Starting from a description of the absolute phase problem in fringe processing and a discussion of existing solutions a general approach for robust absolute phase measurement in optical metrology is presented. Using this method the continous phase field can be reconstructed with high accuracy by a stepwise or so called hierarchical approach without any interaction necessary in conventional phase unwrapping if technical objects have to be investigated. The determination of the sequence of synthetic wavelengths is strongly oriented on the phase measuring accuracy and the known limits of the absolute phase. Keywords: optical metrology, shape measurement, displacement measurement, fringe processing, absolute phase measurement

Optical methods equipped with phase measuring methods of fringe pattern analysis have become recently an important tool in non-destructive testing, remote shape measurement and strain analysis. However they are usually vulnerable to improper settings of operational parameters, algorithm selection, data evaluafion sequence and often require highly qualified operator. These disadvantages may be reduced by implementing smart fringe image processing system, SFIPS, which is equipped in image quality evaluation modules and feed-back and feed-forward decision loops. The paper presents the architecture of SFIPS and the principles of formation and usage of image feature vectors at sequential stages of processing. Example of implementing the SFIPS for analysis of crossed fringe pattern obtained in grating interferometry system is given. Key words: smart fringe pattern processing system, automatic fringe pattern analysis, image feature vector, phase measuring methods, image quality evaluation.

Optical metrology instrumentation produce coded data (fringe patterns for example) that represent a transformation of the interesting variable being measured. Although the coding process is well known and unique, the inverse coding process may have an infinite number of solutions. The inverse coding process is the one that allow us to estimate the quantity being measured from the coded image produce by the optical measuring instrument. Fortunately, one usually have a priori information about the behavior or properties of the searched solution. Regularizing [l} an inverse source problem is a process of integrating prior information about the physical variable under analysis in order to obtain a unique and plausible solution. In this paper we show two cases that uses as prior information linear operators over the physical variable being measured in order to regularize the problem. This regularizing approach is applied to shearing interferometry and to the Hartman test. Keywords: shearograms, hartmangrams, fringes, interferometry, regularization, phase detection, quadratic functionals, estimation.

A new generalized algorithm for phase extraction from interferograms recorded sequentially at different phase shifts is proposed. It is developed from the principle of least-square fining with a weight function. This algorithm removes many of the restrictions imposed by conventional phase-measuring algorithms, such as requiring a constant phase shift between consecutive interferograms. This algorithm can estimate phase from a series of sample interferograms with arbitrary phase shift, as long as the phase shifts between these interferograms are known. By introducing the proper weight function, the proposed algorithm is able to estimate the phase with a high degree of tolerance to common error sources including phase-shift mis-estimation and detector nonlinearity. Consequently, this technique may offer improved phase estimation relative to unweighted generalized algorithms using the same number of intensity frames. Theoretical analysis and results supported by numerical simulation and experiments are presented. Keywords: phase shifting interferometry, optical metrology, phase-measuring algorithms.

To enhance the performance of the Fourier-transform profilometry, a phase unwrapping technique is proposed which is based on the number theory combined with spatial frequency multiplexing. The technique enables the automatic three-dimensional shape measurement of the objects that have discontinuous height steps and/or spatially isolated surfaces, which has not been possible by conventional fringe projection techniques. Another feature of the technique is that it requires only a single fringe pattern, which makes possible the measurement of objects in very fast motion. Experimental results are presented that demonstrate the validity of the principle. Keywords: phase unwrapping, profilometry, fringe analysis, optical metrology, heterodyne interferometry, Fourier transform

It is proposed a quadratic cost functional for calculating a consistent gradient field from an inconsistent one. This inconsistent gradient in obtained by wrapping the first difference ofthe wrapped phase. The derivation ofthe respective Euler equations of the proposed functional is presented. A discrete Fourier transfonn based technique for solving the Euler equations is shown. The calculated unwrapped phase may then be calculated by integrating the consistent gradient with any integration algorithm. This fast (transform) method has the following advantages over existing Fourier technique: their transfer functions are close to one and, the boundary errors are estimated and minimized. So that the global estimation error is reduced. Keywords: Phase miwrapping, Finite differences, Regularization.

