the light source position. By using this method, the shape measurement equipments can be produced with low-cost and compact because of no phase-shifting mechanisms. Also, the measurement speed is very fast because it is possible to switch the LED light sources in very short time. The grating can be projected without defocusing any place because of any focusing lenses in this projector. In this method, it is necessary that the emitting width on the point light source is narrow than the pitch of the ronchi grating. Brightness is also necessary for measuring the shape with accurate. Therefore, in this study, we develop a linear LED device for shape measurement by the light source stepping method. The effectiveness of the device is evaluated with an experimental test of shape measurement.

Akihiro Masaya

Papers

Dynamic shape and strain measurements of rotating tire using a sampling moiré method

High-speed 3D shape measurement by one pitch phase analysis method using brightness values in small square area of single-shot image

Displacement and Strain Distribution Measurement by Sampling Moire Method

Shape Measurement by Phase-Stepping Method Using Multi-Line LEDs

Development of Linear LED Device for Shape Measurement by Light Source Stepping Method