The paper is intendent to give a brief review of Michelson's scientific achievements on the background of his life. The contribution of Albert Abraham Michelson to the development of optics and optical measurements as well as the importance of Michelson's work for modern physics are especially pointed out.

A classification of interferometers is based on the number of quantities needed to describe the interferogram. The aim is to provide the simplest theory that can be applied to a particular instrument and to indicate the limitations.

In considering of the two boundary conditions arising in a fringe-counting interferometer(FCI): the non-zero original optical path difference(OPD) between reference and measurement arms; and the zeroed interference order corresponding to the original OPD at the begining of measurement, an amended length measurement formula and its whole-error distribution equation are derived, on which the concept of optical-origin drift(OOD) iS introduced. The effect of OOD on the measurement accuracy and the geometric design of interferometers is discussed in detail. Practical examples are also presented.

Crystal optic insertions allow a modulation of the amplitudes of the interfering light beams in a multiple beam interferometer and can improve the transmission characteristic considerably. We show experimental results from a Fabry-Perot-Interferometer containing birefringent and optical active plates in the resonator which prove the enhancement of contrast, resolution, and of the sensitivity to changes of the entrance polarization even for resonators with very low efficiency.

Analysis of previous experimental works concerning verification of the relativistic Doppler effect is performed. New results have been obtained in the modern Ives experiment with the canal rays. The beam of excited hydrogen atoms is produced by accelerating H⁺₂ ions with voltages from 150 keV up to 2.000 keV. There is a systematic deviation in the results obtained from those according to the special theory of relativity. The classical approach to understand experimental data is offered. Both theories are compared.

The use of crossed Babinet Compensator (B. C.) combination as simple and effective device for wavefront sensing and evaluation has been described. This method can be utilized for on line evaluation of the wavefront or the surface errors in situations like active optic s system. Advantages of the method and procedure for the reduction of the B. C. fringe data for the wavefront evaluation are presented in this paper.

Michelson interferometer with no interfringes counting is described. Two ideas: controllable phase shift and the properties of divisibility of integers are used. Application of Michelson interferometer for precise measurements of displacements is widely known. But this method is confined to speed of movement of the object under study due to confinement of response of light impulse counters since the method is based on counting interference fringes in real time. Besides it is necessary to provide reversibility of counting and recording of the fractional fringe orders, especially then when small displacement are being measured. At the same time new interferogran decoding methods that have been worked out lately make it possible to build up a Michelson interferometer that would be free from the problems mentioned above. The purpose of this paper is to describe Michelson interferometer with no interference fringes counting.Such Michelson interferometer is devisable thanks to tin) underlying ideas: first, application of controllable phase shift, and second, the properties of divisibility of integers.

For the wavelength measurement using a two-beam Fizeau interferometer an accuracy of about 2 parts in 10⁷ is claimed. To reach this limit the influence of error sources has to be minimized. A discussion of error sources impairing the obtainable accuracy will be given in this paper.

A system for phase stabilization of different interferometric set-ups is presented. A point sensitive high resolution het-erodyne interferometer is integrated into a full field Twyman-Gmen interferometer for optical testing. A phase stability of 0.8 nm (nns) is obtained through a piezo feedback controlled by a computer closed loop control. The system is opted for two-wavelength phase-shifting interferometry (TWPSI) where succesive recordings under well defined phase steps is applied. For optical testing with TWPSI one have to record two sets of phase data with two different wavelengths. These are then used to calculate the phase map corresponding to a longer equivalent wavelength.

Misinterpretation of the fringe order and errors in determining its value is one of the greatest, if not greatest, shortcomings in photomechanics. Three methods are herein proposed which either improve upon or automate existing procedures. The methods, in the order presented are: 1) Carrier Fringe Methods, 2) Coherent Compensation, and 3) Color/Load Coding.

An overview is given on the principle and the recent development of the spatial-carrier fringe-pattern analysis techniques, and their application areas are introduced.

A basic requirement in applying interferometrical methods to measurement, testing and inspection is to evaluate the phase differences between the interfering waves very quickly and with high accuracy. Different methods and equipments to phase detection and evaluation in interferometry have been published during the last years. The aim of this paper now is to present theoretical and experimental results to apply so-called carrier frequency techniques for determining phase differences in interferometry.

An hybrid optical-digital processor using the phase-shifting interferometry and Fourier analysis that computes irradiance moments of rough samples is presented. An example is described to illustrate the performance of these moment functions in roughness classification.

A correlated profile with normal distributed ordinates was computer-generated and the interferometrical measuring process of surface microprofilometry was simulated for a simultaneously measuring interference microscope with a CCD-row and and a profilometer measuring point-by-point. The dependence of the short and high spatial frequency bandlimit on the measured profile and the calculated roughness parameters and statistical functions are shown.

A Twyman-Green heterodyne interferometer with a laser diode source was constructed for testing an optical element. The wavelength induced by laser injection current is continuously changed to introduce a time-varying phase difference between the two beams of an interferometer with an unbalanced optical path length. An automated phase-measuring interferometric system was developed in which the laser current is changed to synchronize intensity data acquisition with vertical drive pulses of a charge-coupled device (CCD). The intensity of interference pattern is integrated with a CCD detector for intervals of one-quarter period of one fringe. A microcomputer calculates the phase to be detected. The experimental results are shown to measure the profile of a diamond-turned Al surface; the rms repeatability of λ/105 was obtained.