The unwrapping of experimental phase maps is not a straightforward process and much research has been devoted recently to the development of robust algorithms that can remove 2ir phase discontinuities in the presence of noise, phase inconsistencies, missing data and holes or shadows. In this paper, the performance of two recently developed phase unwrapping methods are compared. The first uses a least squares minimization formulation whose solution is provided by a fast discrete cosine transform. Areas ofbad data are removed from the differential equation by means of a weighting matrix and the unwrapped phase distribution is evaluated using an iterative approach. The second is a path-independent method based in the Thikonov regularization theory. This theory finds solutions that correspond to minimizers of positive definite quadratic cost functionals. The solution to the unwrapping problem by this method is a generalization of classical least-squares . The introduction of a regularization term permits the reduction of noise and the interpolation over regions with invalid data in a stable and controlled way. The performance ofboth methods are compared in their application to computer generated and experimental phase maps. Their main advantages and limitations are discussed. Keywords: Optical metrology, fringe analysis, cosine transform, regularization methods.

Two-directional method was proposed for analysis of crossed or closed fringe paUerns. This paper focuses on the analysis of closed fringe pauern and the major limitations for the N-point algorithms (standard five-point, modified five- and threepoint algorithms).The limitations include the influence of the tilt of fringes, variations in the background intensity and contrast functions, the nonlinearities in a detection system, random noise. Computer simulation reveal the character and the magnitude of the major errors for all algorithms tested. The comparison of the results obtained is given and the advantages ofusing the modified five- and three-point algorithm are described.

A least squares procedure to fit irradiance measurements ofa digitalized interferogram data to a sinusoidal function has been described in the literature by Greivenkamp. On the other hand, a general theory of phase stepping algorithms based on Fourier theory has been described by Freischlad and Kouliopoulos. In this paper it is shown that Greivenkamp results for a least squares procedure may be easily obtained from this Fourier theory.

One of the main error sources for phase shifting interferometry is the linear phase shift error. This paper presents a self-calibrating phase-measuring algorithm that is free from errors produced by this error source. In the other words, the proposed algorithm is able to obtain an accurate phase at every pixel point in the interferograms over a wide range of equally spaced phase shifts. The algorithm requires the acquisition of five phase shifted interferograms. It resembles the well-known Carre' s algorithm, but with one extra frame. This algorithm, however, has considerable advantages over Cane' s algorithm.

Polarization interferometers are widely used in microscopy. In these interferometers, the two beams traverse almost identical paths, so that conventional phase-shifting techniques cannot be used. However, because the two beams leaving a polarization interferometer are orthogonally polarized, it is possible to use a phase shifter operating on the geometric phase to introduce a variable phase shift between the two beams without any change in the optical path difference. Since this phase shift is very nearly independent of the wavelength, small variations of the optical path difference over the field can be mapped accurately, even with white light. Achromatic phaseshifting can also be used with two-wavelength illumination to provide a quick and simple method for profiling surfaces exhibiting steps with heights of a few micrometres.

Holographic microscopy with conjugate reconstruction for the interferometrie determination of three-dimensional displacement is described. Three double-exposed holograms for different illumination directions recorded on one holographic plate are reconstructed conugately , and spatial heterodyne technique was used to evaluate the interferograms. Only by conjugated reconstruction it is possible to obtain a perfectly optimized interferometer for the static evaluation method. The evaluation of strongly disturbed interferograms by speckle noise can be performed successfully. A comparison of the spatial heterodyne with the phase shift technique is given.

