Method Of Holographic Interferometry Research Articles

Application of holography method for the restoration of the Williams series near the crack tip

The article describes the processing of the results of a series of experiments performed by the interference-optical method of holographic interferometry (holographic photoelasticity) aimed at computing the amplitude coefficients of the M. Williams series constituting the stress and displacement fields at the crack tip for several cracked configurations. The main objective of this study is the experimental and computational determination of the coefficients of the M. Williams series for the stress, strain and displacement fields associated with the crack tip in an isotropic linearly elastic medium taking into account regular (non-singular) terms in the multiparameter Williams series. These coefficients are named generalized stress intensity factors. The method of holographic interferometry is shown to be a convenient and efficacious tool for reconstructing the stress field near the tip of the crack, because during the experiment it is possible to obtain two families of interference fringe patterns: absolute retardation fringes (isodromics) for vertical and horizontal polarizations. Experimental outcomes were thoroughly processed using the developed digital application allowing us to accumulate the isodromics orders and coordinates of points belonging to absolute retardations. In this work, absolute retardation fringes in a plate with a central horizontal crack and a crack inclined at different angles are obtained. For each type of experimental sample, the coefficients of the Williams series were calculated taking into account non-singular terms (in the representation of M. Williams, fifteen terms were preserved). A procedure for linearization of nonlinear algebraic equations following from the relations of Favre’s law is proposed. By solving the obtained overdeterministic system of linear algebraic equations, the generalized stress intensity factors (coefficients of the M. Williams series) are estimated. Conjointly, the finite element analysis of the specimens with same geometry was effectuated. The experimentally determined values of the Williams series are compared with the results of the finite element calculation of the stress-strain state performed in the SIMULIA Abaqus software.The results of the numerical and experimental studies were found to be quite consistent. It is lucidly shown that it is imperative to keep the higher order terms in the Williams series expansions for the fields associated with the crack tip.

Estimation of the sensitivity of optical measurements using a holographic interferometer

Various interferometers used for high-precision spectroscopic measurements are considered, and the choice of a holographic interferometer based on the spatial-spectral method of holographic interferometry is justified, with the help of which the movements of the phase center of a coherent light flux in a wide dynamic range are measured in real time and measurement information is recorded digitally. On the basis of mathematical relations proposed by the authors in previous publications and based on the results of experimental studies, the sensitivity of a holographic interferometer to spatial displacements of phase centers (focus points) of light streams – point light sources forming a holographic interferogram is numerically estimated. The dependence of the level of the normalized intensity of the luminous flux in the central region of the holographic interferogram on the movement of the actual point light source along the normal to the plane of the Fourier hologram is established. Based on the results of mathematical modeling, it is shown that the sensitivity of the holographic interferometer to the movements of a real point light source along the normal to the plane of the Fourier hologram depends on the parameters of the optical scheme of the holographic interferometer when exposing the hologram and during measurements. At the same time, the sensitivity of the holographic interferometer to the indicated displacements of a real point light source can only be evaluated experimentally. It is proposed to increase the sensitivity of the holographic interferometer by using a thin collecting lens in its optical scheme. For the first time, a mathematical relation was obtained and investigated for the gain coefficient of the light flux phase with a spherical wavefront, which makes it possible to numerically estimate the increase in sensitivity of a holographic interferometer implementing the spatial-spectral method of holographic interferometry with known parameters of a thin collecting lens in an optical scheme. It is shown that the sensitivity of a holographic interferometer to the movements of an imaginary point light source along the normal to the plane of the Fourier hologram is 2.86 times greater than its sensitivity to the same movements of a real point light source. It is established that the sensitivity of a holographic interferometer with a volumetric Fourier hologram and a thin collecting lens in its design can be increased by at least an order of magnitude compared to the sensitivity of known optical interferometers. The results of assessing the sensitivity of a holographic interferometer implementing the spatial-spectral method of holographic interferometry to the movements of point sources of real and imaginary light fluxes, as well as the obtained ratio for the gain of the light flux phase gain by a thin collecting lens will be useful for high-precision measurements of linear and angular displacements of objects, as well as for the construction of photonic device designs. Based on the results of the study, an experimental sample of an acousto-electric converter was developed and manufactured on the basis of a holographic interferometer, which has high sensitivity in wide dynamic and frequency ranges and is intended for use in acoustic location of unmanned aerial vehicles.