The Singular Value Decomposition (SVD) of an image matrix, followed by image restoration by part of singular values terms is employed for high frequency noise reduction. The Fisher criterion or an optimal filtering are implemented to the singular value image spectrum in order to remove or correct singular values corresponding to the variation due to additive noise. This procedure is proposed as a preprocessing step of interferogram processing.

The paper presents the recent contributions to the automatic fringe pattern analysis by the phase stepping method applied to moire interferometry. Two approaches are considerd. The first one is suitable for analysis of stable fringes directly in the moire interferometry set-up where a polarizing phase shifter is used. The second one is applied while unstable conditions during the experiment are encountered or a transient event is tested. This approach requres recording of an intermediate fringe pattern with carrier frequency and examining it in an additional double-diffraction or "sandwich"-type analyser. The experimental results of the analysis performed in the arrangements mentioned above are presented.

The system of retrieving the phase from a single interferogram with carrier frequency based on 2-D Fourier transform method is presented. Several procedures to modify an interferogram and its spectrum in order to reduce the phase errors and detect the object domain are described. The effects of refinements introduced are shown on experimental data.

A software system for skeletonization of interference images is presented. This system can process interferograms of a different origin (classical, holographic, laser and speckle interferometry) with arbitrarily shaped fringe pattern. In the result, the system produces skeleton interferograms in the form of continuous and smoothed lines related to the maxima of the light-intensity distribution in interference images. The system can operate on microcomputers IBM PC/AT and compatible ones, and it can be utilized in different special systems for automated interpretation of interferograms. A number of experimental examples of the interferogram processing by means of the system is given.

A computer-aided method for determining the displacement and strain fields from holographic interferograms is described. Three holographic interference images simultaneously recorded for different viewing and/or illumination directions are required. Skeleton interferograms obtained from special processing of the images are the program input data. The program can operate on microcomputers IBM PC/AT and compatible ones. Some experimental investigations of the object-surface deformation are presented. The application range of the method is discussed.

For measuring displacement fields by means of holographic interferometry interferograms are analyzed with the skeleton method. To get information about phase distribution after constructing the skelton of the fringe pattern by computer-aided digital image processing an interpolation between skeleton lines is necessary. For evaluating phase values on a regular grid three interpolation methods are described and discussed in this paper.

The suggested method provides a fast noise and background reduction simultaneously as a preprocessing step of interferograms extrema tracing. The method consists with Hartley transformation, filtration, differentiation, inverse Hartley transformation and binary pattern formation. The discussing advantages are in computing aspect.

A computerized method of obtaining distribution of fringe order in points of regular grid from a skeletonized interferogram is prezented. This procedure is based on special algorithm of interpolation, named here as the quasi-gradient double-parabola method (OGP-method). This method is an improvement of the double-parabola method (DP-method). The procedure can be utilized as a subprogram in automated interpretation of interference images in different methods of optical metrology. The procedure can operate on microcomputers IBM PC/AT and compatible ones.

A simple method to retrieve phase modulation of interference fringes with spatial carrier is discussed. A part of the argorithm can be easily replaced by a hardware system of analogue electronic circuite. It is shown that the method is suitable to analyze dynamic fringes which have rather small phase gradient. As an example, displacement measurement by using a modified Michelon interferometer is shown. Accurate measurement in which random errors were less than 7 nm was realized by a simple hand-fablicated system.

Acceptance of holographic displacement and vibration amplitude measurement technique in research and industry depends not only on the degree of automation, reliability and measurement accuracy, but also on its utility with respect to arbitraryly shaped objects. A 3D holographic measurement system, performing as displacement and vibration amplitude determination, as object shape and position measurement is described. For the purpose of fringe pattern analysis the system makes use of a special video processor in order to evaluate interference phase data in the points of a 32x32 grid. Measurements are carried out in an unitary interferometer of four illumination directions and one observation direction.

The name Holographic Fringe-Contrast Interferometry (HFCI) has been proposed for measuring techniques and interpretation methods, which are based on information contained in the fringe-visibility distribution in holographic interference images.

From the various capabilities of holography for image processing and measuring purposes, holographic interferometry has mainly found more extended application in biological and medical research. As a technique allows a non-destructive testing and high resolving deformation analysis, it has gained popularity in the recent years in experimental biomedicine. The most commonly, used techniques of holographic interferometry, as well as other holographic methods of importance for biomedical research, are reported in this review.

The experimental realization of the double exposure interferometry method in the scheme of holography with nonstationary reference wave is considered in connection to the investigation of space-time picture of the processes. The recording was realized by the usage of reference wave with the linear change of frequency in time and along the coordinate in the registration plane. At the reconstruction stage four space-time representations of the reconstructed signal were obtained. The information about phase space-time evolution was experimentally obtained.

A fundamental study on the effect of microscopic deformation on the corrosion behavior of a molybdenum electrode In 0.75 N Kcl solution has been conducted. The study was successful in developing a novel technique for studying the effects of microscopic deformation on corrosion. The development of the new technique Is established based on incorporation experimental methods of electrochemistry and with those of holographic interferometry. In other words, the new technique is capable of measuring microscopic deformation In term of interference fringes and the anodic dissolution current of the molybdenum electrode, simultaneously. As a result, a relationship between deformation and the anodic dissolution current is established.