An optical microscope, utilizing the principles oftime-average hologram interferometry, is described for MicroElectroMechanical Systems (MEMS) applications. MEMS are devices fabricated via techniques such as micro photolithography to create miniature actuators and sensors. Many ofthese sensors fmd their way into applications which rely on, or depend upon, the dynamic behavior ofthe sensor. Typical dimensions of current MEMS devices are measured in microns, and the current trend is to further decrease the size of MEMS devices to submicron dimensions. However, the smaller MEMS become, the more challenging it is to measure with accuracy the dynamic characteristics of these devices. In this paper, the theory and construction of an electro-optic holographic microscope (EOHM) for the purpose ofstudying the dynamic behavior ofMEMS devices are described. Additionally, by performing measurements within an EOHM image, object displacements are determined as illustrated by representative examples. With the EOHM, MEMS devices with surface sizes ranging from approximately 35 x400 microns down to 5 x 18 microns have been studied while undergoing resonant vibrations at frequencies as high as 2 MHz.

Conventional phase shifting methods do not have enough phase resolution less than 1 deg. Although images sampling times for the phase shifting analysis have to be increased for the easy solution of this problem, there are some limits to get more images than five because of limited capacity of memory and detecting time of the image. In order to detect phase distribution of interferogram with high resolution, a local-sampling phase shifting technique is proposed. It is useful to increase the resolution of detected light intensity in the same quantized error. This method is verified by birefringence measurement in 256 x 256 values in short time with 0.02 deg of phase accuracy. This method is applied to measure surface profile measurement.

An optical implementation of real-time preprocessing of interference fringes is demonstrated using Epson light crystal television (LCTV) working as a spatial matched filter in an optical correlation setup. Two methods of optical smoothing for speckle noise removal using both the hybrid modulations of the LCTV were studied. One of these methods is based on the diffraction properties of a sinusoidal phase grating addressed on the modulator. The second one is a global filter operating like a transparency to eliminate speckle spectral components in the input image spectrum. Preliminary results are illustrated by representative examples.

Light-in-flight was introduced as method to record holograms with light of short coherence length: Only the short distance delivers a hologram where the object and the reference wave coincide to have the same optical path. Nils Abramson used pulses of picoseconds with coherent lengths of millimeter to demonstrate how light travels through a lens. The width of the holographic plate was his delay line for the reference wave. However, Fresnel holograms can be recorded directly on a CCD sensor, electronically stored and numerically reconstructed. The method is called Digital Holography. It has been applied to make comparable experiments to those mentioned before. The area of the CCD target was divided into several areas which were hid from the reference wave with changed optical path. The delays for the reference wave performed by glas plates with varying thickness. The different views of a wavefront can be reconstructed from the corresponding parts of one single holographic recording . This means that the temporal evolution of a wavefront can be observed by numerical methods. Experimental results are shown.

The design and performance of an actively phase-compensated fiber-optic speckle pattern interferometer (ESPI) is presented. Due to its portability, illuminating beam flexibility and lightweight design it provides an alternative to standard bulk-optics FSPI systems for many applications. Phase stabilization allows for long-term measurements up to several days. In addition, the provided phase stepping uses the four-step algorithm, is self calibrating, and can be performed at quasi video rate. The use of all highly birefringent fiber-optics components ensures linearly polarized light for the illuminating beams under all operating conditions.

Shape and vibration measurements of structures are required in many automotive product development and manufacturing processes. Optical measurement methods are attractive because they do not require contact with the structure and offer high precision and accuracy. Nevertheless optical techniques also suffer from a number of limitations which prohibit wide application. Typically the object is viewed and illuminated from two different points making objects situated in confined areas difficult to measure. In addition, most optical techniques are not easily scaleable in measurement range. Finally, most shape measurement techniques cannot measure vibration without a change in configuration. This paper presents a single electronic speckle interferometry (ESPI) method to measure both surface shape and vibration. A two-wavelength approach is used to measure shape and a stepped strobed phase technique is employed to measure vibration amplitude and phase. The technique requires only one line of sight to the object and can be scaled to measure surface roughness as well as large surface contours. The technique features the ability to coincidentally measure shape and dynamic behavior for structural design, modification, and optimization. The theory of the technique along with results of an experiment are presented.

