Since its invention 30 years ago, hologram interferometry has grown from laboratory discoveries to full-fledged methodologies. It has not only influenced developments of this period, but has responded to them as well. From its start as a methodology based on silver halide recording materials, it has evolved through thermoplastic, photoresist, crystal, and other recording materials to fully take advantage of the computer revolution of the 1980's which, coupled with the development of solid-state video cameras, led the way to practical holography based on the silicon chip as the recording medium. Now, as new procedures for automated data acquisition and quantitative interpretation of fringe patterns are being developed, it becomes easier and easier to use the state-of-the-art interferometric techniques in nondestructive testing, metrology, and in a variety of other applications. In this paper, some of the developments in the field of hologram interferometry are reviewed as seen from the author's perspective and involvement since late 1960's, with particular emphasis on quantitative interpretation of interferograms and the evolution of hybrid, experimental- computational, solution methodologies. This review is illustrated with representative applications from the studies of macro and micro-scale structures. As we celebrate the first 30 years of the activity in the field of hologram interferometry, I would like to dedicate this paper to all the known and unknown inventors, coinventors, scientists, researchers, workers, students, enthusiasts, and others who have contributed to its development. Also, I would like to take this opportunity to congratulate SPIE on its 40th Birthday and wish many long lasting... 'holographic'... achievements in the years to come, as we approach the year 2000 and beyond.

High-sensitivity grating interferometry is shown as the effective experimental tool in hybrid method stress analysis. The recent modifications in instrumentation aim in the analysis of transient phenomena, measurements on a standard loading machine with simultaneous analysis of in-plane u, v, and additionally out-of-plane w displacement fields, miniaturization of the system, as well as in full automatization of acquisition of data and analysis of the results. The automated grating interferometer is considered as a smart system with adaptive fringe pattern design and macro/micro-scale measurement ability. Fulfilling recent instrumentional requirements enlarges areas of application of grating interferometry. The most recent examples of application discussed in the paper include: fracture mechanics, residual stresses determination, relaxation processes, fatigue testing, local material constants measurement, testing of local phenomena in adhesive joints, surface layers, material grains interaction, and many others.

Digital speckle pattern interferometry is used to investigate the vibration behavior of silicon micromembranes. Mode shapes have been mapped up to the 20th natural frequency for squared membranes with millimeter and submillimeter dimensions. Experimental results are found in very good agreement with analytical and finite element analyses. Assigning vibration modes to the series of natural frequencies measured allows to get information about Young's modulus or membrane thickness, respectively.

A new experimental procedure devoted to analyse deformation patterns due to the contemporary excitation of different vibration modes (mode coupling) is proposed. The proposed procedure, based on use of holographic interferometry techniques, is particularly appropriate whenever coupled modes are expected according to FEM computation and an experimental modal analysis is required for FEM model validation. This work tests the proposed procedure by verifying the reliability of the experimental results worked out in analysing two simple specimens whose modal behavior can be confidently predicted by analytical and numerical computation.

This paper presents several examples of tire vibration analysis under different loads, inflation pressures, and excitation modes. Several consecutive structural resonant modes were also analysed in the frequency range 190-260 Hz to search for their contribution to a phenomenon called the first resonant frequency of the tire cavity as well as to experimentally determine their contribution to the tire noise spectrum. A Lumonics HLS-2 ruby laser system was used in double exposure mode during the experiments. The capability to precisely map a 3D displacement vector field is shown through utilization of an image processing system and a simple fringe order tracking procedure. The examples supplied demonstrate that HI can provide very accurate experimental measurement of mode amplitudes to precisely tune FEA tire models under arbitrary boundary condition. This experimental technique can also be used to measure responses of some 'exotic' materials built into a tire for which the computer models cannot be easily established. The unique capabilities of HI were also applied to studies of the surface shock wave propagation in the tire carcass and sidewall. Several examples of different dynamic response of the tire due to changing experimental conditions are presented.

