As an example of a geometrical nonlinear problem a thin plate-in-bending under large deflection is considered. To determine the inplane- as well as the bending stress-state the photoelastic reflection method and Ligtenberg's moire method are used; the measured information is evaluated according to the principles of integrated photoelasticity. As yet in photoelasticity it has always been supposed Hooke's law of elasticity is valid and consequently linear relations between birefringent effects and stresses are existing. However, in areas of high stress concentration and with reference to some of the mainly used photoelastic material nonlinear strain-stress relations must be introduced. A proper constitutive equation yields an advanced principal photoelastic equation, the solution of which is performed in an iterative procedure. It should be mentioned that extended material testing is demanded to get the various material parameters. Finally proper algorithms and the respective numerical evaluation procedures are described, to analyze plane stress-states, if the material shows viscoelastic response. Then the mechanical as well as the optical rheological response of material must be considered.

Pattern recognition is a part of modern information processing with the objective to automate perceptive abilities. There are three paradigms mainly used for practical solutions: neural networks, statistical procedures, and knowledge based systems. Each of them is based on different assumptions and requirements. In our case the automatic recognition and classification of characteristic fringe patterns being indicative for special kinds of flaws on or under the surface of the investigated object is of interest -- especially with respect to an automatic and non-destructive quality control of industrial products. A serious problem of all optical methods is the fact that the used techniques are sensitive only for changes on the surface. Therefore flaws under the surface can be detected just by their affects on the surface. The conclusion from the characteristics in the observed fringe patterns (ring shaped fringes, displacement or distortion of fringes, varying fringe density, ...) to the kind of fault in the measured object (separation, delamination, debond, crack, inclusion, ...) is based on experimental results and practical experience. To solve the task the implementation of two approaches is preferred: neural networks and knowledge based systems. Both approaches have common qualities such as e.g., the preprocessing of noisy interferograms and the selection of representative features but also important differences such as the used recognition architecture. In this paper these aspects are discussed on examples of simple, so-called basic fringe patterns. For these pattern types spot checks are generated using mathematical simulation and practical preparation of loaded samples. Furthermore, the choice of robust features discriminating different basic patterns (classes) and the proposal for a special system architecture are discussed.

An analysis of the out-of-plane shearing interferometer has been performed which shows that production of in-plane strain partial derivatives, which are not affected by out-of-plane displacement function components, is possible. The in-plane data is represented as substraction correlation fringes and can be formed using two designs of interferometer. One interferometer employs a single diverging illumination beam and is applicable to object plane stress and plane strain loading conditions, while the second design uses two illumination wavefronts and is suitable for the analysis of tri-axial strain conditions. These interferometers are tested and compared using a compact tension crack specimen and the results are correlated with Finite Element software predictions of strain distributions across modeled specimens.

Novel speckle interferometric methods are described which offer a potential for whole field measurement of angular distributions on a curved surface. The technique encodes the angular distribution related phase by introducing topographic information in the interferometer in a controlled manner. The methods are simple to implement and provide broad range tunable sensitivity characteristics. Preliminary results obtained by applying digital speckle pattern interferometry are presented.

The measurement of three-dimensional object shapes plays an important role in machine vision, solid modeling and other industrial applications. Well known optical methods for 3D- shape inspection are moire-techniques and contouring. Unfortunately, as a rule they are lacking because they measure only one coordinate, i.e., the height above a reference surface. The other coordinates in the reference plane have to be determined using the pixel distance of the observing CCD-camera or by other means. Here, we demonstrate a real 3D-coordinate measuring system using fringe projection techniques where the scale of coordinates is given by the illumination-structures. This method has the advantage that the aberration of the observing system and the depth-dependent imaging scale have no influence on the measuring accuracy. Moreover, the measurements are independent of the position of the camera with respect to the object under test.