CALCULATION AND EXPERIMENTAL RESEARCH OF TANK HYDRAULIC TRANSMISSION LAYOUT

In order to substantiate the advanced technical solutions of radial hydrovolume transmissions, it is necessary to study the stress-strain state of their most responsible and loaded elements. In particular, it is of interest to determine the rational parameters of cylinder block, which is subject to significant pressure of working fluid. This leads to the formation of a stress-strain state with a high level of stresses and elastic displacements. They can be dangerous in terms of strength, rigidity and performance of the hydraulic transmission in general. To carry out numerical studies of the stress-strain state of cylinder block of hydrovolume transmission at the design stage, finite element models with varied parameters are developed. However, at this stage of research, it is desirable to have a verified numerical model. For this purpose, the paper describes the computational and experimental studies of the layout of the cyclic part of the hydrovolume transmission cylinder block. On the one hand, these studies were performed using the experimental method of holographic interferometry. On the other hand, calculations were performed using the finite element method. In the course of comparison of the received results, the finite element model parameters are determined which provide high accuracy of the stress-strain state calculation of hydrovolume transmissions cylinder block. Keywords: stress-strain state; hydrovolume transmission; finite element method; cylinder block

Heat transfer enhancement in the novel wavy shaped heat exchanger channel with cylindrical vortex generators

The enhancement characteristics of heat transfer in conjunction with a low pressure drop were experimentally and numerically investigated for the novel geometry wavy shaped heated channel with cylindrical vortex generators. To visualize the temperature distribution there was used the holographic interferometry method while the Ansys Fluent software was used to evaluate the temperature, velocity, and pressure field in the wavy channel. The study is focused on the analysis of the heat transfer coefficients, Nusselt numbers, thermal performance, Colburn factor, and friction factor for the wavy channel and the wavy channel with cylindrical vortex generators of 15 mm diameter located in five different horizontal positions. Moreover, we have performed a comparison with the smooth channel. The results are presented for the surface temperature Ts = 318.15 K, Reynolds number 778 ≤ Re ≤ 7,930, and channel height 0.04 m ≤ H ≤ 0.06 m. At the wavy channel with position “2” of cylindrical vortex generators for the channel height of 0.04 m and Re = 1,669 was noticed the maximum thermal performance factor TPF́ = 0.8167. For this configuration, the novel asymmetric curve geometry in combination with cylindrical vortex generators at position “2” brought the enhancement of the Colburn factor j by 2.48 and 3.28 times compared to the wavy and smooth channels, respectively. The new correlating equations for all investigated channel height and volumetric flow rate in the range of 10 m3/h to 50 m3/h were created. The results show that inserting cylindrical vortex generators into the investigated channels is significant to achieve more efficient heat transfer and thus reducing energy consumption.

Implementation of digital holographic interferometry for pulsed plasma studies

The study of low-temperature plasma generated in pulsed mode at atmospheric pressure was carried out. The purpose of the presented research is to develop a method of digital holographic interferometry for registration and evaluation of parameters of low-temperature plasma at atmospheric pressure in pulsed mode. This type of plasma is currently applied in medicine and biology. Thus, there is a need to control the exposure dose and plasma environment formation regimes. As plasma parameters, it can be considered its electron concentration which can be calculated through the estimation of the refractive index of plasma pulse in relation to unperturbed state. The plasma pulses were activated in Helium. The plasma pulse frequency was 5 kHz and its duration was 750 ns. During an investigation a laboratory set-up for recording holographic images of plasma pulses was developed. Holograms are acquired on a digital camera and a pulsed laser INNOLAS SpitLight Hybrid II at a wavelength of 532 nm with pulse duration of 10 ns is used as a source of coherent radiation. In order to record plasma pulses, the laser, plasma generator and digital camera were strictly synchronized to each other. During the experiment, a series of about 500 holograms were acquired, and the reconstruction of the phase of the object field was calculated. Analysis of the sequence of holograms allowed calculations of phase difference (interferograms) related to the refractive index of low-temperature pulsed plasma in Helium. It is known that low-temperature plasma leads to low phase delay which forms low phase contrast of the evaluated interferograms. For this purpose, we carried out preliminary experiments with plasma-arc that has similar temporary parameters, however, with a higher phase contrast of the interferograms. The paper presents experimental results obtained by studying the phase contrast of the refractive index of pure Helium, plasma-arc and plasma pulses in Helium. Thus, the effectiveness of both the experimental set-up and the method to evaluate the interferograms related to the refractive index of the plasma pulse was verified. The data obtained can then be used to estimate the electron concentration of the plasma. However, it needs to increase the sensitivity of the method in order to enhance phase contrast. Increase of sensitivity can be done by means of extension of the spectral range, for example, toward to infra-red.