Understanding and quantitative modeling of stress relaxation processes are very important for reliable and efficient design of the load resisting structures. In this paper a hybrid ESPI-FEM system for evaluation of time-dependent stress and strain characteristics in small components is presented. Based on results obtained by this method a long term prediction of material behavior can be done. Problems related to the coupling of results from the experiment to an FEM model are discussed and illustrated with reference to speckle interferometry stress analysis of a cantilever beam. Results show that for the conditions tested, stress level in the cantilever beam reduces by 10% of the level at the instant of the loading.

Development of reliable computers depends on effective electronic packaging which, in turn, builds on device interconnections at all levels of packaging. Modern electronic interconnections consist of spring like microcontacts made of metallic materials. When in a functional engagement, these springs must produce the desired contact forces in order to assure reliable interconnections. However, when loaded, the springs undergo stress relaxation thereby reducing the effective contact forces which leads to degradation in the electronic interconnection. An effective way to counteract this degradation is to account for the undesirable effects of the stress relaxation while designing the interconnections. The only way to do so is to understand the processes controlling this phenomenon. In this paper, viability of a computational and experimental hybrid approach for determination of stress relaxation characteristics in microelectronic connectors is studied. This approach combines the computational and the experimental aspects of the finite element and the grating interferometry methods, repsectively. Principles of the hybrid approach are outlined and its preliminary implementation is demonstrated by an application to the specific contact for high density, high speed digital interconnections. Since this contact was designed to be used in applications where quick connects and disconnects are needed, in order to provide separable interconnections reusable a number of times, knowledge of the stress relaxation characteristics of this contact, during each connect and disconnect cycle, is essential to assure its functionality. Preliminary results show good correlation between the computational and the experimental data and demonstrate viability of the hybrid approach for analysis of stress relaxation in the microelectronic connectors.

The possibility of generation and observation of a nonlinear solitary strain wave (soliton) in a solid waveguide is of special interest in connection with undeniable potential applications in solid state physics and mechanics. The present paper deals with new results on the soliton evolution in a relatively long waveguide as well as in a waveguide of varying cross sections.

In order to advance the safety of some important structures that will be required to perform under increasingly stringent conditions, it will be necessary to use materials that are lighter weight, have superior strength, and have the ability to change such parameters as shape, degree of stiffness, and electrical and mechanical properties as needed. These future materials had been named 'smart' material. It is important to measure strain within the materials. A fiber optic sensor may be used to support the necessary sensing functions of these 'smart' materials and has several compelling advantages with respect to electrical alternatives, which are tolerant to corrosion, resisted to disturvance of electric and magnetic, easily to be embedded into composites. Unless the (pi) /2 nonreciprocal phase bias and the phase shifting become a problem, interferometers using single mode fibers as optical propagation paths will be superior. It is well known that the oscillating frequency of coupled cavity semiconductor laser can be modulated by induced current. In this paper we studied the coherent frequency modulated heterodyne interferometer, (used to overcome the problem of (pi) /2 nonreciprocal phase bias, and the phase shifting problem without help of active control by ceramics), and the measuring of strain of smart structures when embedded into materials. The maximum defection range is limited by the coherent length and the dependence of the semiconductor laser.

Three dimensional deformation measurement by holographic interferometry with phase shifting technology is presented. The two-reference-beam holography is applied with phase shift to improve the accuracy in optical phase difference measurement. A least squares algorithm is proposed to substitute the Stetson's algorithm in the calculation of the unknown constant phases in these interferograms. Comparisons of the deformations solved by these two algorithms for the same measured optical phase differences are shown. The results show that the local error in phase measurement has less effect on the final deformation solved by the new algorithm than by the Stetson's algorithm.

