Past and recent progress in fringe analysis is reviewed from a methodological point of view. Some of the current trends are introduced and the potential directions of future studies in fringe analysis are considered.

The possibilities of artificial neural networks in computer-aided evaluation of holographic interference patterns are shown at three examples: demodulation of the interference phase modulo 2(pi) in one and two dimensions by a time-discrete recurrent Hopfield network, fringe tracking by a self organizing feature map network of the Kohonen-type, and the automatic detection of partial patterns due to material defects by a multilayer network trained by backpropagation.

STDCE-2 is a fundamental fluid physics experiment (scheduled for flight in Fall 95) studying steady state and oscillatory free-surface deformations as a function of surface temperature and chamber geometry. During the mission, approximately twelve hours of Ronchigram data is scheduled to be recorded to video tape. Thus, the analysis software must be highly automated. This paper describes a backtracking algorithm for automated fringe center tracking of digitized interferogram data and presents some results.

During the preparation of HNDT applications, it is common practice to carry out a number of experiments in order to gain knowledge about detectable and nondetectable flaws, and to select optimum testing conditions. In many cases, considerable effort is necessary especially for advanced materials with anisotropic properties. This paper proposes an alternate approach: completely simulating the component behavior as well as the HNDT process. Considerable savings occure in both time and cost items, and in addition a direct relationship can be established between the damage significance of a flaw and its visibility by interferometric techniques.

The basic relationships between stress and strain under cyclic conditions of loading are not at present well understood. It would seem that information of this type is vital for a fundamental approach to understand the fatigue behavior of dynamically loaded structures. In this paper, experimental and computational methods are utilized to study the fatigue behavior of a thin aluminum cantilever plate subjected to dynamic loading. The studies are performed by combining optomechanical and finite element methods. The cantilever plate is loaded periodically by excitation set at a fixed amplitude and at a specific resonance frequency of the plate. By continuously applying this type of loading and using holographic interferometry, the behavior of the plate during a specific period of time is investigated. Quantitative information is obtained from laser vibrometry data which are utilized by a finite element program to calculate strains and stresses assuming a homogeneous and isotropic material and constant strain elements. It is shown that the use of experimental and computational hybrid methodologies allows identification of different zones of the plate that are fatigue critical. This optomechanical approach proves to be a viable tool for understanding of fatigue behavior of mechanical components and for performing optimization of structures subjected to fatigue conditions.

Direct recording of Fresnel holograms on a CCD (charge-coupled device) and their numerical reconstruction is possible, if the maximum spatial frequency of the holographic microstructure is adapted to the spatial resolution of the detector array. The maximum spatial frequency is determined by the angle between the interfering waves. For standard CCDs with spatial resolution of approximately 110 lines/mm the angle between reference and object wave is limited to a few degrees. This limits the size of the objects to be recorded or requires a large distance between object and CCD-target. In this paper a method is described in which the primary object angle is optically reduced, so that objects with larger dimensions can be recorded. The principle is demonstrated at the example of deformation analysis. Two Fresnel holograms, which represent the undeformed and the deformed state of the object, are generated on a CCD-target, stored electronically and the wave fields are reconstructed numerically. It is shown that the interference phase can be calculated directly from the digital holgrams, without generating an interference pattern.

Even though interferometric profilers offer excellent axial resolution, their application is limited by ambiguities which arise if the measurement range involves a change in the optical path difference greater than a wavelength. This limitation has been overcome by using white light and scanning the object in height to locate the fringe-visibility peak. In this case, the measurement range can be increased to many wavelengths while maintaining high axial resolution. While various digital filtering techniques have been used to recover the fringe visibility curve from the sampled intensity data, they tend to be numerically intensive. The use of phase-shifting techniques to simplify the processing is complicated by the fact that the phase change introduced by changing the optical path is wavelength dependent, leading to systematic errors in the values of the fringe visibility. We show how an achromatic phase-shifter which operates on the geometric phase and generates the required phase shifts without any change in the optical path difference, can be used to evaluate the fringe visibility directly and locate the position of the fringe-visibility peak along the scanning axis.