We found that any uniform stressed area in loaded birefringent material observed in a polarized, white light shows an extinction effect for different light wavelength (lambda) . The shape and spectral position of the fringes depends on the value of the applied force and the type of material. The new effect is like the Mueller fringes, but we have observed the changing of the material birefringence rather than the thickness. We have studied the interference effect for a `disc-like' whole cylinder of different materials loaded by uniaxial forces acting along the diameter. The cylinder posses a uniform stress area in its center and that area is under study. The measurements were made for various materials on a computer aided spectrometer, (specially constructed for the research), under different loading conditions. The results of the measurements are discussed and compared with theoretical predictions. The effect can be utilized for construction of an optical force sensor.

The portable, grating interferometer for automatic u- and v- displacement measurements is presented. The interferometer modifications, including registration of interferograms by CCD camera and implementing the phase shifting device, are described. The method for fringe pattern analysis using video recorder and spatial carrier phase stepping algorithm is introduced and discussed. The examples of modified interferometer application in fracture mechanics are given.

We present here a non-moire method of displacements measurement, where the image of a crossed network bonded onto a body under examination is acquired with a CCD camera. The zoom magnification is chosen so that the test grid is sampled at a frequency of three pixels by grid period. The processing of the recorded image corresponds to a 3-bucket algorithm, applied to both horizontal and vertical lines. One obtains the two components of the displacements, and, by differentiation, the three components of strains and the local rotations. Experimental results have been already obtained, concerning a novel shear test on composite materials. Only one image is needed to obtain all the information. The method looks similar to the spatial phase-shifting technique proposed in the field of moire, but here no moire is involved.

An optical fiber based moire interferometer for surface shape measurement is described. The technique uses an optical fiber interferometer to project interference fringes and is readily phase stepped without mechanical movement of components.

The paper reviews recent developments and refinements of the optical metrology techniques used for studying mechanical components and structures. In all selected methods the relevant information is encoded in fringe patterns. The automatic fringe pattern analysis techniques provide fast, reliable and unambiguous data interpretation, and facilitate a hybrid approach to strain analysis. Among incoherent light methods the photoelasticity for studying in-plane occurrences of the photoelastic models as well as a photostress method for investigation of real structures, and the fringe projection method for measuring out-of-plane displacements are discussed. Holography and high sensitivity grating interferometry are chosen among coherent light methods. On the basis of experimental results obtained the precision and complexity of the methods are discussed and compared.

Optical interferometric techniques are very fascinating tools for a full-field quantitative evaluation of displacements. While in some applications this information is sufficient, in many cases it is necessary to determine stresses that arise in the inspected object. These quantities are closely related to deformation and can be obtained from the partial derivatives of displacement. In this paper maps of displacement derivatives are retrieved by a direct manipulation of interferograms obtained with the phase-shifting method. Three main advantages are thus achieved: no need of prior displacement evaluation, no need of unwrapping procedures, short processing time.

A new method for measuring the isoclinics and absolute retardations along the principal stress directions at a point in a loaded photoelastic specimen is presented. In this method, a plane polariscope is used with the digital image processing system. Two images of a loaded specimen are captured at different angular positions of the polarizer and analyzer. Isoclinics and retardations at a point are evaluated from the light intensity values measured on these recorded images. The present method for the measurement of absolute retardations overcomes the difficulties in the measurement of retardations in birefringent specimens using the conventional interferometric methods. To verify the effectiveness of this method, principal stresses are directly evaluated using the values of retardations and these principal stresses are verified with the theoretical solutions. The photoelastic specimens -- a circular disk under diametral compression and a simply supported beam with a load at its center -- are analyzed.

