Electronic Speckle Pattern Interferometer Research Articles

Higher-order shear deformation theory for accurate prediction of vibration behavior of thick piezoelectric disks and design of efficient surface electrodes

A modified higher-order shear deformation plate theory (MHSDT) is proposed to predict the resonance frequencies and related mode shapes of piezoelectric disks of various thicknesses. The theory explicitly accounts for the effects of the electrical potential on the displacement of the disk. The equations of motion for the disk are derived using Hamilton's principle in conjunction with a variational approach. It is shown analytically that the distribution of the electrical field on the surface of the disk is quantitatively similar to the distribution of the sum of the total stresses within the disk. Thus, the deformation of the disk can be approximated directly from the stress distribution on the disk, thereby greatly simplifying the solution process. The validity of the proposed MHSDT is confirmed by comparing the solutions for the natural frequencies, displacement fields, and electric field distributions of the disk for various radius-to-thickness ratios and boundary conditions with those obtained using Reddy’s third-order plate theory and COMSOL finite element simulations, respectively. The results show that the solutions obtained from the MHSDT method are consistently closer to the exact solutions than those determined using Reddy’s third-order method. Finally, the linear relationship between the electric field and the flexural displacement of the disk is leveraged to design surface electrodes capable of exciting specific flexural mode shapes of the disk under a free boundary condition. The efficiency of the designed electrodes is experimentally demonstrated using an amplitude-fluctuation electronic speckle pattern interferometer (AF-ESPI).

Investigation into Vibration Excitation and Mode Selection of Thin Rectangular Plates with Multiple Bolts and Stand-Off Supports

The flexural vibrations of a thin rectangular plate with multiple rigid-point supports were examined theoretically, numerically, and experimentally. The analytical resonant frequencies and mode shapes obtained via the superposition method were compared with the finite element method (FEM) solutions. Experimental measurements were obtained using an amplitude-fluctuation electronic speckle pattern interferometer (AF-ESPI). The investigations considered two boundary conditions: (1) a completely free rectangular plate with one bolt and stand-off support at the center and (2) a rectangular plate with five bolts and stand-off supports along the short edge. In both cases, the plate was actuated using four macro-fiber composites (MFCs). The vibration characteristics of the plate varied significantly with the number and position of the rigid-point supports and the configuration of the MFC driving voltage. An analytical solution is proposed for frequency selection and mode control through the strategic placement of the rigid-point supports. The proposed solution provides a simple and efficient approach for controlling the vibration mode of the plate in various applications, such as vibration suppression, energy harvesting, and structural health monitoring.

Accurate Dynamic Electromechanical Solution for Rectangular Piezoelectric Plate Based on Modified FSDT

In this study, the modified first-order shear deformable theory (FSDT) is applied to analyze the resonant characteristics of piezoelectric (PZT) moderately thick plate vibrators with different thicknesses. A simple and straightforward simplification method between mechanical and electrical functions is also proposed based on the modified FSDT. The natural frequencies and associated mode shapes of piezoelectric plates with completely free boundary are analyzed. The displacement fields of the flexural modes are presented based on the superposition method. This analytical method provides a strong-form novel solution for the flexural-dominated motion’s out-of-plane and in-plane coupling displacement fields. The solutions of displacement functions, which are obtained from the superposition method, show excellent convergence for numerical calculation. To verify the validity of the theoretical solution, the resonant frequencies and the corresponding mode shapes are compared with that obtained by the finite element method (FEM) and experimental measurements using the amplitude-fluctuation electronic speckle pattern interferometer (AF-ESPI) technique. According to the electromechanical formula and the derived theoretical solution, four types of electrode are designed to excite the moderately thick PZT specimen for examining the application feasibility of the proposed method. It is shown in this study that the theoretical analysis, numerical calculation, and experimental measurement are fully compared, and excellent agreements of the piezoelectric moderately thick plate are also obtained.

Building an electronic speckle pattern interferometer to visualize modal shapes in an educational setting

An electronic speckle pattern interferometer (ESPI) is an optical system used to investigate vibrating objects and can be a great educational tool for visualizing mode shapes. At the Pennsylvania State University, the Acoustical Society of America student chapter acquired funds to build an ESPI for classroom and outreach use. The design of the ESPI was based on previously published work using equipment purchased for less than $5000. To approach this project, students were split into two groups where one developed a MATLAB application to collect and process images while the other arranged the optical components of the ESPI. To test the system, interferometry was performed on a banjo head which matched mode shapes found using a scanning Laser Doppler Vibrometer (LDV). Future work includes adapting our ESPI system to obtain images in real-time, developing educational demos involving the ESPI, and further refining the MATLAB application. This presentation provides a model for a multi-disciplinary project that could be implemented at the undergraduate or graduate level.

Stress Dependence on Relaxation of Deformation Induced by Laser Spot Heating.

This paper deals with a non-destructive analysis of residual stress through the visualization of deformation behaviors induced by a local spot heating. Deformation was applied to the surface of an aluminum alloy with an infrared spot laser. The heating process is non-contact, and the applied strain is reversible in the range of room temperature to approximately +10 °C. The specimen was initially pulled up to elastic tensile stress using a tensile test machine under the assumption that the material was subject to the tensile residual stress. The relaxation behaviors of the applied strain under tensile stress conditions were evaluated using contact and non-contact methods, i.e., two strain gauges (the contact method) and a two-dimensional electronic speckle pattern interferometer (non-contact method). The results are discussed based on the stress dependencies of the thermal expansion coefficient and the elasticity of the materials.