Two real-time phase mapping methods for finge patterns are presented, which are based on a spatial phase-shifting with three fringe patterns, and on a spatial synchronous detection for a tilted fringe pattern. A digital TV-image processor is implemented which bases on the two fringe processing techniques. Applications of the present methods to surface shape measurements using a polarization interferometer and a fringe projection technique, and to a surface deformation measurement using a holographic interferometer are described. Worst phase errors are analyzed theoretically which are caused by an additive intensity noise of input fringe signals and a multiplicative intensity noise due to misalignments of a measuring system. A phase error due to a digitization of calculations is also evaluated numerically.

A new instrument, the liquid point diffraction interferometer (LCPDI), has been developed for the measurement of phase objects. This instrument maintains the compact, robust design of Linnik's point diffraction interferometer and adds to it phase stepping capability for quantitative interferogram analysis. The result is a compact, simple to align, environmentally insensitive interferometer capable of accurately measuring optical wavefronts with high data density and with automated data reduction. The design of the LCPDI is briefly discussed. An algorithm is presented for eliminating phase measurement error caused by object beam intensity variation from frame-to-frame. The LCPDI is demonstrated by measuring the temperature distribution across a heated chamber filled with silicone oil. The measured results are compared to independently measured results and show excellent agreement with them. It is expected that this instrument will have application in the fluid sciences as a diagnostic tool, particularly is space based applications where autonomy, robustness, and compactness are desirable qualities. It should also be useful for the testing of optical elements, provided a master is available for comparison.

New methods of multimode fiber interferometers signal processing are suggested. For scheme of single fiber multimode interferometers with two excited modes, the method based on using of special fiber unit is developed. This unit provides the modes interaction and further sum optical field filtering. As a result the amplitude of output signal is modulated by external influence on interferometer. The stabilization of interferometer sensitivity is achieved by using additional special modulation of output signal. For scheme of single fiber multimode interferometers with excitation of wide mode spectrum, the signal of intermode interference is registered by photodiode matrix and then special electronic unit performs correlation processing. For elimination of temperature destabilization, the registered signal is adopted to multimode interferometers optical signal temperature changes. The achieved parameters for double mode scheme: temporary stability--0.6% per hour, sensitivity to interferometer length deviations--3,2 nm; for multimode scheme: temperature stability--(0.5%)/(K), temporary nonstability--0.2% per hour, sensitivity to interferometer length deviations--20 nm, dynamic range--35 dB.

The n-point technique (also called the spatial carrier phase-shifting technique) is one of a few fringe pattern analysis techniques. We present modified algorithms for the n-point technique from which the phase modulo 2(pi) can be calculated in a much shorter time versus conventional algorithms. The algorithms are based on spatial synchronous detection techniques, and by analogy to those techniques, the modified algorithms are named low-pass algorithms, as opposed to the convention 'high-pass' algorithms in the n-point technique.

Two-directional spatial-carrier phase shifting method was proposed for analysis of crossed and closed fringe patterns. This paper focuses on the major limitations for phase calculation by the standard 5-point algorithm used sequentially for x and y sampling directions. These limitations include the influence of improper carrier frequencies, nonequally spaced fringes, nonlinearities in the detection system, variations in the contrast and background intensity functions and interaction between the component fringe patterns. Computer simulation reveals the character and magnitude of these major errors.

A comparative study is made of the phase unwrapping algorithms that adopt either phase gradients or fringe amplitudes as a reliability measure in the selection of an unwrapping path. To compare with the minimum phase-gradient spanning tree algorithm, a maximum cross- amplitude spanning tree algorithm is proposed, which searches a spanning tree that maximizes overall edge weights given by the cross-amplitudes, i.e., the products of the fringe amplitudes of neighboring pixels. Noise-immunity of the cross-amplitude spanning tree algorithm is demonstrated by experiment and computer simulation.

The Gabor analytic signal is constructed by means of the Hilbert transform. This linear operator gives the single-valued determination of the envelope and phase of a 1D signal with the support from infinity to infinity. But the wave field has four arguments and the interferogram is a 2D function. Moreover, these functions can be measured only in a restricted domain. These problems are discussed in this paper. In addition, the errors estimation of phase recovering are considered. The results of numerical experiments on the interferogram inversion are given.