A technique of the normal and tangent displacements' determination in thinwalled structures-shells on the basis of the focused images of Fl Holographic Interferometry is developed.(FIHI). The used approach allows with the same satisfying accuracy to determine the displacements components in one experiment , by the unified optic scheme, on one hologram. The high sensitivity to three components of the displacement vector on the structure's illuminated surface is achieved on the account of that on one photoplate two interferential pictures take place, which cany the separated information about the normal and tangent displacements on the surface of the shell or plate. In the kind of examples the result of the investigations for the round plate and the cylinder shell under the P force were presented, the interferograms and speckle-photographs were obtained, on the basis of which the interpreting was produced. Using the relationships of the classic theory of plates and shells(Kirhgoffs-Liav's theory) and the obtained three displacements components, preliminary approximated by the degree polynomials of the high degree by the method of minimum squares on the PECM, the deformations on the illuminated surface of the object were determined. And by the specklephotograph the sunimary deformations from bending and tension were obtained, and by the interferogram-the bending components. Then the separation of deformations to the moment and membrane was done , the dependencies of the deformation levels on the illuminated middle and nonilluminated surfaces were constructed. Such approach to the investigation of the thinwalled shells highly expand the application of the hologram Interferometry methods. Keywords: three-exposure, focused images, holographic interferogram, spatial structures, displacements, deformations, approximation.

A new reflection moire technique is introduced in this paper. The basic equations that relate the measurement of slopes to the basic geometric and optical parameters of the system are derived. The sensitivity and accuracy of the method are discussed. Examples of application to the study of silicon wafers and electronic chips are given.

A high magnification phase-stepping interferometer has been constructed which has a spatial resolution of the order of one micrometers and a sub-mm field of view. Laser illumination is delivered to the microscope head by polarization-preserving single-mode optical fibers. The head itself is a compact unit consisting of collimating optics, objective lens, CCD camera, and a separate white light source. Phase gratings are cast on the polished specimen surface by replication from a master grating, in either silicone rubber or epoxy resin. Subsequent evaporation of a thin layer of gold onto the grating increases the reflectivity and reduces the speckle noise in the images. By switching between the laser illumination and the white light unit, it is possible to view the underlying microstructure in exact registration with the measured displacement fields. The instrument is illustrated with several applications including the visualization of delamination cracks in graphite-epoxy composites and measurement of the strain-to-failure of polymer-bonded-explosives.

High-sensitivity, automatic grating interferometry (AGI) system is shown as the effective experimental tool for the material microstructure studies. Two interferometers, laboratory AGI for static and portable AGI for dynamic loading of the specimen are presented. The full methodology of a sample preparation, measurement and data analysis process with special attention paid to combining the information about grain borders and displacement/strain fields distribution is described. The experimental displacement fields obtained at the borders between grains in bicrystal, tricrystal, and polycrystal aluminum alloy are presented. The strain maps of tricrystal sample are presented and discussed.

A method for the active stabilization of an out-of-plane electronic speckle pattern interferometer (ESPI) is presented. A compact Michelson interferometer is adapted to the ESPI head to determine the relative motion between the ESPI and the object. The signal of the Michelson interferometer is prepared by a microcontroller and supplied as an addition signal to the phase shifting unit of the ESPI. The presented solution is a practical method for applications with real-time ESPI. It increases the potential of ESPI especially for applications outside of an optical laboratory under rough conditions.

MicroElectromechanical Systems (MEMS) are devices fabricated with the techniques of microphotolithography to manufacture miniature actuators and sensors. Dimensions of MEMS devices are typically measured in microns. For a number of reasons, the current demand is to decrease the size of MEMS devices to submicron dimensions. However, the smaller MEMS become, the more challenging it is for engineers to measure with accuracy the static and dynamic characteristics of these devices. In this paper, electro-optic holography (EOH) and computational methods are used to study the resonant vibration behavior of submillimeter- sized cantilevered microbeam sensors. These particular sensors are probe tips made for atomic force microscopes. Important dynamic characteristics of these sensors, which must be verified experimentally, include the frequency of vibration and corresponding mode shapes, the quality factor (Q), the spring stiffness, and the vibrational amplitude. The EOH allows easy determination of these characteristics. Additionally, by performing phase measurements of an EOH image (magnified up to 100X), object displacements are determined. The finite element method (FEM) is used to model cantiliver beam dynamics in order to optimize such parameters as frequency of vibration, Q, spring sriffness, and amplitude of vibration. The FEM results are then compared to the EOH results and show acceptable correlation.