Investigation of nanoscale and microscale structured cooling surfaces of thermal power plants

Studies were conducted of the heat exchange crisis depending on the coolant excess (which determined the underheating and flow rate), the thermal-physical properties of the heating surface, and the ejection of liquid droplets from the porous structure. A model of dynamics of vapor bubbles born on the solid surface in porous structures and the vapor-generating wall (substrate) has been developed. The model is based on cinematography with an SKS-1M speed camera. The removal of high heat flows (up to 2·106 W/m2) is provided through the joint action of capillary and mass forces with the use of intensifiers. Equations are obtained of critical heat flows through the thermohydraulic characteristics of the boiling process in woven porous structures. The research is of practical importance in the limiting state region of the steam-generating surface protected by cooling from overburning. Three mineral media (tuff, granite, marble) of Zaili and Dzungarian Alatau mountains near the city of Almaty (Kazakhstan) were considered. The method of holographic interferometry was used to study porous thermodynamic screens. The stress and deformed state of the samples was studied. Simulation of the acoustic field of the blast wave with th e thermodynamic field created by three thermal sources has shown its high efficiency. The created powerful thermal screen, due to the generation of strain and thermal stress fields, is an obstacle to the propagation of the reflected blast wave, causing the emergence and development of destructive cracks. Nanoscale and microscale structured surfaces in the form of coatings and mesh structures have been developed, which give an integrated effect of industrial meshes with natural mineral media coatings and have synergistic advantages of combining these two developments in an integrated technology of their production, expansion of critical thermal loads and management of the limiting state of porous coatings.

Digital holographic system for layer-by-layer control of additively manufactured component quality

Subject of study. A digital holographic system for layer-by-layer control of component quality in additive manufacturing able to determine the size and depth of defects on the surface of each layer was investigated. Method. The digital holographic system for layer-by-layer control of component quality in additive manufacturing operates based on a two-wavelength holographic interferometry method. The digital holographic system is based on a Michelson interferometer. The considered method involves recording holograms of the surface of each component layer at two adjacent wavelengths. As a result of hologram reconstruction, the complex amplitudes of the object wave in the reconstruction plane are determined, which, in turn, define the phases of the waves and their difference. The wave phase difference allows the depth of the defect on the component layer surface to be determined. A tunable diode laser and camera based on a CCD matrix are used as the radiation source and detector, respectively. Main results. The results of the investigation of the surfaces of additively manufactured components using the two-wavelength holographic interferometry method are presented. The recognition of large irregularities is possible through expansion of the phase pattern. The detection of surface defects with the size of 25 µm is demonstrated. The reconstructed surface of a component manufactured by laser sintering of successive layers using the M250 additive setup for selective laser sintering and the reconstructed surface of a millimeter-scale macroscopic object are presented. Practical significance. The possible use of the digital holographic system for component quality control in industrial settings, including those applying additive technologies, is demonstrated. The component quality criterion is the absence of defects (cavities or protrusions) with size larger than 25 µm.

Holographic interferometry experiments and numerical analyses of the stress field on the Williams series expansion: higher – order terms

The study is aimed at experimental and numeric determination of the higher order coefficients of the Williams power expansion for the near crack-tip fields in isotropic linear elastic materials by two approaches. The first one is based on the experimental method of holographic interferometry, the second one is relied on the finite element analysis. The main problem and difficulty are accurate extracting the coefficients from the whole set of experimental data. To obtain the higher order coefficients of the Williams expansion the program tool which is designed for digital image processing of the experimental fringe patterns. As the first step the plate with the horizontal central crack has been chosen since this cracked geometry is thoroughly studied and the coefficients of the higher order terms are known. The stress intensity factors, T-stress and higher order coefficients are extracted and compared with the theoretical values. Then the mixed mode loading is considered. Using holographic interferometry a lot of tests with the inclined cracks were performed. It is shown that the digital holographic method and the developed programming tool allow us to find the coefficients with high accuracy. The results of digital image processing of the experimental data have been verified and confirmed by the finite element analysis.

