Photorefractive Fourier transform profilometer for the measurement of 3-D object shapes

In the present work dynamic moiré-like fringe patterns, produced by photorefraction with low spatial frequencies, applied for profile determination of small objects is proposed. Basically, a Fourier transform profilometry technique is developed for an automated profile determination. This means, as far as we know, a new experimental procedure that exploits the real time holographic two wave mixing in Bi₁₂TiO₂₀ crystal sample. Besides, the mainly advantages of this procedure are, comparatively to the classical fringe projection method using the Michelson interferometer, best fringe pattern contrast, less speckle noise, absence of noises produced by spurious reflections and, the most significant, a pure sinusoidal shape obtained by dynamic holographic moiré-like process using photorefraction.     

Dynamic moiré patterns produced by sinusoidal gratings superposition in the Bi12 TiO20 crystal

In the present note a real-time holographic moire-like pattern is shown. It is produced by the superposition of two rotated sinusoidal phase gratings and the result represents a promising technique for possible metrological applications. The experiments were performed in a diffusion-only recording mechanism in a photorefractive Bi₁₂TiO₂₀ crystal illuminated by λ = 0.633 μm from a HeNe laser light source.     

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.     

Formation dynamics of nonvolatile crossed-beam photorefractive gratings in doubly doped LiNbO3 crystals: Theoretical investigation

The formation dynamics of crossed-beam photorefractive gratings formed by the method of two-center holographic recording in doubly doped LiNbO₃ crystals is investigated in this paper based on the theoretical model combining the two-center band transport model with the two-dimensional coupled-wave theory. The numerical simulations are presented for two-center holographic recording crossed-beam photorefractive gratings in LiNbO₃:Fe:Mn crystals. The temporal and spatial evolutions of the refractive index modulation and the diffraction efficiency are shown. The spatial variation of the wave intensity is also presented.     

Computer Aided Moiré Methods

Computer aided moiré methods (CAMM) use the versatility of the computer to manipulate gratings rapidly, the basis of all moiré methods. Application of CAMM to moiré teaching, in-plane moiré, shadow and projection moiré and reflection moiré are reviewed in this paper.     

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.     

Moiré fringes as two-dimensional autocorrelation of transmission function of linear gratings and its application for modulation transfer function measurement

In this work, we show that the transmission moiré pattern is two-dimensional autocorrelation of transmission function (2D-ACTF) of two superimposed linear gratings that make a small angle with each other. In this approach, the properties of moiré fringes vs. the relative displacement of the gratings are formulated. By measuring 2D-ACTF of two similar gratings, we evaluate the modulation transfer function (MTF) of the gratings’ generating system. This work is the generalized form of our previous works. The implied MTF measurement method is easier and faster than our previous methods.     

The phase shift method applied to cross grating moiré measurements

The automatic evaluation of the grating deformation in a moiré image is greatly enhanced by the phase shift method. Based on three or more local grey values of a related number of phase shifted moiré patterns, the local displacement of a deformed grating against a reference grating, and hence the total displacement in one direction, is calculated. In this paper an extension to cross gratings is presented yielding a two- dimensional displacement field.     

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.     

Moiré fringes

This review paper clarifies the characteristics of the incoherent-and-multiplicative type moiré fringe phenomenon, presents examples of the application of these characteristics to measurement and explains the profile prediction method and the sharpening conditions of moiré fringes formed by two binary gratings.     

Holographic recording by excitation of metastable electronic states in Na2[Fe(CN)5NO]·2H2O: a new photorefractive effect

Elementary holographic phase gratings can be written in single crystals of Na₂[Fe(CN)₅NO]·2H₂O, sodiumnitroprusside, by excitation of metastable electronic states in the blue–green spectral range. For light polarized parallel to the crystallographic a and b axes of the orthorhombic crystal the light-induced modulation of the refractive index reaches Δn≈2×10^-3 at λ=514.5 nm. Although the largest population of the metastable states is reached for light polarized parallel to the crystallographic c axis, a photorefractive response is not observed. In contrast to electro-optic photorefractive materials the photorefractive effect depends mono-exponentially on the exposure and on the modulation of the incident light interference pattern. Beam-coupling experiments demonstrate that written gratings are in phase with the interference pattern in correspondence with the fact that the excitation of the metastable electronic states is local. The width of the rocking curve shows that the holographic gratings are written completely over the volume of the crystal. Variations of the wavelengths within the excitation range as well as of the crystal thickness do not influence the maximum photorefractive response. Investigations on the grating vector of the written gratings show unambiguously that charge migration is not responsible for the photorefractive effect. Received: 18 November 1998 / Revised version: 26 January 1999 / Published online: 12 April 1999     