Heterodyne interferometry uses beats produced by superposing two light waves with different frequencies at a photodetector. The output from the photodetector then contains a component at the beat frequency which can be processed to obtain information on changes in the optical path difference. We present experimental results which show that beats can be observed down to power levels at which the mean time interval between the arrival of photons at the photodetector is much greater than the transit time from the laser source to the detector and also when the mean time interval between photons is greater than the period of the beat. These results show that the beats are not due to the interference of one photon with another, but arise from a succession of single-photon events. It follows that measurements can be made even at extremely low photon fluxes by using homodyne detection and extending the integration time.

A two-wavelength laser-diode interferometer has been constructed that is based on heterodyne detection with one phase meter. Two laser diodes are frequency-modulated by mutually inverted sawtooth currents on an unbalanced interferometer. The tested phase at a synthetic wavelength can be measured from the sum of interference signals with equal beat frequencies in opposite sign. The experimental results are shown to measure the displacements longer than an optical wavelength with the resolution of a 4.7-micrometers synthetic wavelength. The periodic phase error is theoretically investigated and is experimentally verified.

This paper describes the noncontact ultra-high accurate optical heterodyne profilometry for nanometer region. The tester is based on the heterodyne interferometry with common optical route. The surface of workpiece is illuminated by two laser beams with slightly different frequencies. One of the beams is focused as measuring optical probe to scan the surface of workpiece and the other is used as reference optical beam. The above two reflected beams are allowed to interfere. The optical phase difference of the measuring and the reference signals is in proportion to the variation of surface height. The lateral resolution is less than 2 micrometers and the vertical resolution is less than 1 nm. No extensive alignment of the sample is needed and the sample is used as reference surface also. Through the opto-electronic converter, the signal is handled by microcomputer and the microcomputer can fast accomplish measuring, calculating, displaying, and printing parameters, graphs, etc.

An optical, fiber-based, speckle shearing interferometer is described. The instrument uses a highly birefringent optical fiber to illuminate a test object with equal intensities of light guided by the orthogonal polarization eigenstates of the fiber. A Wollaston prism is used to obtain two sheared images with adjustable shear. Optical phase changes between the sheared images are readily achieved, without mechanical movement of components, by straining the optical fiber. Object strain determination, by fringe analysis with phase stepping techniques, is readily achieved. Vibration analysis by heterodyning is also reported.

A phase-shifting interferometer with a laser diode has been studied that is insensitive to the changes in laser power associated with the current variation. The tested phase is measured from six interferograms by using a newly-developed phase-extraction algorithm. The phase is calculated from a least-squares fit to an interferogram including the intensity variation by the power change. The systematic phase error with the periodicity of 2(pi) rad by the power change of the laser diode has been theoretically investigated as compared with the experimental results for the conventional phase-extraction algorithm. A good agreement between them is shown.

A passive phase stepped signal processing technique for short gauge length interferometric sensors is reported. The technique utilizes three adjacent longitudinal modes from a multimode laser diode to provide three interferometric outputs separated by a phase shift of (pi) /2. The individual outputs are wavelength division demultiplexed using a monochromator and line scan CCD and processed in real time using a PC. The technique is demonstrated for temperature measurement with a 180 micrometers low finesse fiber Fabry-Perot cavity. A 60 degrees C dynamic range and better than 0.5 degrees C resolution was obtained.

The interferometric range finding device with a grating external-cavity semiconductor laser is presented. By modulating the frequency of the laser with a triangular injection current, an optical beat is formed from a Michelson intererometer with unbalanced arms. The frequency of the beat is proportional to the difference between the two interferometer arms. The range finding is complemented by measuring the beat frequency. The spectral linewidth of the laser is greatly narrowed, i.e., the coherence length of the laser is greatly extended, by external optical feedback from the grating. So the measurable range is obviously extended and the effects of the laser phase noise on the ranging accuracy may be reduced distinctly. The experimental results show that the measurable range of the device is as long as 15 meters. The configuration of the device is described. Some experimental results and analysis are presented. The advantages of the ranging device are portable and quick-measuring.