A simple holographic system is described which can be used for routine interferometric tests of spherical and cylindrical surfaces as well as lenses and lens systems. The system can be set up and adjusted quite easily and can be used to test large-aperture optical elements without high quality reference optics of the same size.

In this paper we describe the investigation of interaction of YAG:Er laser radiation with liquid water in micron thickness cell by double exposure holographic interferometry with time delayed sensing. Substantial decrease of refractive index (▵n =-0.3) on a wavelength of probing pulse (λ_p=0.53μm) during erbium laser pulse in the beam waist was found. Afterwards the formation of shock wave was visualised, as well as the development of 2-D instability behind the shock wave front.

We propose to use an off-axis zone plate, as beam splitter and as beam recombiner, to set a cyclic interferometer. We show that this optical device can be tuned to generate, with high stability, cosinusoidal gratings and/or cosinusoidal zone plates.

The methods of holographic interferometry proved to be the most effective tool of vibration research of complicated shape elements. Moreover, when the contact of the measuring instrument with the dynamically loaded surface is undesirable or technically impossible as well as in research of unstationary vibrations and quickly lasting processes , these methods appear to be indispensable. This report is devoted to the authors research in the field of the doublepulse and strobogolographic interferometry.

The experimental techniques developed specially for studying the acoustic systems (AS) and loudspeakers produced by the "Radiotehnika" Production Association are reported. The particularities of the AS parts vibration were experimentally determined. At the same time the plastic panel creeping under the influence of the internal stresses, the abnormal stiffness anysotropy of the LF loudspeaker head movable system were detected. The manufacturing defects in the honey-comb diaphragms were discovered by means of holographic inspection. Using holographic interferometry, the main problem is to record the bending deformations of the LF and MF loudspeaker diaphragms at the working voltage supplied to the voice coil on the background of their piston-like movements ( between 1 mm and 10 mm) which usually cannot be recorded by holographic technique. These difficulties are shown to be overcome partially using the local referance beam. The studies made enable to give the recommendations on the design improvement of the products mentioned above.

Superposed holographic interferometers are used to determine in,-plane and out-of-plane displacements of the tested objects. This technique is presented as an assembly of the object surface section and holographic plate in an immediate vicinity to the object. If a hologram is registrated at a metallized grating surface it restores an information peculiar to some optical methods: holographic interferometry, speckle photography, holographic moire and mirror-optical technique. New simple analytical expressions for the interpretation of interference patterns are obtained. Superposed holographic interferometers are used effectively to solve some deformation measurement problems.

As part of a programme of research into single-point diamond machining to cut-depths of the order of 100nm using an ultra-precision lathe, it was required to continuously monitor and control the axial position of the tool when used in the facing mode. This was done in combination with interferometric monitoring of the rotating spindle/face-plate. Two versions of combined interferometer and piezoelectric actuator are described in which the tool in-feed and optical axes are colinear. In the second version, the tool position is made with measurement interferometrically with respect to the rotating surface.

The usefullness of the zone plates (ZP) to the optical alignment and displacements measurement is discussed basing on examples of parabolic (PZP) and equilateral hyperbolic ZP (EHZP). Any displacement of the ZP from the position occupied during its recording creates the interference patterns between diffracted beam and its undiffracted counterpart. The shape of this pattern is explicitly determined by the kind and range of the misalignment. The PZP enables the accurate measurement of the linear motion in the direction parallel to the foci line with the control of undesired deviations in perpendicular directions. EHZP offers a possibility of strict point positioning for all possible degrees of movement freedom (including in-plane rotations), in contrary to the commonly used spherical ZP. Simple experiments supporting the analysis are presented.

Three laser interference measuring systems based on the Michelson interferometer with a single-frequency He-Ne laser are described. The system for machine-tool industry measures lengths with the resolution of 0.1 μm, velocities, small angles, straightness and flatness. The miniature laser interference system was intended to be built in measuring and testing machines. The system for microelectronics measures position in two orthogonal coordinates with the resolution of 40 nm.

A new arrangement of interferometers allows to measure the movement of a retroreflector in space with high precision. Applications are the testing of the position accuracy of three dimensional coordinate machines, industrial mbots, tooling machines etc. This system uses four Michelson interferometers with deflector units, controlled by a servo system. For the position of the retro-reflector and the position of the deflector units are unknown at start-up, a at least ten point calibration cycle is necessary. A mathematical algorithm, using the signals of the four Michelson interferometers, allows to determine the position of the retroreflector and the deflector units in a given coordinate system.

The work represents a new method of measurement of displacements, based on the coherent interaction of a surface acoustic wave (SAW) and a stationary reference grating (SRO) which modulates the intensity of an optical beam at the same frequency as the SAW. The experimental setup showed, that the resolution was defined by the noise level of electronic part and it reached 0,0IMm when the phasic method of measurement was used.