An interferomeiric system for the determination of surface shape or height profiles of engineering components is presented. The system is based on additive-subtractive phase modulated electronic speckle pattern interferometry (AS-ESPI) and works successfully in harsh environmental conditions. Determination of profiles is achieved via repetitively changing the optical pathlength difference (OPD) between two interference beams in the ESPI setup. As the repetition rate is much higher than that of the video frame refreshing, one can remove random environmental noises that are normally of much lower frequency than the repetition rate by the use of speckle decorrelation and frame averaging procedures. Due to the nature that carrier fringes are automatically generated by the OPD change (namely tilting the iflumination angle of the object beam), Fourier transform approach is employed to extract the phase data. A simplified method for calculating the surface height (profile) is described and the results are compared to an exact solution. Quantitative measurement results obtained under rather noisy conditions for several components are presented.

Digital shearography is a coherent optical method in conjunction with the digital image processing. It allows the shearogram, which depicts directly displacement derivatives, in real time to be observed. Thus, it is suited well for nondestructive testing. However, its application for strain measurement has not been widely adopted in industry, because the shearogram includes usually both the in-plane strain, e.g. c3u/ox, and the out-of-plane component, e.g. 5w/ox. Although the out-of-plane component can be separated from the shearogram by manipulating the illumination, the pure in-plane strain component can be never determined exactly by adjusting the illumination angle. This paper presents the principle of shearography with two independent illuminating directions (usually the same but mutual illuminations) for the pure in-plane strain measurement. The shearograms for each illuminating direction are generated by applying the phase shifting technique. Thus, the phase maps of the two shearograms corresponding the two illuminating directions can be obtained. The result by subtracting the phase maps of the two shearograms yields a new fringe pattern depicting the pure in-plane strain component. The experimental procedure and its applications for determining pure in-plane strains are presented.

A double shear speckle interferometer is presented that can provide information about the curvature, i.e., the second order derivative of the out of plane displacement of an object under study. Here, two shear interferometers are kept in sequence or tandem. The sheared images formed by the first interferometer are sheared once again by the second interferometer. The shears at the image plane can be adjusted for the required magnitude and orientation. A double exposure record is made on a photographic plate before and after the object deformation. When the processed plate is subjected to Fourier filtering, the curvature information is seen as a Moire of the two sheared slope fringe patterns. The results for a centrally loaded diaphragm are presented. The advantages of the present technique over the existing methods are discussed.

Speckle interferomeiry is now being used extensively in a range of engineering metrology applications. This paper reviews how developments in optoelectronic technology, such as solid state laser sources and optical fibre, have led to advances in the measurement capability of speckle interferometer systems. Examples are presented of surface profile, surface slope, static displacement and displacement gradient, and vibration measurement including heterodyning and stroboscopic techniques.

Nowadays in mechanical material testing strains are measured only between two distinctive points on the specimen with probes or by optical analysis of two marked positions on the surface of the specimen. Information about eventual inhomogeneous strain distribution between these two points can not be obtained by these methods. A new laseroptic strain sensor overcomes these restrictions by using the principle oflaser speckle interferometry for measure-ment. In the one dimensional measuring case the specimen is syinetrically illuminated by two bundles of laser light and the image recorded with a high resolution CCD-camera. Computer evaluation of the images shows deformations and strains on the surface of the specimen with high sensitivity. An extended design uses two of these optical setups to provide two inplane measuring directions. Special interest was layed onto the optical set-up which guarantees uniform measuring sensitivities in the whole measuring field and as well very limited adjustment requirements. The laseroptic strain sensor requires no marking on the specimen and gives full field measuring information without contact on nearly any surface. In this paper the operation principle of the laseroptic strain sensor is described. Typical application examples in material testing are given.