This presentation is a formulation of moire and grid methods with the vocabulary of signal processing. It addresses basically the case of in-plane geometrical moire, but, as is well known, any geometrical moire setup can be related to in-plane moire. We show that the moire phenomenon is not a measurement method by itself, but only a step in a process of information transmission by spatial frequency modulation. The distortion of a grid bonded onto the surface of a loaded specimen or structure will cause locally a modulation (Delta) F of the spatial frequency vector F of the grid. The modulation (Delta) F is linearly related to the strain and rotation tensors. An equivalent point of view is to consider the same phenomenon as a phase modulation, caused by the inverse displacements. In this approach, moire is presented merely as an analog means of frequency substraction. The interpretation of the classical fringe processing techniques -- temporal and spatial phase shifting, Fourier transform method -- is made, and some consequences of the zoom-in effect induced by the moire phenomenon are given.

The new method of separation of strains in elastic plane stress state, called the method of characteristics, is presented. The photoelastic experiment for determination of isochromatic order is supported by additional numerical procedure. To determine the fractional order of fringes, the automatic image process is applied.

Traditionally used experimental data interpretation methods try to restore real physical fields by the help of mathematical tools. They do not take into consideration physical equations which must be satisfied, field components are being determined independently. Therefore, pure mathematical interpretation is incorrect for creation of a physical field from experimental data. The proposed method is physically based, that means it allows one to find a solution of a combined experimental-theoretical problem. It takes into consideration experimental data, boundary conditions and basic theoretical relationships. One numerical process gives both the searched field and its derivatives. Moreover, that field may be extrapolated to the region where there is no experimental data. The method has been devoted to photoelasticity, moire and strain gauge techniques.

This work presents a computer aided method of determination of object surface displacement in terms of data reading from holographic interferograms. The options are included in a computer program, which takes into account the physical data known a priori or from separate measurements. These are: e.g., the condition of an object and the load symmetry information or displacements of chosen points determined after measuring by means of displacement gauges. The method allows one to eliminate the necessity for localization of the zero fringe order.

Different sets of linear equations describing the relations between the vectorial displacement field on the object surface and the quantities of the values known a priori from optical and/or mechanical measurements are presented. Physical conditions of solvability of these equation sets are discussed. Applications of these equations to quantitative interpretation of holographic interferograms in terms of deformation analysis are described.

The simulation procedures based on the exact theoretical description of the interference-image formation in the real-time or double-exposure holographic interferometry are discussed. The theory takes into account not only the displacement and strain distributions on the object surface but also reconfiguration of measuring-system parameters between two recorded states of the whole set-up. These state changes influence the form of fringe pattern, with a possible carrier frequency of fringes, as well as the fringe-contrast distribution in theoretical description of the interference image. The program makes it possible to create interference images of the form like that obtained in a real measuring system. The algorithm calculating the displacement and strain fields for a theoretical model of the loaded object is the exchangeable part of the program. The program can be applied in designing real measuring systems, in verification of theoretical models of loaded objects, in analysis of computer-aided systems for quantitative interpretation of holographic interferograms, as well as in eduction in the field of photomechanics.

Speckle photography is a very accurate method of experimental strain analysis. Because specklegramm is not a counterfeitable document of the state of the analyzed object, the method can be used to test the most important elements. The analysis of the specklegramm must, however, be free of systematic errors. In the paper the sources of errors in point by point analysis are quantitatively described and some ideas of elimination are presented. The algorithms are tested on specklegramms recorded in laser light or in white light.

A great number of image processing problems can be stated as approximation problems. A class of approximates can be selected optionally, however, it is more effective to select by function, which parameters have a simple physical or technical interpretation. To verify the theoretical model of the effect or of the research object measurement of a difference between theoretical data (or hypothesis) and experimental data only is useful. The measurement problem can be stated as follows: (1) We have a hypotheses about the class of object function. (2) We have some nonoptical quantitative data. (3) We have an image connected with the object. (4) We have a hypothesis about errors of all data sets. (5) We are looking for an object function fitted to the experimentally determined image. The problem can be solved by use of the Tichonov regularization method, which is a good idea for stable solution of inverse problems.

