Realization of high sensitivity displacement field from moiré interferometer with rough phase shifting mechanism and pattern matching technique

In this study, phase shifting method is used to modify moiré system into micro moiré interferometer which can measure displacement field with highly improved sensitivity. Apart from existing micro moiré technique, a low cost and less precise translation stage with rough resolution (10 μm resolution) is adapted for the phase shifter. Least square algorithm is applied to estimate the arbitrary phase shifted amount and to minimize the errors induced by lowering the cost. Moreover, specimen grating is phase shifted instead of reference grating which enables simple construction from given moiré system. To compensate for rigid body in-plane translation of specimen that may occur during phase shifting, pattern matching algorithm is put into practice to ensure pixel correspondence for each phase shifted images. To verify the newly constructed micro moiré technique, local displacement fields of Fine pitch Ball Grid Array package and Wafer Level Chip Size Package with elevated sensitivity up to 26 nm per fringe was acquired.     

Phase shifting SEM moiré method

A new phase shifting scanning electron microscope (SEM) moiré method is proposed in this paper. The phase shifting technique is realized in four steps from 0 to 2π by shifting electron beam in the y-axis direction controlled by the SEM system. It is successfully applied to determine the residual strain of a deformed holographic grating with a frequency of 1200 lines/mm in an electronic package. As a further application, it is used to measure the virtual strain of a MEMS structure with a 5000-line/mm grating and to determine the phase distribution of a SEM moiré formed with a 6000-line/mm grating fabricated by electron beam lithography. The experiments show the feasibility of this method. It provides a new way for disposal of fringes pattern in sub-micro moiré method.     

Contribution to analysis of the reflection grating method

The reflection grating method is a special case of the well-known reflection moiré principle. Whereas this moiré effect is suitable for measurement of the slope and curvature of deformed object surfaces by superposition of at least two grating images, the same results can be determined using only one reflected grating image without moiré lines.Some fundamental relationships between grating lines, optical setup and the desired deformation are developed and compared with the simplifications that are known from the moiré principle. The theory is tested using a circular plate, uniformly loaded and clamped at the circumference.     

Phase shifting nano-moiré method with scanning tunneling microscope

In this paper, a new nano-moiré method using scanning tunneling microscope (STM) is proposed. This method is capable of measuring nanoscopic deformation of matter. The formation mechanism of the STM moiré fringe and the phase shifting technique used in STM moiré fringes are explained in details. Typical experiments are conducted with the crystal lattices of freshly cleaved highly oriented pyrolytic graphite, are used as specimen grating, to generate STM moiré fringe patterns. Phase shifting is realized in four steps from 0 to 2π by controlling the PZT in the STM system to shift the specimen in the vertical direction. This method provides a new way for disposal of moiré fringes pattern in the nano-moiré measurement.     

Holographic implementation of holographic moiré inspection

Implementation of holographic moiré inspection is demonstrated using one hologram to project the reference grating and a further hologram to produce moiré patterns. Well contrasted moiré fringes are obtained. Results of calibration tests are reported and an example of object contouring is presented.     

Formation of unsymmetric moiré fringes and their use in moiré topography

An analytical method of predicting the intensity profile of the moiré fringes formed by a three-dimensional grating is proposed. The proposed method is proved to be effective in determining the appropriate structure of the grating and the experimental conditions for directional moiré topography.     

Automatic fringe analysis for moiré topography

Two digital systems are developed for the automatic measurement of 3-D shapes using moiré techniques—an automatic 3-D shape measuring system using the scanning moiré method and an interactive fringe analysing system for moiré fringe photographs. In the automatic 3-D shape measuring system, a deformed grating is scanned and sampled with an electronic image scanning device so that moiré fringes are generated in a computer. This technique of electronic fringe generation eliminates ambiguity with regard to the sign of the moiré fringes. The interactive fringe analyser provides a flexible and versatile tool for moiré fringe analysis. Medical applications of these analysing systems are discussed.     