The operation and behavior of arrays of active transducers comprising complex compliant structures depends on their true structural dynamics. Such structures are characteristic of control elements for adaptive optical systems, sonar system assemblies, and other continuously deformable complex compliant structures. The mechanical and physical interfaces between transducers and their supporting and radiating structures relate directly to their dynamics. Sophisticated bonding and processing of compliant and rigid materials in such complex assemblies determine their operational parameters. Understanding the effects of structural anomalies and defects is of critical importance to insuring correct array operation and a nondestructive method for the visualization of anomalous structural characteristics would be of great value in both development and testing of such systems. Also, mechanisms for acoustic energy transfer through these structures into adjoining media can be inferred from such visualizations. Holographic interferometry presents itself as a viable and useful method for the realization of this type of information.

Many interferometric measurements require the introduction of a controllable phase shift in one of the beams. This is commonly done by changing the optical path length by means of a tilting glass plate or a mirror mounted on a piezo-electric translator, but the change in the phase of the beam is then strongly dependent on the wavelength. An alternative way to shift the phase of a beam is by means of the Pancharatnam phase. This is the phase shift experienced by a light beam as a result of a cyclic change in its state of polarization. We show how the Pancharatnam phase can be exploited to produce a series of achromatic phase-shifters. One such device uses mica half-wave and quarter-wave retarders and produces a phase shift proportional to the rotation of one element which is independent of the wavelength from 450 nm to 700 nm. Another uses two quarter-wave retarders and two ferroelectric liquid-crystal devices which can be switched to produce phase shifts of 0 degrees, 90 degrees, and 180 degrees which are nearly independent of the wavelength over a wide range of wavelengths.

A technique for the slope measurement of objects by using an electronic shearography system is presented. To detect the gradients of an object shape, a laser diode is modulated to produce two wavelengths on successive image frames. These two frames are then subtracted to generate the correlation fringes which depict the slope variation. The theory of this technique is derived and objects of conical, cylindrical, and spherical shapes are measured. Experimental results are demonstrated.

To measure a number of components of displacement with electronic speckle pattern interferometry (ESPI), multiple interferograms are usually captured in succession for different sensitivity vectors. Simultaneous measurement of a number of orthogonal components of displacement using ESPI can be carried out by application of the Fourier transform method. An object is illuminated by several object beams, and the scattered light is combined with one reference beam to form a first speckle image. After providing different tilts to the object beams, a second speckle image is recorded. A third speckle image is then recorded with the object loaded. The difference of the first and second images contains a set of straight carrier fringes. The difference of the first and third images contains a corresponding separate set of modulated carrier fringes due to the loading. The Fourier transforms of these two difference images show multiple peaks which correspond to the carrier fringes of the different object beams. By appropriately masking the corresponding peaks in the two Fourier transforms, the different sets of carrier fringes for the loaded and unloaded object configurations, can be separated. The phase corresponding to the different orthogonal components of displacement can then be retrieved from the ratios of the real to imaginary parts of the two inverse Fourier transforms of each filtered peak. An example of the measurement is presented.

The process of the focused Gaussian beams diffraction from the surfaces with both small and large-scale relief inhomogeneities is considered. The analytical expressions describing the probability function of dynamic speckles intensity fluctuations have been derived. The numerical modeling of focused coherent beam scattering with a small number of scatterers has been conducted. As shown, this case corresponds to non-Gaussian scattered radiation statistics. The range of parameters, when the scattered field statistics are close to Gaussian ones, has been determined. The analysis of probability density function of amplitude fluctuations shows that speckle fields formed when the number of scatterers is small are statistically inhomogeneous ones. It was established how the statistical characteristics of a diffracted radiation depend on the correlation length and the standard deviation of random screen phase fluctuations.

The optical schemes of speckle interferometers for measurements of vibrations and microdisplacements that provide matching of interfering speckle fields are considered. Matching of wave fronts provides the maximal, on the average, magnitude of the output signal of the interferometer working in the mode of many speckles recording. It is shown that these interferometers with reference Gaussian beam operate in the mode of a confocal scheme and in the one-speckle mode of recording. In this case the photoreceiver aperture is determined by the reference beam aperture that is comparable with speckle sizes in the output field. The confocal scheme can be realized also using the reference speckle modulated beam and the multispeckle mode of recording. The schemes of differential speckle interferometers for investigations of longitudinal and transverse displacement are considered. The distinctions in statistical characteristics of the output signal of speckle interferometers with smooth and speckle-modulated reference waves are discussed.