Four pieces of halved blank for violin making, two cut from tone spruce wood and two from maple wood, have been investigated. The method used for determination of the elasticity constants of the wooden plates is based on the knowledge of eigenfrequencies and shapes of the first few vibration modes. The electronic holography system visualizes the time-average interferograms in real-time. The electro-optical measurements are supported by the separation of eigenmodes electroacoustically. The frequencies are compared with the results of the Chladni method and a measurement of frequency responses. The obtained knowledge can be helpful for the selection of wood plates before they are used in a production process.

Many advances in optics theory and technology have been stimulated by the demands of engineering research. From another viewpoint, the science of optics unifies diverse important areas of experimental research. Fundamental problems in fluid mechanics, rock mechanics, biomechanics, fracture mechanics, materials science, manufacturing technology, nondestructive inspection, and glacier mechanics are being solved by methods of optical metrology. The development of expertise and facilities to have in hand the most appropriate of available techniques is a forbidding task, but it is necessary in order to solve problems in the most efficient way. This paper describes in elementary terms some examples of applications which are relatively uncommon, including biomechanical contouring, glacier strain and flow measurement, 3-dimensional fracture mechanics, and nondestructive inspection of composites. In each case, one or more techniques, some fashionable and some old-fashioned, were adapted, extended or combined to perform the necessary measurements. The rationales for choosing the methods to solve each problem are outlined. The techniques include electronic speckle, electronic shearography, moire interferometry, moire photography with optical filtering, differential moire contouring, Doppler velocimetry, and noncoherent-light speckle photography.

Because of the increase of catastrophic crack propagations at the middle of this century, it became necessary to develop a fracture theory in order to extend the life of structures and for evident reasons of security. These first search works have given a better understanding of the fracture in a linear medium by defining the stress distribution around a crack-tip. The stress singularity is then characterized for each fracture mode by a factor independent of the mechanical properties of the material, the stress intensity factor. This linear theory is always useful because of the common employment of brittle materials. A few decades after, the progress in the study of non-linear behaviors has induced a theory of ductile fracture. For this kind of material, the singularity amplitude is then characterized by the energy release rate. These theoretical works have required the development of experimental methods to test some results to understand special fracture phenomena. Among the experimental methods, the optical ones, which allow non-contact and so non-disturbing measurements, are every powerful. The advent of the laser, the use of image processing and numerical procedure to analyze the experimental data allows by optical methods the determination of stresses or kinematic values with a high precision. Our purpose is to present a few optical methods and the associated analysis techniques developed in our laboratory which seem to be well adapted to measure characteristic parameters of brittle or ductile fracture.

A stroboscopically illuminated ESPI system is described for the simultaneous measurement of vibration amplitude and phase. The technique involves modulating both the illumination pulse phase relative to the vibration, and the optical phase of the interferometer reference beam to generate eight video frames which are processed to yield vibration amplitude and phase.

Two distinguished methods of tracking of natural or artificial surface structures have been utilized for deformation measurements in the microscopic domain. The first method regards classic speckle photography and involves Young's fringes evaluation, the second one bases on a direct cross correlation of structures by digital image processing means. Displacement and strain values are obtained within a regular data point grid automatically. Possible resolution limits for strain values are about 1 (DOT) 10^-4. The typical displacement resolution is about 10 nm, but strongly depends on the structure imaging method. In order to use the measurement data together with numerical finite element simulations interfaces have been installed. The usefulness of the applied algorithms to problems in microtechnology is illustrated by a scanning electron microscope analysis of the complex solder deformation on surface mounted devices. Another example of application deals with the measurement of thermal expansion coefficients on adhesives of the electronics industry.