ДВУХПАРАМЕТРИЧЕСКИЙ МЕТОД ОПРЕДЕЛЕНИЯ КОЭФФИЦИЕНТА ИНТЕНСИВНОСТИ НАПРЯЖЕНИЙ KI ТРЕЩИНОПОДОБНЫХ ДЕФЕКТОВ МЕТОДОМ ГОЛОГРАФИЧЕСКОЙ ИНТЕРФЕРОМЕТРИИ

A new method has been developed for finding the stress intensity coefficient and the nominal stress σox for a plate with a crack-like (elliptical) defect. As an experimental basis, the patterns of bands of absolute path difference obtained on the basis of the method of holographic interferometry are taken. Using Favre ratios and approximate decomposition of stress components for the plane case, the stress intensity coefficient and the nominal stress σox are determined. The difference of the proposed method is in a more accurate representation of the stress tensor in the vicinity of the vertex of a crack like defect. Such representation allows one to take the geometry of the defect into account. The values of the correction function calculated by the proposed method in the formula for theoretical determining of the intensity factor have been higher than those obtained by previously used methods. This indicates a possible underestimation of the magnitude of the intensity factor when using the previously proposed methods. In addition to using more precise formulas for the stress tensor, the approach implies considering the nominal stress and the intensity factor as independent parameters. Full consideration of the crack geometry and loading features is very difficult from a mathematical point of view; however, this property of the method allows partially compensating for the simplifications of the stress tensor analytic expressions. Also, this method makes it possible to determine the main stresses and the intensity of stresses in the vicinity of the vertex of the defect. The obtained formulas agree well with experimental results.

Stress-Strain Behaviour of Reparable Composite Panel with Step-Variable Thickness.

There is an urgent problem of finding an economically viable method of maintenance and restoration of the bearing capacity of structures of various applications. Repair of structures with patches made of polymeric composite materials is one of the most promising repair technologies. However, an improper choice of parameters of the composite patch leads to unjustified increase in the structure mass and the cost of its further operation. These situations result from the lack of reliable methods for developing the repair process, which take into account the influence of the patch geometry and conditions for performance of repair works on the bearing capacity of the repaired structure. The mathematical model of the reparable composite shell–type panel taking into account inhomogeneity of transverse shear deformations at stepped variation of its thickness has been developed. In contrast to the classical theory of layered shells, the model allows simplifying a three-dimensional problem by setting of the displacement field on the layers’ interfaces and their linear interpolation over thickness of the panel, as well as considering the transverse shear deformations resulting from the strength, temperature, or shrinkage loading. According to results, the maximum rise in stresses in the case of a notched panel occurs in the weakened layer, and it is from this layer the failure of the structure will start. In the event of the patch, the panel surface opposite the reinforcement is the most loaded (i.e., susceptible to failure) surface. To confirm the reliability of the developed model, we compared the analytical calculations with the results of experimental and numerical studies of the deformed state of a panel of step–variable thickness by the method of holographic interferometry and modelling by the finite element method. Displacement fields available from experiments correspond to the predicted theoretical results. The resulting maximum error does not exceed 7%. The data obtained during numerical modelling allowed us to conclude that the accuracy of theoretical calculations is sufficient for engineering practice. Results of the work can be used to solve the practical problems such as determination of stress–strain behaviour of a damaged structure or structure after repair, specification of the permissible delamination dimensions, and defining of parameters of the bonded repair process.

Study and quantitative assessment of the structural inhomogeneities parameters of composite materials

The possibility of determining the size of the delamination region and the depth of its location in non-metallic multilayer weakly conductive materials using a unique pulsed eddy-current equipment by scanning the sample and registering the region of increasing amplitude of the differential signal has been practically confirmed. The nonstationary thermal and holographic interferometry method is used to obtain information on the shape and size of the bundles. For experimental testing, samples were used made of carbon fiber composite materials with artificially created defects in the structure of the material in the form of delaminations of various sizes and shapes.

Experimental study of thermal convection in dry air by holographic interferometry method

The convection of humid and dry air was studied experimentally. The observed fluid convection involves two mechanisms of heat and mass transfer: thermal convection produced by temperature gradient and concentration convection occurred due to the inhomogeneous vapor distributions induced by evaporation and condensation of water. The convection stability of humid air was described in terms of two (thermal and concentration) Rayleigh numbers. Laboratory experiments were performed using holographic interferometry and thermocouple techniques. Experimental holograms were processed numerically in order to calculate the space distribution of the refractive index in relation to temperature and vapor concentration. The results show that the difference between moist convection and dry convection can be measured even in the absence of evaporation and condensation. The experimental interferograms for dry air (intentionally dried up to 4 % relative humidity) are given. The justification of this research requires an additional quantitative comparison with the measurements obtained for humid air (with 100 % relative humidity) undergoing the first-order phase transition of the “gas-liquid” type.