An infra-red interferonieter for testing optical elements and assemblies in their operational wavelength band is described. The interferoineter is a phaseshifting, LUPI-style Twyman-Green interferometer operating at a wavelength of 3.392pm. The system is designed for optical testing in a vacuum chamber. For that purpose the interferometer is contained in a hermetic, vacuum-compatible enclosure, and all internal alignment functions are remotely controlled. The light source is an infrared HeNe-laser at 3392 p m. The camera sensing the interferograms consists of a PtSi CCD-array with 256x256 pixels. For operating the system in a vibration environment, short exposure pulses are generated from the laser light. In addition, a specialized phase.shifting data acquisition and reduction algorithm is employed which senses the random phase shifts and adapts the phase algorithm accordingly. A vacuum compatible diverger (f/2.5) and beam expander (250mm beam diameter) allow for a wide variety of optical testing configurations. Measurement results and system performance parameters are presented.

A laser diode interferometer which uses an optical fiber is proposed. The laser diode simultaneously functions as a light source, a phase modulator, and a phase compensator. The detection of the vibration and the reduction of external disturbance are carried out, by using a feedback control for the injection current of the laser diode. So it can measure the vibration accurately in real time with a simple signal processing circuit. The optical fiber not only functions as a flexible probe, enabling us to measure the vibration of the object that cannot be moved onto the vibration absorption board, it also acts as a reference mirror, thereby simplifying the unit construction.

A novel DHI technique of precise targeting of moving object in space has been made. The major advantage of this technique is automatic self-adjustment of volume adaptive supersmall (0. 12 mm) holographic grating in a new syntezed double doped photorefractive crystal of BTO. This results in the creation of 70 % diffraction efficiency adaptive holographic grating using 0.632 mm laser radiation. The targeting angle deviation of 10 radians in real time testing has been verified using low power CW He-. Ne laser at a distance of0.5 meter.

The spectral behaviour of a laser diode during its modulation was investigated in order to find the correlation between the spectral properties of a light source and the appearance of an interferogram resulting from its radiation. The expected fringe visibility curves for a laser diode working in a stable as well as in "mode hopping" regions are given. The experimentally obtained interference patterns which visualise such effects as wavelength shift and coherence collapse are also presented.

Two optical methods for obtaining the partial derivatives of in-plane and out-of-plane displacement fields in the in-plane ESPSI configuration using temporal phase stepping for automatic analysis of fringe patterns are described. In the first method lateral shear interferograms of object image fields generated by individual symmetrical illuminating beams are recorded independently. The phases are calculated and their subtraction/addition gives required in-plane/out-of-plane displacement derivatives, respectively. Phase stepping is readily performed in the setup based on fiber optics and modulated laser diode illumination. In the second method two primary interferograms: a conventional in-plane displacement ESPI recording and one with object images mutually laterally displaced are recorded. Similarly, software subtraction or addition is performed to separate the out-of-plane displacement derivatives and double sensitivity in-plane displacement information.

We have combined the principles of phase-shifting interferometry (PSI) and laser-feedback interferometry (LFI) to produce a new instrument that can measure both optical path length (OPL) changes and discern sample reflectivity variations. In LFI, coherent feedback of the incident light either reflected directly from a surface or reflected after transmission through a region of interest will modulate the output intensity of the laser. LFI can yield a high signal-to-noise ratio over a broad range of sample reflectance. By combining PSI and LFI, we have produced a robust instrument, based upon a HeNe laser, with high dynamic range that can be used to measure either static (dc) or oscillatory changes along the optical path. As with other forms of interferometry, large changes in OPL require phase unwrapping. Conversely, small phase changes are limited by the fraction of a fringe that can be measured. We introduce the phase shifts with an electro-optic modulator (EOM) and use either the Cane or Hariharan algorithms to determine the phase and visibility. We have determined the accuracy and precision of our technique by measuring both the bending of a cantilevered piezoelectric bimorph and linear ramps to the EOM. Using PSI, sub-nanometer displacements can be measured and, as with other forms of PSI, there is no sign ambiguity to the displacement measurement. We have also analyzed the behavior ofthe interferometer for both low and high reflectivity samples. Since the change in the laser's intensity is a non-linear function of the reflected amplitude, additional measures are required before applying PSI methods to high reflectivity samples.