The phase of the complex degree of temporal coherence of visible light is shown to be deducible from a three-beam interference experiment without any wavelength-scale accuracy on measuring a pathlength difference. Methods are discussed where the phase is obtained from the amplitude of rapid oscillations of the corresponding interferogram.

The factors that affect the accuracy of photo-carrier technique are mainly speckle noise, additive random noise, gradient change of phase function and boundary. They have been simulated by a microcomputer and their effects on phase demodulation when FFT method is used have been studied in this paper. Besides, the bandwidth and undistorted demodulation characteristics in photo-carrier measurement have been investigated with FFT analysis method.

This paper proposes a heterodyne interferometer using a dual longitudinal mode HeNe 633 nm laser for absolute distance interferometry. It can measure the fractional fringe of the synthetic wavelength by an electrical phasemeter with high acccuracy. The measuring period is very short. The common optical path configuration in the interferometer eliminates the affection of air turbulence effectively.

The point diffraction interferometer (PDI) is modeled using the GLAD diffraction code. Behavior of the interference fringe pattern is examined as a function of F-number, aberration type, and lateral and axial translation of the PDI.

A contrast modulating technique for interferometric fringe analysis is introduced. The basic idea of the interferometry is employing an amplitude-stepped reference wavefront in an interferometer to generate contrast-modulated interferograms and evaluating the phase of a test wavefront based on intensities of the interferograms. A general phase evaluation algorithm for the interferometry is derived. As an example of the phase measuring technique, we describe a three-step algorithm and an interferometer used to realize a three-step measurement.

A method for measuring deformation using diffraction of light from a grating attached to the surface of flat specimen is presented. By detecting the amplitude and the phase of the diffraction pattern of this grating, its transmission or reflection function can be calculated by the Kirchhoff-Integral. The comparison of these functions in different state of load, leads to the whole-field information of the inplane strain and the out-of-plane dispacement distribution for the illuminated area of the specimen.

Semi-solid metalworking (SSM) incorporates elements of both casting and forging for the manufacture of near-net shape discrete parts. The SSM process capitalizes on thixotropy, a physical state wherein a partially molten material behaves like a fluid when a shear stress is applied. Effective process control depends on the accurate measurement of the ratio between solid and liquid in the feedstock. Due to the high temperature of the material, only noncontact measurements are practical. Surface temperature measurements are not reliable and do not give accurate readings of the bulk material temperature. Since the speed of sound changes during the transition from the solid to the liquid state, ultrasonics offers the potential to determine when a material becomes semi-solid. This paper summarizes attempts to use this change as the means of measuring the solid fraction of semi-solid feedstock. A real time solid fraction sensor system using noncontact laser ultrasonics was developed to measure the SSM material's solid fraction during heating. The system includes a high power Nd:Yag laser for ultrasound generation and a Fabry-Perot interferometer for receiving. The interferometer was optimized for maximum light efficiency and for immunity to the electro-magnetic noise generated by the induction furnaces used in heating the SSM billets. Tests have demonstrated excellent signal to noise ratio at room temperature and at temperatures up to 579 degrees C. A summary of the test results is presented.

Lateral shear interferometers (LSI) are nowadays widely used for the analysis of optical wavefronts. These LSI are robust to vibration of the experimental set-up and of easy implementation. Application of these interferometers is large and well documented in the literature. The analysis of the interferograms produced by LSIs have been made using derivative approximations. These approximations are valid whenever the wavefront being analyzed is smooth and/or a small amount of shearing is used. In this work we present a frequency domain analysis for LSIs and we point out some of the errors that may arise using the standard analyzing techniques.

A real-time dual grating shearing interferometer with an online spatial filtering arrangement has been applied for interfacial fracture mechanics investigation. This optical technique, called coherent gradient sensing (CGS) measures out-of-plane slopes when used in the reflective mode with opaque objects and in-plane gradients of ((sigma) _x + (sigma) _y) when used in the transmission mode with phase objects. The attributes such as real-time measurements, simplicity of the optical set-up, and the relative insensitivity for rigid motions/vibrations are useful in mapping deformation fields to study the failure of dissimilar material interfaces subjected to quasi-static as well as dynamic loading. Here, large elastic mismatch bimaterial systems such as polymer-metal interfaces between model materials (PMMA and Aluminum) are considered. The crack tip fields are mapped using CGS and fracture parameters are subsequently quantified by analyzing the interference patterns. A linear relationship between the remote load mixity and the crack tip mixity is observed. Crack tip parameters are examined under quasi-static conditions for a wide range of remote field loading ratios of shear and tension. Also, low velocity impact loading experiments are conducted to study transient crack tip fields using CGS and high speed photography, and dynamic fracture parameters are extracted from the fringes.

