Motoharu Fujigaki

Deformation measurement by phase-shifting digital holography

The out-of-plane displacement of a cantilever is measured by phase-shifting digital holography. From four phase-shifted holograms of a cantilever recorded by a CCD image sensor, a complex amplitude at each pixel of the CCD plane is obtained using the conventional phase-shifting method. The complex amplitude of a cantilever is reconstructed from the complex amplitude of the CCD plane using the Fresnel diffraction integral. The phase difference distribution on the cantilever before and after deformation, i.e., the out-of-plane displacement distribution, is calculated. In order to decrease the effect of speckle noise, a new method using divided holograms is proposed. The theory and experimental results are shown.

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.

Phase-measuring profilometry of moving object without phase-shifting device

A new phase-measuring surface profiling technique of a moving object is proposed in the present paper. An interference fringe pattern is projected onto the object that moves at a constant speed. Multiple linear sensors are used for recording the deformed fringe pattern on the object. The phase distribution along the recording line can be calculated using a phase-shifting algorithm without any phase-shifting devices. The length of a target is not limited and a long object can be measured by the proposed method. It is expected that the proposed method can be used for the profile inspection of products moving on a conveyor system in a factory.

Real-time shape measurement by integrated phase-shifting method

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.

Automated analysis of 3-D shape and surface strain distributions of a moving object using stereo vision

Abstract An automated method for analyzing the three-dimensional (3-D) shape and the surface strain distributions of a moving object, using stereo vision, is proposed. A two-dimensional (2-D) cross grating is drawn on the surface of the object and it is recorded as images with two charge coupled device cameras. For correspondence between the surface of the object and the images, the Fourier transform grid method (FTGM) is used. By separating each directional first harmonic of the Fourier spectrum of the images using the FTGM, the 2-D cross grating can be easily separated into each directional grating, and each directional phase information of the grating brightness distribution is obtained. The correspondence between arbitrary points on the surface of the object and the images is determined, using the phase values instead of the grating line numbers. The correspondence algorithm is much more easily applied than the conventional image processing method, using the pixel positions of the center lines of the grating lines. The analysis of the 3-D shape is faster. Accordingly, analysis of large quantity images becomes possible and consequently the effective measurement of a dynamically deforming object can be performed. As an application, in the case of elastic-plastic buckling of a curved steel plate, the 3-D shape and the surface strain distributions changing with time are measured.

Intensity range extension method for three-dimensional shape measurement in phase-measuring profilometry using a digital micromirror device camera.

Phase-measuring profilometry is an accurate and effective technique for performing three-dimensional (3D) shape and deformation measurements of diffuse objects by fringe projection. However, phase analysis cannot be performed in underexposed or overexposed areas of the detector when an object with wide reflectance is measured. A novel intensity range extension method using a digital micromirror device (DMD) camera is proposed. In the optics of the DMD camera, each pixel of the CCD corresponds exactly to each mirror of the DMD. The phase-shifted fringe patterns with high contrast can be easily captured by programming an inverse intensity pattern that depends on the reflectance of the object. Our method can provide a wider intensity range and higher accuracy for 3D shape measurement than other conventional methods in both underexposed and overexposed areas. The measurements of a replica of a metallic art object and a flat plane are analyzed experimentally to verify the effectiveness of our method. In the experiment, the percentage of invalid points due to underexposure and overexposure can be reduced from 20% to 1%.

Separation of isochromatics and isoclinics from photoelastic fringes in a circular disk by phase measuring technique

A new polariscope system involving two rotating optical elements and a digital camera for whole field fringe analysis allows automated data to be acquired quickly and efficiently. The developed phase measuring technique that uses eight images through a circular polariscope is presented for the digital measurement of isochromatics and isoclinics, respectively, from photoelastic fringes in a circular disk under diametric compression. Isochromatics can directly be obtained using wrapped isoclinic phases calculated by the arc tangent operator which is the four-quadrant operator from −π to π. It is not required to unwrap isoclinic phases for the calculations of isochromatics. Unwrapped isoclinics are directly determined from isochromatic parameters. Distributions of digitally determined isoclinics are in close agreement to manual measurements. The errors which would appear in unwrapping process of isoclinics can be avoided in the determination of isochromatics.

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.

Three-dimensional surface profile measurement of a moving object by a spatial-offset phase stepping method

This study proposes a new method for measuring the 3-D surface profile of an object moving at constant speed. A sinusoidal grating pattern is projected on a moving object. Then, grating patterns that are deformed according to the profile of the object are acquired by three linear array sensors. Since a linear array sensor records light intensity along an original grating line, the resultant image forms a fringe pattern that represents the profile of the object. Using three images obtained by the three linear array sensors, the phase distribution of the fringe pattern is calculated by a phase stepping method without any phase stepping devices. Consequently, the profile of the moving object can be evaluated from the phase of the fringes, since the value of the phase is simply proportional to the height of the object. Experimentation demonstrates that the accuracy is about 4.3% for the wrapped phase range of 2π rad with a speckle pattern present. The proposed method can be used for inspection of moving objects such as products on an assembly line.

Absolute phase analysis method for three-dimensional surface profilometry using frequency-modulated grating

The authors propose a new high-speed and accurate phase analysis and subsequent phase unwrapping method for grating projection surface profilometry. In the proposed method, a special grating pattern is used for the projection. The light intensity distribution of this grating pattern has a form of a frequency modulated sinusoidal wave. In this grating pattern, two different phase distributions are included. The frequency modulated grating, which can be generated with an LCD projector or a film projector easily, is projected onto an object. Then, nine frames with phase stepping at a regular interval for a cycle are taken by a CCD camera. From these nine pictures, the two wrapped phase distributions are analyzed simultaneously. Then, using these phase distributions, phase unwrapping is carried out at each pixel independently. The 3-D profile of the object can be reconstructed using the absolute phase distribution. Since this method is suitable for high-speed shape measurement, applications to various inspections and 3-D surface digitizing are expected.