A three illumination beam, phase-shifted interferometry system is used to measure 3D surface deformation fields to study the mechanics of cracks loaded in shear. The interferometer, which is mounted to the actuator of a servohydraulic loading machine, is augmented with a piezoelectric phase shifter to obtain a sequance of differential phase maps over small load increments. This avoids problems with speckle decorrelation and provides more detailed information about the phenomena of interest. The displacement fields were accumulated relative to the unloaded state by sampling at appropriate locations in the incremental fields to optimize spatial resolution and compensate for large rigid body motions. Features of the effect of fracture surface interference on a shear-loaded crack inferred from the displacement fields are described.

The influence of a technological surface layer on the strength of machine element is confirmed by an increasing number of theoretical and numerical investigations. However, due to the use of modified finite elements in the small region of layer, as well as implementing the variation of hardening moduli in the material model, the experimental verifications of FEM results is strongly required. In this study, automated grating interferometry is applied for in-plane u and v displacment maps determination. Experimental results are compared with numerical analysis performed for the sample with and without surface layer. The increase of the strength of machine parts with the technological surface layer is confirmed experimentally. The possibility of interactive application of experimental results in order to improve numerical FEM model is discussed.

Deterioration of historical murals often leads to partial detachments of the paint carrying plaster layers. To identify such regions an acousto-optical method is described. Loose portions of the plaster are excited by sound waves and the resulting vibrations are detected by sensitized analog TV-holography.

In this paper, an attempt is made to visualize the temperature fields developing under a low density environment with the aid of a laser holographic interferometer. The objectives of this paper are to confirm the environmental pressure effects onto the fringe formation and to analytically establish an evaluation procedure for a taken interferogram to estimate local temperatures, in which the refractive index of air depends on not only the temperature but also the pressure. In the interferogram analysis, the axial-symmetric 3D temperature field formed under the various environmental pressures is divided into infinitesimal sub thin rings and the respective refractive index, namely the local temperature, is expressed as a function of fringe order shifts and the environmental pressure. Then the validity of this procedure is verified by the experiment. In the experiment, the temperature fields at the low density environments are realized by natural convection developing under a circular disk cooled by a thermoelectric cooling device, which is set in a chamber evacuated by a vacuum pump. The chamber pressures are varied from P_c approximately equals 0 mmHg to atmospheric pressure and the interferograms are taken for the conditions. As the results, the critical pressures for the visualization and for the temperature estimation of this system are well designated and the procedure for temperature estimation proposed here is considered to be reasonable.

A phase-conjugate holographic measurement system has been developed for the study of 3D fluid velocity fields. The recording system produces 3D particle images with resolution, signal-to-noise ratio, accuracy, and derived velocity fields that are comparable to high-quality 2D photographic PIV (particle image velocimetry). The high image resolution is accomplished by using low f-number optics, a fringe stabilized processing chemistry, and a phase conjugate play-back geometry that compensates for aberrations in the imaging system. In addition, the system employs a reference multiplexed, off-axis geometry for determining velocity directions using the cross-correlation technique, and a stereo camera geometry for determining the three velocity components. The combination of the imaging and reconstruction sub-systems make the analysis of volumetric PIV domains feasible. Recently, a new geometry for the HPIV system has been developed for imaging flows through thick-walled, curved windows. In the older geometry, there have been two sources inhibiting the use of windows: window scattering and window-induced aberrations. In the new system, these difficulties are avoided using side- scatter illumination of the particles and phase-conjugate reconstruction with a substitute window in place.