Self-reference single plate shearing interferometric technique used for collimation testing of light beams are briefly reviewed. Two improved configurations of this self-reference interferometry with an inclined screen and matched half-field interferograms are described in detail. Sensitivity of these configurations is analyzed and compared with that of the existing ones.

Phase measurements using digital speckle pattern interferometry are subject to random errors due to speckle decorrelation and electronic noise. A phasor description of speckle decorrelation is introduced from which the r.m.s. phase error is calculated. Phase noise due to additive Gaussian errors on the phase-stepped images is shown to be statistically equivalent to that from decorrelation, allowing the r.m.s. phase error from electronic noise to be obtained analytically. The currently used noise reduction strategy of speckle averaging is shown to be optimal in that it provides the maximum likelihood estimate of speckle phase change. Finally, the effect of speckle integration implicit in digitization by pixels of finite size is considered using computer-generated speckle patterns. It is shown that the phase errors decrease monotonically with decreasing speckle diameter.

This paper presents several practical techniques for processing and analyzing speckled fringe patterns. Speckle averaging by known phase shifts or random phase changes is used to acquire quality fringe patterns. Speckle location rearranging is employed to tolerate rigid body motion and speckle rearranging in phase gives enhanced speckle fringe patterns. A simple recursive filter is designed to further suppress speckle noise and an iteration algorithm applied to reconstruct quality fringe patterns. A digital Fourier transformation is utilized to process and analyze carrier like fringe patterns. A computer generated carrier combined with a reconstruction technique is developed to eliminate speckle noise. Combined use of the techniques optimize the results. The techniques and applications are described.

This paper extends an optical strain gage/rosette technique to measure derivatives of out-of- plane displacements. The principle of the technique is interference of light reflected and diffracted from two or three closely spaced indentations on a specimen surface. The technique measures derivatives of in-plane and out-of-plane displacements simultaneously through analyzing the phase shift of the interference fringes. Movement of the interference fringes is monitored by a photodiode system and collected via a microcomputer in real time to obtain the specimen deformations. There are a variety of the indentation configurations. The configuration of two pyramidally shaped indentations enables measurements of one derivative of in-plane and one derivative of out-of-plane displacements. Three indentations with six or eight reflective faces allow determination of three derivatives of in-plane and three derivatives of out-of-plane displacements. The derivatives are with respect to the directions of the indentation separations. The theory of the technique is presented. Associated instrumentation for data acquisition and analysis is also described. Experiments are conducted on a cantilever beam to verify the capability of the technique to measure small deflection angles. The comparative results between measurements and theoretical predictions show that the method is feasible to measure derivatives of out-of-plane displacements.

This paper briefly reviews present situation on optical fiber-speckle method used for measuring displacements or deformations of an object, and the optical fiber-digital white light speckle patterns correlation method for whole field displacement measurement on a remote surface of a trial object is revealed. The principle of correlation method is demonstrated. A special program for image correlation analysis by computer C language, according to the fundamental principle of digital speckle patterns correlation searching and reading/writing mode of MS4213 image board has been written. The set-up was that a coherent multimode fiber bundle (MBE) was used to transmit white light speckles on a test surface onto a target of CCD camera, then, using microcomputer, monitor system, the displacements on the surface have been obtained. Two experiments which were used to measure displacements of a rigid rotational disk around its axis and deflections of a beam in three-point bending had been made. The experimental results agree well with theory. We came to a conclusion that under the circumstances of a large displacement/deformation, the method contributed in this study has an obvious advantage in measuring a whole field displacement/deformation of a remote object or an interior of nontransparent structure.

In this paper, a new technique to reduce speckle noise from interference patterns is proposed. This method, called cross absolute filter (CAF) is well suited to the case of noisy interferograms with phase error pixels. It is demonstrated that CAF performs better than classical median-type filters, preserving more subtle details.