The optimization of three-mirror illuminating system for the four-beam Moiré interferometer

The three-mirror illuminating system for moiré interferometry consists of a Lloyds mirror and two additional mirrors at right angles to each other. This arrangement makes possible the design of a four-beam moiré interferometer system for a cross-lined specimen grating, to determine the u and v displacement components of the object under test. The design problems, including optimization of dimensions of the optical elements and adjustment by a user, are discussed and analytically solved. The analysis was verified by the construction and laboratory use of the interferometer.     

Bandwidth controllable transmission filter based on Moiré fiber Bragg grating

A new and efficient technique for fabrication of bandwidth controllable π–phase-shifted fiber Bragg grating (FBG) based on moiré grating using a uniform phase mask is demonstrated. The feasibility of writing a moiré grating into an ordinary SMF-28 fiber using stretching and double exposure by ultraviolet fringe is reported. We analyzed the relation between the initial differentia of phase of two exposures and the transmission spectrum of phase-shifted FBG. Moreover, we present a novel method to control the initial differentia of phase of two exposures. Using this technique, two kinds of resonant filters with a 3-dB line-width of 0.01 nm centered at 1553.79 nm and of 0.5 nm centered at 1554.57 nm respectively were fabricated with same uniform phase mask.     

Bandwidth controllable transmission filter based on Moiré fiber Bragg grating

A new and efficient technique for fabrication of bandwidth controllable π–phase-shifted fiber Bragg grating (FBG) based on moiré grating using a uniform phase mask is demonstrated. The feasibility of writing a moiré grating into an ordinary SMF-28 fiber using stretching and double exposure by ultraviolet fringe is reported. We analyzed the relation between the initial differentia of phase of two exposures and the transmission spectrum of phase-shifted FBG. Moreover, we present a novel method to control the initial differentia of phase of two exposures. Using this technique, two kinds of resonant filters with a 3-dB line-width of 0.01 nm centered at 1553.79 nm and of 0.5 nm centered at 1554.57 nm respectively were fabricated with same uniform phase mask.     

Analysis of CCD moiré pattern for micro-range measurements using the wavelet transform

A new approach based on the moiré theory and wavelet transform (WT) is proposed for measuring the micro-range distance between a charge-couple-device (CCD) camera and a two-dimensional reference grating. The micro-range distance is determined by measuring the pitch of the moiré pattern image, which is digitized by a CCD camera. A one-dimensional WT algorithm is applied to estimate the pitch of the moiré pattern. Experimental results prove that this technique is very efficient and highly accurate. The moiré range finder is an economic technique for measuring a micro-range distance.     

A compact, robust and versatile moiré interferometer

A moiré interferometer was designed and constructed based on a general system design using a reflective crossed-line diffraction grating to produce the four beams of light necessary for moiré interferometry. The design concept, basic design and tuning procedures are discussed. The important features of the interferometer, i.e. compactness, versatility, polarization insensitivity, relaxed collimation requirements, low laser power and remote optics, are addressed. Several such interferometers have been constructed and successfully applied to engineering problems. These include examining the displacement fields surrounding drilled and preformed holes in composite laminates loaded in tension, and the evaluation of nonhomogeneous behavior in textile composites.     

Diffraction grating interferometers for mechanical characterisations of advanced fabric laminates

It is demonstrated that two grating interferometers with high spatial resolutions can successfully be applied for the mechanical characterisation of the advanced fabric composite materials. Based on these two techniques, the mechanical properties of two kinds of fabric laminates are obtained without assumption of uniform strain fields to be used in the characterisation approaches using the local strain sensors. The degree of the yarn crimp effects of the two laminates is compared in terms of the out-of-plane displacement derivatives. Especially, it is shown that the grating shearing interferometer is appropriate for the crimped fabric structure requiring a three-dimensional analysis. The modification from moiré interferometer to grating shearing interferometer is performed by introducing a Michelson interferometer modified for image shearing.     