In this paper a super high precition displacement measuring device with resolution better than 0.001um is introduced. We have improved Michelson interferometer using He-Ne laser and co-optical path with double optical beams. So high stability (<0.0015um/h), high repeatability (<0.001um) and 2A sensitivity are achieved. A reference mirror excited by a osillating source forms two trains of sinusoidal waves, after being processed electronically, a subdivision of X /800 is obtained i.e. equivalent value is 0.00079um/pulse. Through special calibrating method we find the accuracy of fringe subdivision is ±0.0025um. The instrument is used to check the accuracy of micro displacement measuring comparator of which the sensitivity is 0.01um--0.001um.

The analytical description of a closed optical fiber interferometer system based on Jones calculus is presented. This calculus adapation for the optical fiber elements analysis allows for a uniform description of system built on the basis of a single-mode optical fiber. The analysis of a Sagnac fiber optic interferometer is an example of this method application.

In the study, the value of the transverse interferometric method in determining the refractive profile of a four-core optical fibre*) with a two-layer core situated on the fibre axis was demonstrated. By means of the transverse interference method, using differential interference contrast with a fringe interference field, the refractive profile of the fibre was determined for a wavelength λ= 546 nm. For the interference measurements a shearing type microinterferometr - the Biolar PI microscope - was used.

The construction principles and researches results of Sagnac fiber interferometr are described in this paper. The model was built as modified minimal configuration and it made possible an application of nonpolarized couplers and polarized fiber loop. The sensitivity 0,25 deg/h and drift about 5 deg/h was obtained as the results of investigations. The method of drift limiting and experimental test are described in addition.

Interaction of phase-modulated light beams in photorefractive local inertial responce media was analysed. Interaction of this type allows to registrate phase-modulated signals adaptively under low frequency phase disturbtion. The experiments on multimode fiber-optic interferometer with demodulation element based on photorefractive bacteriorhodopsin-doped polimer film are described. As the writing of dynamic phase hologram is an inertial process the signal fluctuations with the frequencies up to 100 Hz can be canceled. The hologram efficiencies are enough to registrate high frequency phase shifts ~10^-4 radn.

A fiber-optic heterodyne correlation-processing system is devised to investigate the spectral characteristics of the fluctuating optical waves propagated in a length of externally perturbed birefringent single-mode fiber. The power and cross-power spectra for the complex-amplitude fluctuations of the initially excited and cross-coupled modes guided in the orthogonal axes of the fiber are taken out of a beat-photocurrent spectrum with the help of a computer-aided processing system. The theoretical background and its experimental demonstrations are presented.

A simple method for interferometric measurements of chromatic and polarization mode dispersion os single mode fibres and devices is presented. Accuracy of the method and resolution limits are discussed.

This paper will discuss measurements of refractive index differences in optical fibres using an image shearing interference microscope. The technique has been used to characterise a multi-step index fibre suitable as a transfer standard to calibrate other more convenient fibre profiling instruments, eg refracted near-field. The technique of axial interferometry, where a thin slice of the fibre about 100 pm thick is viewed along its axis, has been developed so that uncertainties of about ±1% in refractive index differences are considered possible. The implementation of the technique, sources of error and interferometric measurements of slice thickness will be discussed along with the measurement uncertainties. Finally, an intercomparison of results obtained from interferometry, refracted near field, phase contrast microscopy and far-field measurement of light emerging from the fibre end, will be discussed.

A measurement of gradient index optical fiber profile by means of transverse differential shearing interferometry is described. By incorporating an automatic fringe processing system the accuracy of the fringe shift data reading equal to D/140 ( D - interfringe spacing) is obtained. Due to the accurate method of reconstruction of the profile from interferometric data the refraction of the probing beam is completely compensated. The immersion - cladding index mismatch is considered and it is shown that the immersion of refractive index higher then cladding refractive index can be used.

Chromatic dispersion is one of the relevant parameters which describes optical transmission systems by defining their bandwidth. It can be measured by determining the spectral group delay tG(λ) or τG - the group delay normalized with respect to the fiber length L. The measuring results are presented in an analytic form by a polynominal, the coefficients of which will be calculated by the method of the least square fit. The chromatic dispersion is the differential quotient dγG(λ)/dX. The group delay is not measured as an absolute value.

Two-beam and multiple-beam microinterferometric methods have been used in studying and analyzing polymer fibres. These techniques are ideally suited for measuring refractive in-dices and birefringence of these fibres. Multiple-beam Fizeau fringes in transmission and at reflection were used to investigate the optical properties of layers of fibres with irregular transverse sections having a skin-core structure. The area enclosed under the interference fringe shift was considered to represent the path difference across the fibre. Cylindrical multi-layer fibres were also studied interferometrically. Information about the molecular orientation and some structural parameters of fibres are available using interferometric techniques. The change of optical anisotropy of fibres due to γ-irradiation has been investigated and was suggested to develop a simple method for γ-ray dosimetry. The effect of drawing the fibres on their optical orientation function has been studied interferometrically. Refractive indices and birefringence changes with strain produced by different stresses in undrawn fibres have been measured dynamically by interferometry using a device connected to the wedge interferometer. A fibre manipulation device was designed, constructed and used to study the dependence of birefringence on strain in case of polymer fibres. This device was used with the Pluta polarizing interference microscope to determine the refractive indices and birefringence under strain. It enables one to study stretched, twisted and rotated fibres and can be fitted easily to the interference microscope. Microinterferograms are given for illustration.