Snap-shot topography measurement via dual-VCSEL and dual wavelength digital holographic interferometry

In this paper, we propose a dual-wavelength digital holographic interferometry method based on a compact dual vertical-cavity surface-emitting laser (VCSEL) source. The source simultaneously emits light from two highly stabilized coherent light sources with slightly different wavelengths. A highly stabilized and adjustable current source enables the application of digital holographic dual-wavelength techniques to measure the shape of an object with height steps of a few millimeters. The wavelength drift over 12 h over the entire measurement range, which was evaluated using a wavemeter, was smaller than 1 pm. In addition to the low measurement uncertainty at large height jumps, the dual-wavelength digital holographic system distinguishes itself by its robustness to environmental disturbances such as air turbulence, heat load, and/or mechanical vibrations. This is enabled via a fiber-based almost common-path single-shot digital holographic acquisition of the information of the two different wavelengths using angular multiplexing. The experimental setup and data evaluation are discussed, and we present measurements of non-cooperative objects with specular reflective and/or diffuse reflective surfaces having different colors.

Simultaneous measurement of cloud microphysical parameters based on digital holographic interferometry

Investigation of cloud microphysical is of great significance in deepening the understanding of the radiation energy budget, water cycle process, and precipitation mechanism, and improving the scientificity and effectiveness of artificial precipitation. Especially under the action of turbulence, in addition to shear and inertia, the turbulence in the cloud will accelerate the collision of cloud droplets through vortex superposition. The above process will further complicate the cloud microphysical characters. At present, the methods of measuring cloud microphysical parameters based on light scattering, collision and imaging theories encounter bottlenecks: the inversion process needs to make the assumptions about cloud droplet spectrum and particle characteristics, the impact process will destroy particle characteristics, and the three-dimensional characteristics of cloud particles cannot be obtained. Because of its many advantages, such as fast, real-time, non-destructive, non-invasive, high-resolution, full-field optical measurement, etc., in-line digital holographic interferometry is considered as a new potential tool for the dynamical measurement of cloud microphysical property. In particular, the mutual interference between the particle image and twin image is small under far-field recording conditions. In this paper, the measurement method of the on-line digital holographic interferometry based on interference theory, combining optical information processing, depth of field compression, and gray gradient variance technology of fusion holograms, is investigated. This method, with a <i>z</i>-axis position accuracy of 0.01 mm and system resolution of 2 μm, is employed for simultaneously and finely detecting the cloud droplet spectrum, cloud particle diameter, and number concentration. In the experiment, the liquid droplet with a median diameter of 3.9 μm, produced by the ultrasonic atomizer, is used as an example of the cloud particle. The measurement results are consistent with realistic scenario. By using a high speed charge coupled device or complementary metal oxide semiconductor camera, this method can solve the technical bottleneck of three-dimensional fine characteristics of cloud particle in airborne measurement by using cloud droplet spectrometer. It can provide effective support for the research of liquid water in the cloud, entrainment, condensation, collision, and temporal and spatial evolution laws. In addition, it has reference significance for the study of particle dynamics. Simultaneously, this method provides a feasible solution for the measurement of cloud in land-based and airborne platforms.

Determination of Deformation Fields of Diffuse Objects by Phase-Shifting Digital Holographic Interferometry

A modification of the method of digital holographic interferometry for the determination of deformations of an object with a diffuse surface by comparing two complex wavefronts reflected from the object at its two different states is considered. The difference of the proposed method with classical digital holography methods is that digital holograms by which the images are reconstructed have complex values determined by the phase shift method (‘‘complex’’ hologram), while classical digital holograms have only real values. Besides, digital holograms are reconstructed with allowance for inhomogeneity of the reference beam, which improves the reconstruction quality. For this purpose, a tunable neutral optical filter is introduced into the reference arm of the optical scheme of the interferometer. The method is verified experimentally.

Noise and bias in off-axis digital holography for measurements in acoustic waveguides.