Analysis of moiré fringes for measuring the focal length of lenses

We describe a technique based on fast Fourier transform and least-squares fit for automated analysis of moiré fringe patterns for accurately measuring the focal length of lenses. An interference fringe pattern is produced by a reflective diffraction grating interferometer and illuminates the test lens. Moiré fringes are generated by digitally superimposing the magnified fringe pattern imaged by the lens on the interference fringe pattern without the test lens. We analyze two common ways to generate the digital moiré effect: multiplication and subtraction with successive rectification of the two digitally stored intensity distributions, and we show that in the latter case by means of the described technique it is possible to determine the moiré spatial frequency by a simple and fully automated procedure.     

Enhancement of visibility of fringes and exposure time for moiré topography

The aperture filtering of lenses for the purpose of moiré topography is described. By replacing the circular iris of a lens with a rectangular one whose long side is parallel with the bars of the grating, both the visibility of the fringes and the exposure condition are greatly enhanced. Using this technique, it becomes possible to take pictures of moiré fringes on a moving, living human body.     

A study on the digital moiré technique with circular and radial gratings

A digital moiré technique with circular and radial gratings is proposed to measure in-plane displacement and strain distributions of soft materials in a polar coordinate system. By introducing the coordinate-transform technique, the concentric circles and radial lines in the Cartesian coordinate system are converted to cross gratings in a polar coordinate system. Then, the digital moiré fringes are generated using logical and filter operations on the one-bit binary images. Finally, the in-plane displacement distributions are obtained by means of the four step phase-shifting procedure. Also, the measurement principles and the basic procedures of the new digital moiré technique are explained in detail. An application for rubber sheet with a single-edge crack is studied, and the experimental results show that the presented method is feasible.     

A moiré method of visualizing electromagnetic force lines

We propose a simple moiré method of visualizing electromagnetic force lines. The indicial equation is first derived for the tangent (or normal) curve to the electric field (or magnetic induction) around two parallel-line charges (or currents). The derived equation is then shown to have a one-to-one correspondence with that of the moiré fringe formed by two overlapped radial gratings. Since the tangent (or normal) curve to the electric field (or the magnetic induction) corresponds to the direction of the electric (or magnetic) force on a test charge (or current), the radial grating moirés can be used for the visualization of electric (or magnetic) force lines.     

Interpretation of fringes produced by time average reflection moiré on a circular disk

Inverse problem of reconstruction of dynamic displacements from the fringe pattern generated by time average reflection moiré is investigated in this paper. A technique for numerical simulation of time average smoothed reflection moiré fringes is proposed. The smoothing procedure is incorporated into the finite element formulation of the problem. Reconstruction of the field of deflections is illustrated for a centrally clamped disk. Such techniques can be effectively exploited in hybrid numerical–experimental procedures for different objects and grating geometries.     

Refractive power mapping of progressive power lenses using Talbot interferometry and digital image processing

A method of refractive power mapping of a lens is presented which is based on Talbot interferometry and utilizes a digital image processor. By adding a digital image processing system, fast measurement of a lens power distribution is feasible. A test lens is placed in front of two collinearly arranged gratings. The light passing through the test lens produces a shifted Talbot image of the first grating on the second grating and generates moiré fringes. Given the inclination angle of moiré fringes, the refractive power of the lens can be calculated. The calculation is performed using a digital image processor. This method is effective in finding the refractive power distribution of progressive power lenses.     

Electron moiré method and its application to micro-deformation measurement

In this paper, the single and two deposited metal layers method were proposed to produce the model grating for electron moiré method. The measurement principle of electron moiré method and the techniques for manufacturing model grid are expounded in detail. The accuracy of measuring strain using this method is discussed. The gratings with single deposited layer and two deposited layers with high frequency up to 5000 lines/mm were produced on different substrates. From the experimental results, both single deposited metal layer and two deposited metal layers gratings showed their heat resistance ability. Using the gratings produced and a replicated model grid, the electron moiré method was applied to measure the deformation of the strain around holes in a polyimide resin substrate, thermal strain of electronic packaging component and tensile creep around grain boundary in a pure copper specimen.