The relationship between cell adhesiveness and motility is being studied extensively for its paramount importance in the normal development of an organism and in pathological conditions such as tumour metastasis. Although they have been intensively studied at both the cellular and molecular levels, correlative studies of cell structure and adhesiveness, and the precise determination of cell adhesion to a substratum in living cells have been hampered by the fact that cell adhesion has been very difficult to visualize. Two techniques have emerged recently which have allowed successful visualization of cell adhesion. The most recent one, total internal reflection fluorescence, is technically complicated and thus not widespread and so it will not be dealt with here. The other one is a variant of incident light interferometry of thin layers, known as interference reflection microscopy (IRM).

The uniform field version of the variable wavelength interferometry for transmitted light and a double refracting microinterferometer with Wollaston prism were used for the verification of the Michel-Levy's scale of interference colours of polarized white light emitted by a tungsten halogen lamp (12V/100W). It was stated that the first purple occurs between crossed polars when the optical path difference Δ= 555 to 558 nm, while Δ= 565 nn corresponds to the violet colour near the indigo. Consequently, the other purple colours were observed for the optical path differences slightly smaller than the values of Δ given in the Michel-Levy's scale for both crossed and parallel polars.

Determination of the relationship between the light wavelength and the interfringe spacing is a basic calibration operation in interferometry. A simple and accurate method of the calibration of double refracting microinterferometers is proposed. The method is based on the object-adapted variable wavelength interferometry (AVAWI) developed recently by the author of this contribution. Only a birefringent plate of known thickness or a glass plate with a step whose height is known are required for the calibration process.

Some double refracting microinterferorneters available commercially suffer from a variable interfringe spacing across the image plane. This defect is especially produced by typical birefringent Wollaston prisms and is responsible for some errors in the measurement of optical path differences or related quantities. In particular, the errors arise when the interfringe spacing is directly measured in the image plane of the microinterferometer or determined from an interferogram recorded on a photographic material. To overcome this defect, the Wollaston prism must be adjusted so to obtain a uniform distribution of interference fringes in the image plane. It has been stated that bichromatic interferometry is a useful tool for precise adjusting the Wollaston prism of double refracting microinterferometers.

Liquid crystal televisions are being evaluated increasingly as spatial light modulators in a wide variety of optical image processing applications. Relevant performance characteristics of these devices and their application to the implementation of optical logic gates is discussed. A description is given of a novel technique which employs liquid crystal televisions to demonstrate real-time speckle metrology. Some modifications to the TV which may increase the potential of these devices as spatial light modulators are briefly considered.

To solve the problem of quality control in rolled metal (localization of technological defects, determination of differences in thickness), various methods of nondestructive control are made use of, including, rather widely, acoustic methods. The main demerit of these methods is the necessity of a good (acoustic) contact between the irradiating and receiving surfaces of the piezoconverter, on the one hand, and the surface of the object under examination, on the other hand. Such contact is in a number of cases, hard to ensure, and any control of objects at high temperatures is practically impossible.

The problems of optical differentiation of displacement fields are actual as much as the problem of interferometric displacement, when the image shear value exceeds the surface microstructure correlation radius.

The proposed work shows that the application of special focusing reflective diffraction coatings leads to a significant gain both. in aperture ratio of a speckle interferometer and in the quality of the interference pattern produced. Possible circuits have been studied for the obtaining of interference patterns of the derivatives up to the second one inclusive of the deformed object surface points shift function in one and the same exposure. By way of experimental verification interferograms of bendings w, angles of the normal swing in respect to the surface w' and curvatures wt" of a round plate restrained along the edge have been received by means of the suggested devices.

In Digital speckle-pattern interferometry the interferograms are corrupted by strong speckle noise having high amplitudes. The simplest method of speckle reduction is two-dimensional lowpass filtration by spatial averaging. The implementation of such filters is simple and they run very fast, but they always result in image blurring, which affects the following segmentation procedure negatively if the fringes are dense. For the digital filtration of speckle noise in digital holografic and speckle pattern interferometry, we have achieved good results with a modified WIENER-filter to improve the filter process. The filter algorithm based on Fast Fourier Transformation (FFT) was implemented in a micro-computer system with a fast grafic memory. This method will be described and demonstrated by practicle examples.

An application of one-beam speckle interferometry to polymer systems is presented with emphasis on measuring of speckle pattern correlation. The system for an interactive picture analysis useful for the extraction of various types of physical information from "speckled" images is described.

This paper experimentally investigates the spatial correlation properties of the doubly-scattered speckled speckle intensity patterns produced from a cascade of two transparent diffusers. The experiments are conducted by using the digital speckle intensity interferometer under illumination of the speckle pattern. The experimental results show that the fringe visibility depends not only on the rms surface roughness of the diffuser used for producing the speckle illumination but also on the distance between the two diffusers. As a result, we propose the new surface roughness measuring method which has the advantages that the measurable range of the surface roughness and the sensitivity of the measurement are controllable by changing the distance between the two diffusers.

Two new techniques of quantitative analysis of ESPI patterns obtained while testing transient event are presented. The first one uses an exact solution of four intensity equations (speckle patterns), that removes the effect of the random speckle distribution of the phase and the contrast respectively. It gives the possibility of high accuracy phase retrieving if the stability of the system is assured. In the second technique the speckle interferometer is modified by introducing a phase grating between the object and the interferometer. The grating separates three (or two) phase shifted images of object in space . This enables transient condition of an object to be captured while allowing full quantitative phase measurement to be performed. This technique may be used for real time measurements although phase is retrieved with low accuracy. The recomendation for the engineering application of the methods of automatic analysis of ESPI interferograms are given.