Real-time analysis of component deformation under service conditions would form the optimum experimental optical technique. Approaching this ideal is pulsed laser electronic speckle pattern interferometry (ESPI) which can provide in-plane displacement information from high speed rotating components over a wide range of rotational speeds with tangential velocities currently up to 300 m s^-1. With the rapid advancement of computers, the Fourier transform method of analysis of interference fringe patterns for full field information has been reduced to just a few minutes. The testing of high speed discs in air, with particular reference to gas turbine disc behavior has provided the ability to display the effects of windage heating of the discs, in addition to changes of speed. The technique is sufficiently accurate to record both short term differential heating across the disc, as well as the longer term overall growth.

An equal-thick-fringe F-P interferometer for ultrahigh-speed multiframe recording has been reported in this paper. The initial process of laser produced plasma on the dielectric film layer has been explored by using this interferometer, and five interferograms with the frame interval time of 30ns are obtained.

The use of a new interferometric cineholography system allows new possibilites in the field of in-situ vibration analysis of structures: determination of phase and magnitude maps, calculation of the structural intensity and calculation of its divergence, and modal analysis of plates under complex excitation. This paper gives some results showing the feasability of such applications.

Optimum dynamic characteristics of an aluminum cantilever plate containing holes of different sizes and located at arbitrary positions on the plate are studied computationally and experimentally. The objective function of this optimization is the minimization/maximization of the natural frequencies of the plate in terms of such design variable s as the sizes and locations of the holes. The optimization process is performed using the finite element method and mathematical programming techniques in order to obtain the natural frequencies and the optimum conditions of the plate, respectively. The modal behavior of the resultant optimal plate layout is studied experimentally through the use of holographic interferometry techniques. Comparisons of the computational and experimental results show that good agreement between theory and test is obtained. The comparisons also show that the combined, or hybrid use of experimental and computational techniques complement each other and prove to be a very efficient tool for performing optimization studies of mechanical components.

An interferometric technique of a position and beating control for an axial rotating body position is described in this paper. A Michelson interferometer without a signal spectrum transfer in a high-frequency range is used as a position and beating sensor of rotating body. An autocollimator as a reflector insensible to angular rotating is used in a measuring level of the interferometer. The autocollimator is hard connected with a cylindrical information carrier by a magnet lock for motion dynamics investigations. It is found that the position error of the proposed position sensor is no more than (lambda) /8.

This paper presents a method for obtaining the shape of an object using digital shearography. The technique makes use of two types of phase shifting. One provides a nonuniform phase shift which is related to the shape of the object. The other is independent of the shape of the object and utilizes uniform phase shifting. Theory together with experimental verification are demonstrated.

The purpose of recent developments of profilometry by using white light interferometry is to provide new tools for the analysis of rough samples which when studied by monochromatic phase-shifting interferometry, may cause phase calculation ambiguities. The usual way to perform depth measurements by white light interferometry is to analyze the coherence-limited interference fringes while the optical path difference is scanned. The method proposed here does not use optical path difference scanning. A spectroscopic device is used instead to separate the interference intensities associated to each spectral component of the light source. Phase variations due to wavelength change are proportional to the optical path difference and allows depth measurement to be performed without axial scanning. The profile of one line of the inspected sample is obtained from only one 2D interferogram. In this 2D interferogram one direction corresponds to the inspected direction of the surface while the other one is the chromatic axis which allows phase to change with wavelength. Experimental results show the ability of the proposed method to obtain the profile of 1D surface with nanometric resolution.

This paper describes a database of wavefront measurements of large aperture optical components. This database is being compiled as part of our component development program in preparation for the National Ignition Facility (NIF). The data is stored electronically in the form of 3D phase maps of the reflected or transmitted wavefront, measured by phase shifting interferometry at 6328 angstrom. The database will serve both technical and administrative purposes for the NIF project. These purposes will be described, as well as the type of data and measurement techniques used.