Starting with the basic equation of standard holographic interferometry for small deformations a generalization of the real-time technique with modification in the case of large deformations is laid out. Ultimately, the problem of recovering previously invisible fringes when reconstructing and the following fringe analysis is discussed. In the past, necessary equations derived from two first derivatives have been established to ensure a proper spacing and a sufficient contrast of these fringes, by a careful choice of the modification parameters at least locally around some point for such a general set-up. In order to make the fringes visible not only locally, but also in a larger domain, further equations resulting from the second derivatives of the optical path difference must be considered, in other words: the remaining modification parameters must be determined in such a way that the optical path difference becomes quasi-stationary in an extended domain. This second derivative reveals a particular relation to the aberration theory of the holographic image and to an integrability equation. It is composed of a mechanical deformation term containing the curvature change of the object surface, a completely dual term of the virtual optical deformation due to the modification, also implying the astigmatism of the image points, and finally a mixed term which is dual to itself.

A further development of the optical method of an interior 3-D stress-strain determination is presented. It is shown that the influence of a light refraction cannot be ignored in the great stress gradient regions. The correction of basic equations has been carried out. The results of this analysis were confirmed by the test experiments. The combined technique using interferometric and inverse methods was proposed for the interior strains determination.

A simple technique, based on metallized photoresist gratings, offers a method of using moire interferometry on components which are subjected to high temperatures. The approach has been used to measure residual stresses in components by the process of annealing.

We describe here a practical implementation of phase stepping moire interferometry for determination of a strain field in areas located close to optical fibers embedded in composite materials. The results show that fibers introduce only a local perturbation without noticeable influence on mechanical properties of materials.

The automatic grating interferometry system for analysis of residual stresses is described. An annealing process of stress relieving connected with the application of high temperature resistant grating is presented and the efficiency of this process is discussed. The experiments are conducted on two types of samples: a railway rail vertical slice and copper sample formed by the explosive method.

Two high accuracy, high productivity measuring devices for checking mechanical products in fine mechanics factories are described. The first one enables the evaluation of the mechanical characteristics of dial indicators. The second is dedicated to metrological checking of graduated rules, used as length standards for the traveling parts of machine tools. The operating principle as well as the parameters of both devices are given.

A general approach providing the best possible results of approximation of experimentally measured data is discussed. It is based on simultaneous use of all information available for the problem in consideration. All experimental data obtained by moire interferometry technique and other measurement techniques may be used in analysis at the same time, as well as our theoretical knowledge about the problem. Smoothing of experimental data is done on physical bases. In the present paper, as a particular application of this concept, formulation of the problem of residual stress reconstruction in an annular plate under internal pressure using all data measured in the saw cut test is discussed.

We are examining the possibility of deriving vibration parameters from statistical parameters of the dynamic speckle pattern formed by reflection of a coherent beam from the in-plane vibrating rough object.

The correlation holographic interferometry is applied in the present paper to studies of laser- induced erosion of solid surface and, in particular, to determination of its energy threshold of damage. Evaluations of the method accuracy are made. Preliminary experiments on energy threshold determination for aluminum surface are performed.

Current trends in development of components, structures, and systems place unprecedented requirements on their designers. To satisfy these demands, new, highly efficient materials and structural designs are being employed and integrated utilization of the most sophisticated technologies is being made. This paper addresses some of the pertinent issues relating to this integration and explores how to take advantage of the analytical, computational, and experimental solution methodologies in relation to a given problem. More specifically, a hybrid approach to deformation analysis is described, based on recent developments in merging, or unifying, of the finite element method with experimental methodologies, and especially with optical metrology. This approach emphasizes the analogy between the methodologies used and employs them to obtain solutions that may not have been otherwise obtainable, to ease the existing solution procedures, or to attain improvements in the results. The paper begins with an introduction to the methodologies used, continues with a discussion of the analytical fundamentals, and concludes with a presentation of representative results.