Geometric micron-moiré

A high spatial resolution and high-sensitivity geometric micron-moiré method is presented. The method is based upon classical geometric moiré method and microscopic principle, the frequency of the specimen and reference gratings used in this method can be higher than 1000 lines/mm. By a microscopic moiré system, the high-frequency gratings could be magnified to a low-frequency level, so geometric moiré patterns can be formed. Experiments show that both the spatial resolution and the sensitivity can reach or exceed micron-level.     

Holographic displacement analysis using wave front modulation techniques

The wave fronts from two holographic displacement patterns are modulated by equal but opposite plate rotations and are superimposed to form a moiré pattern. Displacement information contained in the Fraunhofer diffraction pattern of the two superimposed gratings is analysed, and spatial filtering techniques are used to isolate full-field projections of displacement along and normal to the line of sight. Experimental results taken from a pipe subjected to pure torsion show that the method is not only accurate but that the technique is applicable to curved surfaces.     

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.     

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.     

Localisation of fringes in moiré topography

The moiré pattern produced by two separate gratings is characterised by a fringe localisation phenomenon. A theory based on the geometric shadow of light can account for the spatial location of moiré fringes in topographical applications. The fringe location depends on the optical arrangement of the system and also on the surface slope of the specimen. Experimental results are introduced into practical usage.     

Effect of recording conditions on the anisotropic diffraction of volume holographic gratings

The anisotropic Bragg diffraction of the volume holographic gratings in photorefractive crystals are investigated based on the model of anisotropic coupled-wave theory. The effect of the initial intensity ratio and the recording angles of the two recording waves on the anisotropic Bragg diffraction properties is discussed. It is shown that both the ratio of the initial intensity and the incident angles of the recording waves are selective action for the anisotropic Bragg diffraction efficiency of the volume holographic gratings, while these two recording conditions are not selective action for the isotropic Bragg diffraction. Furthermore, the Bragg phase matching condition of anisotropic diffraction is analyzed when the recording angles change.     

Dynamic effects in photorefractive crystals at simultaneous read–write of holographic gratings

A two-level model of a simultaneous read–write of holographic gratings in photorefractive crystals has been developed for the nonstationary case at the applied electric field and unequality of recording beam intensities. The recurrent relationships both for the internal field amplitudes and for the amplitudes of the optical waves involved in interactions have been obtained. The use of a truncated power series expansion has allowed to obtain the expressions for diffraction efficiency and intensities of optical waves in nonstationary case. The obtained results were used for the analysis of simultaneous read–write dynamics in Bi₁₂SiO₂₀ crystals.     

Field structure in a photorefractive holographic grating in a planar waveguide

A theoretical investigation is made of the field structure in a holographic grating formed by TE₀ modes in a planar photorefractive waveguide by the photogalvanic recording mechanism. Waveguides with three characteristic refractive index profiles are considered, namely, a step function, a parabola, and a hyperbolic secant squared. A comparison is made between the light field distributions of TE₀ modes in waveguides having the different profiles. The field structure of the space charge in planar holographic gratings is analyzed for their initial formation phase. It is shown that the space charge field has a similar structure for all three waveguide types considered when planar photorefractive gratings are recorded by TE₀ modes.Institute of Automated Control Systems and Radio Electronics, Tomsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 85–92, November, 1993.     

Photorefractive response and optical damage of LiNbO<Subscript>3</Subscript> optical waveguides produced by swift heavy ion irradiation

The photorefractive behaviour of a novel type of optical waveguides fabricated in LiNbO₃ by swift heavy ion irradiation is investigated. First, the electro-optic coefficient r ₃₃ of these guides that is crucial in the photorefractive effect is measured. Second, two complementary aspects of the photorefractive response are studied: (i) recording and light-induced and dark erasure of holographic gratings; (ii) optical beam degradation in single-beam configuration. The main photorefractive parameters, recording and erasing time constants, maximum refractive-index change and optical damage thresholds are determined.