Current optical interferometric methods for reconstructing 3D surface profiles of thin films from phase measurements are often inaccurate because of the effects of phase changes on reflection. A new method has been developed that automatically determines the film thickness and reconstructs the surface profile of thin films from conventional interferometric phase measurements. This method uses known optical constants of the materials that compose the test surface. By measuring the film thickness at each point of the test surface, a 3D surface profile can be reconstructed. Experimental results are presented for a set of thin film standards consisting of SiO₂ film on silicon substrate. The thin film thickness determined using this method is within the uncertainty certified by the standard manufacturer.

A new interferometric method for measuring thickness and refractive index of thin films on substrates without a priori information about these two parameters is presented. For measurements, the substrate is produced in the form of a wedge, with the investigated film only on a part of it. Two complex patterns of interference equal-thickness fringes are observed, produced by interference in a two-beam interferometer with the sample, and by interference of two beams reflected by the sample surfaces, each for two different wavelengths. The values of the thin film thickness and refractive index are calculated from the values of relative shifts of interference fringes between two parts of each interference pattern. The thickness of a thin film is measured with accuracy of 5 nm.

Digital recording and numerical reconstruction of holograms is a new method of laser metrology: two or more Fresnel holograms, which represent different loading states of the object, are generated directly on a CCD-target and stored electronically. In contrast to speckle interferometry, no lens or other imaging device is used. The reconstruction is done from the digitally stored holograms with numerical methods. For both states, the intensity as well as the phase of the object wave can be calculated in the reconstruction process. This makes it possible to calculate the interference phase directly from the holograms, without generating an interference pattern. In this paper, applications of digital holography in the field of nondestructive testing are presented. A thin-walled pressure vessel (satellite tank) is loaded by changing the internal pressure and the resulting deformation field is measured quantitatively. Defects in the wall become visible as local peaks in the global deformation field.

The purpose of this paper is to relate several automotive industry applications of holographic interferometry, or holometry. Holographic nondestructive test methods are now routinely used in industry to study structural integrity and to assess vibrational response of components. This work is usually performed to verify that a component will not fail in service. The work cited in this paper was performed instead for the purpose of assessing the noise, vibration, and harshness implications of various hardware configurations. Four examples of such work will be presented; objectives, methods, and results will be discussed for each example.

A new single-beam technique for a continuous reconstruction of volume holograms in photorefractive crystals of symmetry 23 is presented. The doped crystal Bi₁₂TiO₂₀ (Fe,P) possessing diffraction efficiency above 70% is used for real-time holographic interferometry. The major advantage of this technique is an automatic self-adjustment of diffraction in volume holograms, continuous reconstruction of volume holograms, high diffraction efficiency without application of external electric field, high resolution (more than 3000 lines/mm), high vibroprotection stability, low cost using of He-Ne or diode lasers, and portability (single-beam device). A 1 mm crack was detected at a depth of 1.5 mm in airplane wings near a rivet zone using protable adaptive holographic interferometer.

Cracks and defects in structures can be detected by observing the changes of the vibrational modal patterns and surface responses to stress. Features are made visible with dynamic holographic interferometry combined with parameter estimation. The procedure involves an unconventional, optimized, laser-illumination method. The methods are especially applicable to large structures and could prove pivotal to improved designs, monitoring, and maintenance. Components and structures could be designed to better withstand operating stresses, and existing structures could be analyzed to predict their response to stress. Since the modal characterization of a structure can act as a type of fingerprint, holographic interferometry can also be used to monitor structural degradation due to operating and aging. Modal characterization includes indentification of resonant frequencies and also the corresponding mode shapes. Holographic interferometry provides for direct modal characterization of a structure as well as measuring its small loading dynamic response. This research demonstrated that a wide variety of defects can be located in structural components, vessels, and pipes. An analytical exercise also demonstrates the ability to use global modal characteristics to determine the presence of local corrosion and erosion.