The three-dimensional intensity correlation coefficient pi of speckled laser light fields reflected from diffuse scattering surfaces is calculated analytically and numerically for rectangular and circular apertures. μi is shown to be constituted by a Fresnel transform of the square modulus of the aperture function and is used to determine the average three-dimensional size of the speckle grains and its space dependence. General properties and special cases are discussed and compared with data reported by other authors. The results, several of which are stated for the first time, should give support in further developments of speckle metrology and holographic interferometry.

The partially developed, Gaussian speckle pattern generated by TEM₁₀ laser mode is considered. The statistical properties of the speckle pattern are discussed by means of the interference effect associated with propagation of the TEM₁₀ laser mode. The average contrast of the speckle intensity was measured and the experimental data are compared with theoretical results.

A new speckle photographic technique is proposed to measure the 3-D displacement of a curved surface. The movement of the image speckle is recorded on a cylindrical surface, whereby the defocussing is dismissed. The principle of the method is described. The relations between the displacement of the model and the speckle movement on the cylindrical image surface are derived. Experimental results are given and compared with those calculated by the finite-element method.

A new, technique is proposed to reconstruct an astronomical image by using a phase retrieval from exponential filtered and unfiltered images based on the Fourier series expansion method. The amplitude of the Fourier transform of the filtered image is a mixture of the information of the Fourier amplitude and phase corresponding to the unfiltered image. Therefore, the phase information can be derived from the Fourier modulus of the filtered image based on the Fourier decomposition method. We have tried to apply this method to stellar speckle interferometry and the successful reconstruction of a double star image has been obtained.

An application of the speckle velocimetry to the problem of a fluid in a high aspect ratio cavity has been carried out. The impossibility of a higher seeding makes it difficult to obtain a great deal of information and then, the multiple exposure and the two-step methods have been applied to our problem and evaluated in order to reach a solution.

A laser interferometer with highly linear transfer characteristics for the undistorted measurement of mechanical vibrations is described. The linear transfer behavior is derived by a control loop which holds the optical phase difference within the interferometer on a constant value. As a phase-shifting element we use a linearized PZT actuator with integrated displacement sensor. With this interferometer harmonic and nonhannonic vibrations can be measured over 5 decades in the range of 1 Å to 25 μm. The frequency range extends from really DC to about 10 kHz (-3dB limiting frequency). Within the control loop we use primarily a proportional-integral controller with an integrated Wien-Robinson band-rejection filter which suppresses the resonance frequency of the PZT-actuator. This allows to increase the limiting frequency of the closed-loop interferometer by a factor 3 in contrast to a control loop without a rejection filter.

In this report the systematisation of the angular differential interferometers with the plane and corner-cube reflectors is performed. The analytical formulas for calculation of the path difference, relative shifts and angles intersection of the interfering beams are obtained. The features of the optimum use of the angular interferometers in two principal optical schemes of laser scanners with preobjective and post-objective scans are analyzed.

The single-frequency cw YAG:Nd laser with frequency stabilization onto spectroscopic standard at 1.06 μm - molecular cesium absorption lines - is described. It is shown, that the spectrum of saturated absorption of Cs₂ gives for this spectral range the optical scale of reference frequencies, which is convenient for the utilization in interferometric systems and in the heterodyne systems in particular. Spectroscopic properties of this cesium reference are presented. The heterodyne measurements of Allan variance in the experiments with two independent frequency stabilized YAG:Nd lasers which gave the highest value of relative frequency stability at a level of 6x10^-11 are described.

Ultrasensitive interferometer measurement technique using laser response to cavity loss modulation is described. The advantages and possibilities of this method are analyzed. The model of laser displacement sensor based on cw stabilized YAG:Nd laser with intracavit.v Michelson interferometer has been built and tested.The sensitivity of 10^-16 m/√Hz has been achieved in the frequency range above 40 kHz, which is close to theoretical limit determined by natural laser amplitude noise.

A design of a laser interferometer eliminating a zero drift type error is presented. The differential interferometer was used in making the angular displacement transducer and the probing complex for measuring sea-water refractive index variations.

In this paper the application of photorefractive BGO-crystals in a Michelson-interfero-meter with a phase conjugating mirror is discussed. Especially the time dependence of the intensity and the phase of the phase conjugated wave have been examined. Using these results we propose a method to evaluate the interference fringe pattern cf this Michelson-interferometer.

Particle sizing based on the phase Doppler technique is investigated for spheres having sizes of several light wavelengths by using a laser interferometer(a laser Doppler velocimeter) that has the receiving optics composed of paired optical fibers. The phase dependence on the particle size is calculated by means of multipole expansion of electro-magnetic fields and the calculated results are compared with those obtained from geometrical optics. Experiments using silicon resin particles have been conducted on the basis of oscillatory part of the phase curve.