Direct injection-current modulation of a diode laser source is demonstrated for phase-stepping, heterodyning and stroboscopic illumination in a shearing interferometer. The techniques are proposed as an alternative to the use of mechanical phase-shifters such as piezoelectric transducers, offering the advantages of ease of implementation, extended measurement bandwidth and elimination of active elements from the measurement head. The phase-stepping and heterodyning techniques require the interferometer to be unbalanced, which introduces an unwanted magnification mismatch into the shearing interferometer. A compensation technique using a block of high refractive-index material is described, and experimental demonstrations of each of the three techniques are presented.

A new passive-alignment technique using Becke lines is proposed for assembling optical devices. Optical devices with a waveguide structure, such as planar lightwave circuits and laser diodes, have a core or active layer whose refractive index is slightly higher than that of the surrounding area. The Becke lines are diffractive stripes appearing at the boundary between materials having different refractive indices such as cores and the surroundings. For low-loss optical connection between the devices, their cores must be precisely aligned with each other. In our technique, the optical devices are aligned by observing the Becke lines located on both edges of the core, which make it possible to determine the exact core position. With this technique, optical devices can be precisely aligned without using the thin metal-film markers used for conventional passive alignment. The position of an optical waveguide was experimentally aligned by illuminating it with infrared (IR) light, obseving the Becke lines with video system and moving it with motor-driven stages. The positioning uncertainty was less than 0.2 tm, which is the same as the resolution of the video system used. This technique is thus practical for precisely assembling optical devices.

Holographic interferometry of vibrating specimens using two-wave mixing in photorefractive Bi12SiO20 (BSO) crystals is achieved in reaJ-time. Real-time acquisition (30 frames per second) of holographic interferograms from vibrating objects is performed using repetitive sequences of separate record and readout times synchronized with the ccd acquisition rate. In this two-wave mixing experiment, the reference beam is collinear with the optical imaging system (the object beam) and an external AC electric field is applied onto the BSO crystal. This configuration improves the diffraction efficiency and keeps the time response to a minimum, compared to configurations where the reference and object beam interfere with a large writing-beam angle, 0. The performance of the photorefractive holographic interferometer using onaxis reference beam (0=0°) and off-axis reference beam (0=30°) are compared. Example of real-time acquisition with good fringe contrast is demonstrated.

Conventional interferometers are not always appropriate for measurement of rough or uneven non-optical surfaces. For the solution of this problem, an oblique incidence interferometry was proposed with a spatial phase-shifting technique of only one image. This technique can analyze surface profiles using only one image which contains high carrier frequency, and in this method such mechanical shifting device as requires high repeatability is not necessary. Therefore, more accurate and speedy measurement can be realized by using this principle. As an application of this technique, the Poison's ratio values of brittle materials are analyzed. The surface deformation after pure bending can be easily measured by this technique. Therefore Poison's ratio is calculated by relationship between Poison's ratio and the contour pauern of displacement from only two fringe images acquired before and after the bending.

A simple method which can be used to map the small-scale irregularities of the reference surface in an interferometer is described. This reference data set can be stored and subtracted from interferograms recorded subsequently with any test surface to evaluate the small-scale irregularities of the test surface.

A general recording model of off-axis holography is first proposed, which includes three illumination modes: divergent, convergent and collimated beam illuminations. The interference pattern is then derived based on the general recording model. The general solutions on the recordable depth of view (RDV) and allowable farthest far-field distance (AFFD) are given analytically, which show that the RDV and AFFD may be improved by using non-collimated beam illumination and placing particle fields into a special spatial zone.