This paper discusses noise and bias in the method of holographic interferometry applied to the study of acoustics phenomena. The influence of noise on the measurement of acoustic pressure is described by an analytical approach. Relationships to quantify the minimum measurable fluid density and acoustic pressure are given by taking into account the experimental parameters of the setup. These parameters are related to the spatial bandwidths, number of electrons in pixels, readout noise, and quantization noise. Experimental results show that theoretical relations are relatively close to experimental data and that the lower pressure measurement limit is on the order of 15 Pa for the acoustics pressure. The case of waveguides excited by an internal or external acoustic source is investigated. Specifically, for the case of studies in thermoacoustics, this paper demonstrates that the parasitic coupling of vibrations can be compensated. The proposed method is based on the determination of the amplitude and phase of the parasitic oscillation, requiring a few assumptions related to the physics of the underlying phenomenon. Successful compensation is obtained and yields experimental data in agreement with the theoretical predictions.

СВОБОДНЫЕ КОЛЕБАНИЯ ЛОПАТОК ОСЕВОГО КОМПРЕССОРА ГАЗОТУРБИННОГО ДВИГАТЕЛЯ

The required level of reliability of modern gas turbine engines cannot be achieved without ensuring the vibrational strength of the compressor blades. One of the tasks of ensuring vibrational strength is to determine the frequency spectrum of free vibrations, as well as the arising forms of vibrations. Moreover, the most reliable results are achieved by combining experimental and theoretical research methods. Experimental studies of the free vibrations of the blades were carried out by the time-dependent holographic interferometry method. A description of the experimental stand is given, the features of using optical equipment and processing units are indicated. The implemented algorithm for conducting experimental studies is described, the features of the digitization of optical signals implemented in the developed software are indicated, the mathematical equations used in the implementation of this software are presented, and some emerging experimental forms are illustrated. To verify the experimental data based on the finite element method, an updated mathematical model of the free vibrations of compressor blades has been developed. The characteristics of the finite element from which the mathematical model is formed, the basic equations used in the simulation of free vibrations are given. As an object of study, we considered a compressor blade 54 mm high and 37 mm long chord with a peripheral section twist angle of 17°, the considered blade is made of a titanium alloy. For this blade, some waveforms were obtained, the location of the nodal lines was shown, and data obtained experimentally and analytically were compared. An analysis was made of the frequency spectrum of the natural oscillations of the compressor blades, which showed that the difference between the vibration frequencies obtained by experimental and numerical methods for the same modes does not exceed 5 %.

Measuring tooth vibrations induced during cavity preparation with time-averaged holography and its influence on near vision acuity in dentists.

The aim of this study was to quantify vibrations and their influence on visual acuity. The study consisted of two parts, laboratory and clinical. Time-averaged holographic interferometry (TAHI) method was used in laboratory for measuring the amplitude of tooth vibrations induced by dental handpiece. The amplitudes of tooth vibrations were measured for the three diameters and three speeds. The larger diameter coupled with increasing speed resulted in greater vibration amplitudes, whereby a maximum amplitude of less than one micrometer was detected. For quantifying the natural visual acuity for the corresponding tooth vibrations, we have used the clinical condition approach with miniaturized Snellen optotype as an assessing tool. Central visual acuity did not display variance in visual acuity at rest or under load. Results indicate that the vibrations induced during cavity preparation are not sufficient to negatively affect visual acuity of dentists.

Application of holographic interferometry in the analysis of stress states in a crack root area.

This paper deals with the visualization and analysis of interaction of a cutting wedge disintegrator with plastic at low loads. For exploratory research, a contactless optical holographic interferometry method was used, allowing a comprehensive picture of the stress state when opening microcracks. An experimental model was set up for the purposes of the research. The structure of the model as well as its geometric parameters had to comply with the applied optical method. The method of holographic interferometry enabled us to record even the initial stages of the crack. Pictures of holographic interferograms allowed us to observe stress fields on the cutting wedge as well as on the loaded body in the form of interference fringes. In order to record the interferograms, we used the method of two exposures so that we gained double-exposure interferograms, which represent the state of the object during the second exposure. The first exposure was caused by superposition of object-related and reference wave after the object was subjected to a load; the second exposure occurred after the load was removed. We used quantitative analysis to determine stress intensity coefficients from holographic interferograms as followed by the calculation of stresses with respect to axes $x$x and $y$y. The analysis was done for loading forces 1.57 N and 3.14 N. As the load applied to the cutting material was increasing, the density of interference fringes was increasing, too.

Изучение деформирования бетона методами голографической интерферометрии

Изучение деформирования бетона методами голографической интерферометрии