This paper reports on a Fabry-Perot interferometer arrangement acting as a beam splitter with variable reflectivity for intense CO, laser radiation up to kW cw-power.By means of the tuning of the spacing between this two plane parallel interferometer plates the intensity of the transmitted as well as the reflected part of the incident laser beam can be modulated. The properties of the interferometer in dependence on the parameters of the laser radiation and on the parameters of the interferometer plates are given in detail in the paper. Furthermore specific applications and arrangements, e.g. numerous uses in laser materials processing, the spectral diagnosis of CO₂ laser radiation, the effective stabilization of the radiation power and bietable operation, which are based on the beam splitting function and the typical transmission characteristic of the Fabry-Perot interferometer as well as the principle of tuning, are discussed in the paper.

Interferometry, generally two-beam interferametry, is widely used to test the quality of optical instruments. At all stages of their manufacture this method is employed. First, it is to choose the materials, glasses or crystals, to be sure that they do not show refractive index variations and that they do not present mechanical strains. Second, the interferometric testings occur when the optical components are manufactured. They concern the shape of the surfaces, possibly their roughness, the centering of the lenses, the angle measurements. Of course the materials which are used are always of the best quality and so it is of the workshop productions. Then the obtained interference patterns are always near the flat tint and it is useful to dispose of means able to increase sensitiveness of two-beam interference patterns, that will be opening on the information processing. To test optical systems, there is also a difficult problem concerning especially the high aperture objectives used in microscopy and microlithography which are diffraction limited and require quality testing during their manufacture and for their delivery. The instruments which are measuring the MTF are not at all suitable in the field of spatial frequencies transmitted by these optical systems. Knowledge of the deformations of the wavefront by means of normal interferometry require a very perfect reference system at least of same aperture. On the other hand, the differential interferometry which is able to obtain the self comparison of the wavefront for a given spatial frequency offer solutions proposed by several authors. We will consider the use of a polarization interferometer associated with a phase modulation to increase accuracy. In spite of some-non negligible experimental complications, it is effectively possible to obtain directly the components of the MTF. In so far as a limited number of informations about some discrete frequencies are interesting the user such an instrumental project could be considered. On the other hand, to satisfy the designer it seems more useful to obtain the lateral aberrations of the objective that is leading to the restitution of the true wavefront by means of integration. That is possible from the analysis of interference pattern resulting of very small shearings in two orthogonal directions.

Automatic interferometry is employed for extended refractive index inhomogeneity measurement of optical glass disks intended e.g. for manufacturing lenses of microlithographic optical systems. The effect of stress birefringence of the glass on the measuring accuracy and the influence of an optical wedge on the imaging quality of a high performance optical system are examined.

An infrared (10μm) wavefront is recorded holographically on a dynamic recording medium consisting of a thin oil film on a glass substrate. The phase hologram obtained is used to restore the information of the infrared wavefront or alternatively as a diffraction grating for a visible reconstruction beam. This property is applied to implement a single hybrid interferometer (Michelson or Mach-Zehnder) for the simultaneous testing of infrared and/or visible optical components. Experimental results both for visible and infrared components (parallel plate, lens) confirm the usefulness of this interferometer.

The problem of centering the long focal length interferometric objectives is discussed together with the method to control the optical quality of the system after the assembling process. The practical aspects of using the inverting confocal Fabry-Perot inteferometer for solving those problems are presented. The achievable accuracy is discussed and proved by testing the asymmetrical deformations of the wavefront behind the system under test. In the cases discussed the sensitivity of lens centering is of order of few seconds of arc. The asymmetrical wave aberration, is tested interferometrically using the FFT-technique for analysing the fringe pattern with accuracy of λ/80. The asymmetrical wave aberration of the system under test is equal to λ/38.

Speckle methods are described to determine density gradient distributions in gas flows. The results are presented on speckle photography measurements of density gradient fields and temperatures in jets, flames, gas flows, both laminar and turbulent. Study deals with gas jets from conic nozzles used for laser treatment of materials in a gas medium, with different-configuration flames at natural-gas burning in a pumping volume as well as with gas flows directed into the submerged space in shock tubes and into the cavity part of mixing high-power lasers. The main optical schemes and experimental set-ups for obtaining specklegrams are used by the present authors and are given here. Specklegrams are recorded by double exposure when a diffuse scatterer is placed before and behind an investigated object. Use of the measured values of speckle shifts at laser scanning of a specklegram allows reconstructing local parameter distributions for different cross-sections of axisymmetric objects.

The theory and the experimental results on interferometry determination of thermal diffusivity are given. The method is based on interferometry registration of an unsteady temperature field in a flat transparent layer of a medium. Using Clausius-Mossotti equation and the long-time asymptotic behavior of an exact solution to the one-dimensional unsteady heat conduction equation, the formula has been derived which relates the thermal diffusivity of substance to the time derivative of some function of the number of fringes. Measurements for air have been made. The obtained results are compared with the known experimental data.

A laser plasma produced under interaction of high-power Nd-glass (λ=1.06μm) smooth quasi-continuous laser radiation with the carbon target has been study experimentally by means of nonlinear dispersion and holographic interferometry. The distribution of electron and atom denity, pressure and temperature with high spatial resolution for intensity I = (0.3 - 2)•10⁸ W/cm² has been determined.

The measuring system designed for optical diagnostics of plasma focus device is described. Some experimental results obtained on the PF-150 device are given as well. Special attemption is devoted to synchronization between phenomenon being investigated and diagnostic equipment.