Multiaperture overlap-scanning technique (MAOST) has been successfully used to measure larger optical flat with a smaller reference flat. This paper extends the technique to measure an optical cylinder. Utilizing the information in overlap area between subapertures, MAOST connects them to one aperture called full aperture. With the technique, half a cylinder or even a whole cylinder can be accurately measured. In the paper, the fundamental is discussed, mathematical model is given and connection results of 2 interferograrns and 17 interferograms are shown. Results indicate that the error in principle of the method is about the order of 108 A

We have successfully designed and prepared gain-guided high power 1 .3- 1 .55i m leaky waveguide (LWG) laser diodes. taking into account their loss mechanisms such as Auger electron non-radiative recombination, carrier leakage over the heterobarrier, and inter-valence-band absorption etc. This is the first time to incorporate the leaky waveguide structure into the quaternary 111-V compounds in order to obtain in long wavelength region high power laser diodes for advanced manufacturing and metrology. In this work we have shown that the incorporation of the leaky waveguide structure into the material system would reduce the threshold current density and alleviate the loss mechanisms. This would result in a reduction in lasing threshold current and an improvement in the temperature sensitivity. It was grown by a unique liquid phase epitaxy (LPE) and was modified by growing an intrinsic InGaASP waveguiding layer which replaced its n-type counterpart as in usual large optical cavity devices and provided a higher temperature stability than that of conventional DH lasers. Using the LWG structure, we have obtained 1 .55 i m laser diodes with threshold currents comparable to common lasers ( th 2.7 KA/cm2) but with the characteristic temperature T0 near to those of GaAs-AlGaAs lasers (140K).Especially, we have attained the peak output powers up to higher than 2W per facet in pulsed operation at room temperature.

This paper will report on the methods of compound regions average (CRA) and the adaptive visual primitive elements matched (AWE). By CRA method, the high frequency noise of the digital speckle pattern interference (DSPI) fringe could be filtered. Further. the directions of the fringes were determined with AVPE method and the fringe skeleton could be obtained accurately by directional derivative. Results are presented for center determination from DSP! fringe patterns.

This paper illustrates a real time desensitized outof-p1ane displacement configuration for the measurement of large deformations of a diffusely reflecting object. The optical configuration is implemented to study the behavior of engineering structures subjected to large static as well as vibration deflections. Phase stepping is provided in the optical set-up to obtain the deformation maps from the interferograms. For vibration analysis, the possibility of incorporating both phase stepping and bias vibration on a single mirror is also demonstrated. Theoretical analysis along with experimental results are presented.

A computer-controlled imaging conoscope has been used for investigation of optical homogeneity in undoped LiNbO3 crystals pulled by the Czochralski method, and also for testing of optical elements, like e.g. electrooptic modulators. The two maps acquired for two perpendicular directions in the crystal (Zoptical axis, and usually Y-axis) are utilized simultaneously for eliminating optically inhomogeneous areas from their use in optics and electrooptics, as well as in a wider research program including optimization of the growth technique and investigation of influence of crystal perfection on device performance.

The most important problem in stereometry is to establish a correspondence between the points on two images representing different views on the same scene. We have developed an algorithm which avoids some disadvantages of previous approaches to this problem. Our approach was based on matching of correlation of some regions from both images. We use a Gabor representation of the images. We define regions on both images and assign the vectors of coefficients of Gabor functions to all those regions. Those vectors are used for comparing of the regions. We adjust an accuracy of matching using local phase information from the coefficients. We also measure the diameter of correlation peek near the region and we increase the diameter of the region if it is smaller than this diameter. In this way we avoid a problem of large areas of the same texture. We also propose implementation of this algorithm in a real time system. The optical method is suggested for computing coefficients of (iabor functions in that system.