Within the planning stage devoted to realize an innovative turbine for an aircraft engine, an experimental prototype has been made. Several measurements have been carried out to experimentally verify the expected structural and dynamic features of such a prototype. Expected properties were worked out by finite elements method, using the well-known Nastran software package. Natural frequencies and vibration modes of the designed prototype were computed assuming the turbine being in both `dynamic condition' (rotating turbine at running speed and temperature), and in `static condition' (still turbine at room temperature). We present the experimental modal analysis carried out by time average holographic interferometry, being the prototype in `static condition;' results show the modal behavior of the prototype. Experimental and computed modal features are compared to evaluate the reliability of the finite elements model of the turbine used for computation by the Nastran package; reliability of the finite elements model must be checked to validate results computed assuming the turbine blade is in hostile environments, such as `dynamic condition,' which could hardly be tested by experimental measurements. A piezoelectric transducer was used to excite the turbine blade by sine variable pressure. To better estimate the natural vibration modes, two holographic interferograms have been made for each identified natural frequency, being the sensitivity vector directions of the two interferograms perpendicular to each other. The first ten lower natural frequencies and vibration modes of the blade have been analyzed; experimental and computed results are compared and discussed. Experimental and computed values of natural frequencies are in good agrement between each other. Several differences are present between experimental and computed modal patterns; a possible cause of such discrepancies is identified in wrong structural constraints imposed at nodes of the finite elements model. Slight structural differences among different blades of the same prototype turbine are pointed out and discussed.

As a consequence of the recent qualitative improvement of the phase fringe patterns by Thierry Floureux (1993) using electronic speckle pattern interferometry, the ability to precisely measure local displacement fields exists. With this new ability speckle interferometry becomes a tool for many applications where local effects are of great theoretical concern. The technique can be used to test and, if necessary, correct assumptions or simplifications used in theoretical models. This paper shows new applications of the improved speckle interferometric method, one being the detection of the various crack forms such as splits and delaminations (NDT) occurring in the above-mentioned fatigue-loaded specimens and their affect on the displacement field at the surface. The other one is using speckle interferometry as a tool for verifying or, respectively, updating FEM-damage models of fatigued specimens.

The paper proposes new experimental, mechanical, and numerical procedures for solving the problem of experimental determination of rail residual stresses. Basically it brings an idea of a new and original experimental scheme, which can be looked upon as modification and development of the established in the field and informally recognized as standard Battelle technique. The new methodology of examination, however, discontinues expensive and troublesome Meier sectioning, replacing it with oblique slicing that brings information of the residual stresses in rotated coordinate systems. Based only on transverse and oblique slice measurements a new mechanical procedure restores iteratively a full 3D stress state that was originally in the rail. Application of complex mathematical procedures like physically based approximation techniques (embodiment of physical relations into approximation equations) and a full 3D model of the continuum (finite element analysis) along with moire interferometry measurements ensures high quality final results that are mechanically consistent with the applied model of the continuum. The paper discusses in detail mechanical background of the technique, experimental procedure and algorithms of numerical data handling and enhancement. An extensive range of tests show results of an in-depth investigation into the technique that has been carried out on simulated data. Possible extensions to the technique and further research plans also are shown.

One of the widely used methods for determing residual stresses is hole-drilling. in which the radial strains proGJced when residual stresses are relieved by the hole and are meutred by differem experimerUJ tedniques, including the holographic interferomeby. Jn this paper a superposed holosraphic interferometer is used to determine in-plane radial displacemera cbs to releasing of residua1 atreues by hole-drilling. 1be tam •superposed holographic interferometer' denotes the assembly of the object 81.rlace section and holographic plate in an immediate vicinity to the object. With the purpose of raising the interference patterns comut the hiah-frequency gratiqJ is used. Residua1 stresses are obtained by the bomdary i!Ugral equations method. Jn this method the distribution of interference fringe orders along the 2-3 concentric holes is used for determine the bomdary conclitions. The combined e111<loyment of holowaphic interferometry and bomdary i!Ugral equations method allows to calculate the residual stress clistribution along the hole's round and inside this region too. ~ between stress holographically determined with a COl11JUled value is satisfactory.