The very important step of the crystal growth or dissolution process is mass transport in solution. The concentration changes around the crystal caused by the diffusion and convection may be detected by the optical methods. The paper presents some results of our investigations of such process with the use of moire fringes and interferometric techniques. The discussion of the problems appearing when using these methods in crystal growth experiments is presented.

Ray-crossing effect and importance of focusing accuracy at optical probing of strongly refracting, partially nontransparent, radially symmetric objects are discussed. Quantitative results based on exact formulas are given. Analysis was carried out assuming refractive index field characteristic of laser-driven plasma and within geometrical optics limits. Maximum penetrated electron density and the influence of focusing errors on the reproduced density values for exponential density profiles are investigated.

The paper reviews recent contributions to the theory and experimental improvements of moire interferometry. After short reintroduction of the principle some modifications of the optical system to broaden the measurement capabilities are presented. They include real-time differentiation of displacement patterns, three dimensional displacement measurements, configurations for shear strain determination, and new techniques for producing molds of specimen gratings. Separately, the progress in information processing from fringe patterns is presented. Selected aspects of manual and automatic approaches are discussed.

We discuss the formation of self-images of a 2-D grating composed by two rulings of equal period, but in-plane rotated. We describe the in-register condition for setting the lensless Lau effect, with this type of gratings; and we propose to use the above configuration for interferometrically visualizing, in noncoherent light, phase structures, in two nonorthogonal directions.

The problems of colour interference bands forming in the double screen system are considered on the base of the theory of diffraction. It is shown that in the screen system the phenomenon of the selective filtration of diffracted waves arises when the conditions of the Lau effect are realized (they are typical for the near diffraction band). The theoretical grounds of selective filtration phenomenon in far diffraction band of the screen system are given. The peculiarities of colour interference bands forming in the far and near diffraction regions are analysed taking into account the spectral distribution function of the incoherent light source.

Methods of the space-frequency spectral analysis of the screen system were used for designing a system of programmed computation of conditions for contact screens making. A computation algorithm of calculation is described and the results of the application of the elaborated system are given.

Diffraction interferometers used in diagnostics of phase objects and optical detail control are dealt with in the paper. Some systems with two or more diffraction gratings providing an arbitrary alignment of interference fringes relative to wave-front shear are described. Circuits of interferometers with synthesized reference beam are shown. Such interferometers allow to obtain ordinary and holografic interferograms with wave front shear and interferograms of Zehnder-Mach type ensuring , at the same time, measurement sensitivity increase both in conventional and holografic variants. It is shown, that symmetric and non-symmetric diffraction holographic elements can be used as diffraction gratings allowing to obtain simultaneously several interferograms with different fringe orientation. In conclusion, some applications of described interferometers in heat flow diagnostics and in control of optical elements are cited.

We describe an optical setup based in the Talbot effect, which uses two mutually incoherent sets of self-images to display simultaneously interferometric bright-field and dark-field images, in almost any combination of two complementary view-fields. This feature allows us to sample the object under test in many different places. A spatial filter can be used, to visualize the interferametric fields with uniform irradiance; as gray variations. Several experimental results that verify our technique are shown.

We proposed in this paper a new approach to analyse a phenomenon of 'free - diffraction beam'. An intensity distribution in focal region of annular beam , which waist is placed in front focal plane of optical system, can be considered as a 'free - diffraction beam'. We worked out a simple, analytical model of propagation of annular beams in optical systems in cylindrically and rotationally symmetric cases. There are examined properties of diffraction field in focal region in both cases .We determined formulae describing dimensions of diffraction fringes and compared them with previous results. The results of calculations in 2-D case can be applied to describe intensity distribution of working field of laser anemometer.

A simple method based on the interferometry principles was developed for control and analysis of photoresist layers at the stages of their thermal treatment and exposure. Application of this method makes it possible to increase integration of VLSI by creating elements with characteristic measures less than one micron.

One of the main problems related to the modern optical measurements concerns the rapid, accurate and parallel data acquisition of one or bi-dimensional images, in order to transfer their information to a computer for further processing. Traditionally, camera tubes or mechanical scanning systems working in conjuction with a detector (photomultiplier or photodiode) are used to pick-up information from the input image. A breakthrough in the optoelectronic interface implementation was achieved by the introduction of all solid-state image sensors (SSIS) for visible and IR radiation.

Artical is dedicated to solving some problems connected with lanufacturing accurate master scales with standard graduation of 10 μm - master scales making and checking on machine controlled by laserinterferometer - achievment the best quality of photoprocess

An interferometric stand with a laser source is described and the results are presented of the investigations of plasmodynamic processes in a compact magnetoplasma compressor carried out using this stand.

An image processing system to process interference patterns has been developed. Basic image processing tools are used and specific software has been developed to perform a quantitative analysis of interferometric data. In the case of a single interferogram the analysis consists of the following steps: linear and non-linear filtering to suppress noise and to correct shading, masking of areas without fringes, detection of fringe extrema, interactive fringe ordering and computation of the phase surface or the fringe density by interpolating between the fringe extrema. This paper discusses the problems involved in interferogram analysis and several image processing techniques to solve those problems. Some of these techniques will be illustrated using an interferogram of a vibrating diskl.