This paper presents an overview of methods of error elimination during image processing and analysis, and more specially ofthe problems ofsetting the threshold errors, shading and noise. Of all the steps involved in measuring objects in an image, setting the threshold is the one which should be considered most careftilly. There are described following errors: threshold setting error, the offset threshold error, "halo" error and elimination methods. The process of setting the detection level should be standardised, whichever technique is adopted, and some form of check on a standard specimen should be incorporated into the image analysis routine if at all practicable. Shading is the best dealt with by using a shading correction step in the image processing, but operator can help by ensuring that illumination system of microscope for example is correctly centred, that specimen is flat, that the lamps on macroviewer all have the same wattage and are at the same distance from the specimen. Shading can be asymmetrical, and it can be present in the specimen itself as well as being introduced in the optical system. Noise is a function of system design, with no room for operator of the system to affect it, except by increasing the gain of the video amplification. Noise is minimised by operating the system at the optimum conditions of incident lighting.

On the basis of the combination of phase measurement and integer periodic phase measurement, a signal processing scheme, which is used for optical heterodyne interferometer with large range, is described. It not only maintains the high measuring resolution , but also enlarges the measuring range, with solving the problem of large range and measurement of dynamic displacement.

In the experimental set-up for measuring temperature fields in fluid flows by using speckle interferometry ( e.g. electronic speckle pattern interferometry or phase shift speckle interferometry ), the part of the; arrangement for the object light beam is just like a subjective speckle photographic system. Therefore, in general, speckle displacements are generated. The speckle displacements can change the intensity distribution of spatial speckle fields. As a result, the intensity distribution of a speckle interferogram is also changed. In this paper the effect of speckle displacements on the speckle interferometry is analyzed and discussed in detail. A physical model and mathematical treatment for the effect are proposed. Experimental results are shown. A method for elimination of the effect is provided. Using the provided method, the temperature measurement error of speckle interferometry can be reduced and the measurement accuracy can also be increased.

An instrument to measure the convergence or divergence power of a wavefront using moire fringes or software synchronous detection is described. This instrument could be used to measure the dioptrical power of ophthalmic lenses. The working principle could also be applied to measure angles with high sensitivity.

A holographic analogy ofthe analysis of thterferograms with a spatial radial carrier introduced by means of defocusing and its practical applications is describei Special emphasis is made ofthe conditions imposed on the Fourier spectra ofthe interferogram.

This interferometer is designed to measure 75x40 cm laser glass. The entire surface is measured at a Brewsters angle, 56.57°, with an s-polarization beam. The reflected beam is retro-reflected by a highly reflective mirror. Thus, a 75x40 cm surface can be tested with a 60-cm aperture. The most troublesome problem is the ghost reflection from the rear surface of a flat while the front surface is being measured. After the second surface is polished, both surfaces are reflective and their beams can interfere. However, the second surface of a flat is to be polished to ensure the transmitted wavefront quality, not the quality of the surface itself. Therefore, the second surface does not need to be measured directly. To avoid reflection from both surfaces, the laser is switched to a p-polarization after the first surface is measured while the flat is still at a Brewster's angle. Thus, the transmitted wavefront is not affected by the reflection. We believe that a 60-cm clear aperture, Fizeau phase-shifting interferometer is the most practical and accurate instrument for testing 75x40 cm optical flats. In this paper, we briefly summarize the important design factors, and show in theory that the design can meet the required performance.

A two color laser speckle shift strain measurement system based on the technique of Yamaguchi was designed. The dual wavelength light output from an Argon Ion laser was coupled into two separate single-mode optical fibers (patchcords). The output of the patchcords is incident on the test specimen (here a structural fiber). Strain on the fiber, in one direction, is produced using an Instron 4502. Shifting interference patterns or speckle patterns will be detected at real-time rats using 2 CCD cameras with image processing performed by a hardware correlator. Strain detected in fibers with diameters from 21 microns to 143 microns is expected to be resolved to 15 pe. This system was designed to be compact and robust and does not require surface preparation of the structural fibers.