One of the major challenges in the development of avionics is the requirement to assure their reliable functionality while subjected to the actual operating conditions which are static and dynamic in nature. Of particular interest to the developments presented in this paper are the dynamic loading conditions. Because the avionics have certain mass and elasticity, they respond to the loads encountered during operation with a specific vibration behavior. Therefore, development of reliable avionics packages depends upon our ability to determine the dynamic characteristics which define and control their vibration behavior, particularly as it relates to the dynamic environment within an aircraft which is a major contributor to the failure of airborne avionic systems. In this paper, computational and experimental hybrid methodolgy is used to quantitatively study the vibration characteristics of avionics. The computational methodology is based on the finite element method. The experimental methodology is based on the electro-optic holography method, which allows direct electro- optic recording, processing, and display of the laser holograms at the rate of 30 holograms per second, making it capable of producing quantitative data in nearly real-time. Using the electro- optic holography method, displacement magnitudes in the submicron range are measured noninvasively over the full field of view, as a function of the resonance frequencies. Although some of the experimentally observed mode shapes were not predicted using the computational model employed in this study, the correlation between the results obtained using the finite element and the electro-optic holography methods was otherwise good and the agreement between the corresponding resonance frequencies was within 2%.

Presented is the possibility of full-field displacement measurement in a wide dynamic range, using the hardware and software of a standard ESPI system. In-plane displacement measurements are performed by double symmetrical ullumination of the object, successively for each illumination direction, at a step-wise increase of the loading. The final result is the sum of the individual displacments for each loading step, thus overcoming the constraints due to decorrelation of the interference patterns, and ensuring high accuracy in a wide dynamic range. The out-of-plane displacements are measured by the method of interference fringe projection. The phase-stepping technique with digital processing of interference patterns provides high accuracy in a wide dynamic range, as well as real-time observation of displacements, typical for TV ESPI systems. Presented are experimental results; the prospoects for additional noise filtering are pointed out.

The pressure variations from a sound source lead to corresponding variations in the refractive index which can be measured using TV holography. We measure cross-sections of the integrated sound fields from different directions. To obtain a complete map of the volume distribution of sound field we use tomographical backprojection of these recordings to reconstruct the amplitude and phase of the sound field in any plane of the volume.

A Shack-Fizeau interferometer has been designed and constructed to test concave conical telescope mirrors. Many interesting practical problems and results were found on the way. Some of these problems are, for example, the design of each optical element and the imaging of the interference pattern on the detector, etc. Here, we describe the design parameters with some detail.

A very elegant theory for the autoimaging of diffraction objects has been developed some years ago where the concept of the Montgomery rings arouse. Using the concept of the Montgomery ring we may obtain a large variety of structures that produce autoimages. Many of these structures are periodic and well known, but some others are not periodic and not so well known. Here, we discuss some properties of these rings and their practical consequences.

This paper deals with a Michelson-like interferometric apparatus in air to determine the thermal stability of an optical table. The flowing air is an efficient tool to uniform the temperature of the objects under test. With some precautions it is possible to use the noisy modulations in the interference pattern, due to the presence of air, to perform a 'temperature- scanned' interferometric measurement. The derivative in temperature of the refraction index of air is negative, less the 2 micrometers per K, nearly constant in a small temperature range. Therefore in the center of the Haidinger rings a monotone sinusoidal irradiance versus temperature can be calculated. The FFT analysis of this signal shows a 'quasi-monochromatic' line in the inverse temperature domain whose position is proportional to the thermal expansion coefficient of the air. The actual signal will depend also from the thermal stresses undergone by the interferometer arms. The FFT analysis of a set of experimental data shows a line shifted from the calculated 'pure-air' position. The amount of this shift is proportional to the equivalent thermal expansion coefficient of the table: (alpha) _z equals -2.4 X 10^-7 +/- 1.2 X 10^-8K^-1 in the temperature range t equals [ 17.7, 22.5 ] degree(s) C. The resolution of the method and the main sources of noise are discussed.

A portable feedback opticoelectronic system for measuring the shape of large-format objects is presented. It is based on the projection of phase-shifted interference fringes on the measured surface with subsequent digital processing of the interference patterns. The density and orientation of the projected fringes are set by an adjustable Michelson's interferometer, utilizing a phase-shifting mirror with three-point suspension and low-voltage control (0-12 V). The opticoelectronic feedback determines the value of the phase steps and monitors the level of the tolerable vibration noise. The system also includes a measurement CCD camera with high resolution and a personal computer with the relevant software for the measurements. Laser light sources in the visible and near-IR region with a power of up to 10 W in continuous mode can be used. Narrow-band interference filters with high transmittance make possible measurements under normal, daylight illumination of the working premises. When powerful lasers are used (for example, 10 W CW Ar laser at 488 nm) the mirrors should have dielectric coatings. The interferometer is sealed and under pressure with an inert gas (Ar) maintained in it in order to protect the optical elements against dust, burning, and coherent noise. A description is made of the design, operating procedures, theoretical background, and experimental results from measurements of real objects in working conditions.

In this paper, we propose a novel technique for quantitative phase measurements of vibrating structures based on additive-subtractive speckle interferometry. Additive fringe patterns (of poor visibility) corresponding to the object deformation are obtained by pulsing the laser illumination at times when the deformation is at its maximum and minimum amplitudes. A relative inter-pulse phase shift is introduced within each repetitive deformation cycle (e.g. +(pi) /2 for the maximum and -(pi) /2 for the minimum amplitudes respectively) to obtain two consecutive conjugate pairs of phase-shifted additive fringe patterns. Additionally, and inter-frame phase shift is introduced between the conjugate pairs of additive fringe patterns, which are then subtracted and rectified to provide a phase-shifted additive-subtractive fringe pattern of good visibility. Typically four such phase-shifted additive-subtractive fringe patterns with relative phase shift of (pi) /2 between each other are obtained, and these are used to calculate the deformation phase map from which the vibration measurement of a circular membrane. The ability of the technique to perform in relatively severe noisy environments is demonstrated.

Packages such as microelectronic packages require hermetic seals, as the reliability of such devices is extremely important. One possible failure is due to leakage resulting from imperfect hermetical seals in microchips and microelectronic packages. Imperfect sealing may allow moisture and other impurities to migrate into the packages and cause the devices to malfunction. Current methods of testing hermetics are very slow and cumbersome and thus they cannot be used for mass inspection in production. This paper presents a novel technique based on digital shearography, which allows hermetic seals to be rapidly tested. This method employs a technique of digital shearography for measuring time-dependent deformation. In this paper, a figure is shown of the technique whereby the object to be studied is illuminated with a point source of coherent light and it is imaged by an image-shearing video camera which produces a pair of laterally sheared images on the image sensor of the camera. In other words, two object points are brought to meet in the image plane; they interfere producing a speckle pattern. When the object is deformed, a phase change is induced in the speckle pattern which measures the relative displacement between the interfering points. In the study of a time-dependent deformation of a test object, the speckle patterns received by the image- shearing video camera are continuously digitized at a predetermined rate depending on the deformation rate via a frame grabber into a micro-computer such as a PC, and stored in the memory of the computer. After recording, the displacement derivative versus time for any point of interest can be extracted by plotting the phase change of the speckle pattern at the point versus time from the computer memory. The total phase change can be obtained by integrating the phase curve. The evaluation of hermetic seals in microelectronic packages is based on measuring the time-deformation of the package's lid. The package to be tested is placed in an enclosure inside which the pressure can be varied. A change of pressure in the chamber is applied and held constant; the package surface will be deformed. If the package is perfectly sealed, the deformation will remain constant. Whereas, if the package leaks, the deformation of package surface will gradually recover cuasing a time-dependent deformation. Hence by measuring the deformation of the package's surface as a function of time with digital shearography, leaky packages can be revealed. Figures in this paper show a typical test result of a perfectly sealed package, and a typical result for a slow leaker, and a fast leaker. In the data, each cycle in the curve represents a deformation of $w/x of about 100 X 10^-6. This process of detecting leaks in microelectronic packages is extremely fast, typically a couple of seconds. The conventional methods would probably require a couple of hours.