Scoliosis Brace Finite Element Model and Preliminary Experimental Testing Using Electronic Speckle Pattern Interferometry

This article presents the results of numerical finite element method (FEM) simulations in the Ansys environment of a Boston orthopaedic brace. The geometric model was developed based on the results of digitisation performed by means of a three-dimensional (3D) optical scanner. A test stand for measurement of the brace’s field of displacements, utilising a laser electronic speckle pattern interferometer (ESPI), was used to experimentally verify the FEM model. During experimental testing, special attention was given to applying the loads and boundary conditions used in the numerical simulations. As a result, the relative difference between the experimentally and numerically determined displacements in the central part of orthoses amounted to approximately 0.6%. The experimentally verified FEM model was used to determine the force flow lines characteristic of the brace, indicating the general working method of the brace’s structure. The primary parts of the orthoses, carrying loads correcting the spine and the position of sites exerting little effort from the perspective of their participation in the orthoses’ essential therapeutic application were identified. The results obtained allow for the proposal of methods for mechanical optimisation of the brace’s design. The analysis conducted is universal in nature and can be adapted to other types of orthopaedic braces.

Hooke’s law experiment using an electronic speckle pattern interferometry

This paper presents an approach based on a laser interferometer set-up to perform an experimental study of Hooke’s law for the case of the bending of a cantilever beam. We used weights and a pulley to deform the beam laterally and measured displacement with an electronic speckle pattern interferometer (ESPI). The ESPI set-up was built using items commonly found in an undergraduate optics laboratory and the software used for the measurement as presented in this paper is available for anyone to use. This represents an attempt at content development with an ESPI; development of various types of content with ESPIs can broaden the horizons of higher education and enhance classroom environments.

Variations on the common electronic speckle pattern interferometer

Electronic speckle pattern interferometry is often used to visualize deflection shapes of vibrating objects. We discuss variations on this common laboratory technique, emphasizing unique applications as well as methods for reducing the cost and complexity of theexperimental arrangement.

Visualization of Acoustic Standing Waves in a Closed Pipe Based on an Electronic Speckle Pattern Interferometer

We visualize acoustic standing waves supported in a closed-end square pipe based on an electronic speckle pattern interferometer and measure the wavelengths of the acoustic standing waves for undergraduate physics lab courses. Generating four acoustic standing waves of frequencies below the cutoff frequency governed by the physical dimensions of the pipe, we obtain the distribution of the irradiance difference of the speckle patterns in the interferogram and compare that to the result of a theoretical calculation. In addition, we estimate the wavelengths of the acoustic standing waves by measuring the distances between adjacent nodes of the speckle patterns. We show that the experimental results and the results of the theoretical calculations are in good agreement. This work facilitates the understanding of electronic speckle pattern interferometers and their applications in visualizations of acoustic waves for undergraduate physics laboratories.

Application of speckle interferometry to the mechanical characterization of a biopolymer sample.

In this work, we present an optical and mechanical characterization of the behavior of an inhomogeneous biopolymer sample through the use of an in-plane electronic speckle pattern interferometer with a pulling system along the $y$y direction. The characterization of the sample subjected to stress comprised the acquisition of speckle patterns for 1360 states. Displacement maps and their corresponding strain maps were computed for every state. Since the information of the maps changes with size due to the sample being pulled at the upper end while it is clamped at the lower end, a scaling method to relate the maps to each other, point-to-point, is presented. The method allows the correct evaluation of sequential strain maps, which depicts the mechanical evolution of the material. Upon managing to relate the strain maps, it is possible to extract strain values for zones of interest from every map in order to build the respective stress-strain curves. Three stress-strain curves associated with three zones in the sample (upper, middle, and bottom) are constructed. When sequential displacement and deformation maps are optically obtained by the interferometer, we present a full-field characterization, along with the obtention stress-strain curves associated with the three zones of strain maps. The curves represent the inhomogeneous performance of the sample. Three different elastic moduli (${E_u} = 2.59\;{\rm MPa}$Eu=2.59MPa, ${E_m} = 1.97\;{\rm MPa}$Em=1.97MPa, and ${E_{b}} = 1.67\;{\rm MPa}$Eb=1.67MPa), associated with three respective zones, were obtained. The experimental results for a biopolymer sample here presented show that the technique, in conjunction with the scaling method, is a novel proposal to characterize inhomogeneous materials.

Effect of Residual Stress on Thermal Deformation Behavior.

This paper discusses a non-destructive measurement technique of residual stress through optical visualization. The least amount of deformation possible is applied to steel plates by heating the specimens +10 °C from room temperature for initial calibration, and the thermal expansion behavior is visualized with an electronic speckle pattern interferometer sensitive to two dimensional in-plane displacement. Displacement distribution with the thermal deformation and coefficient of thermal expansion are obtained through interferometric fringe analysis. The results suggest the change in the thermal deformation behavior is affected by the external stress initially applied to the steel specimen. Additionally, dissimilar joints of steel and cemented carbide plates are prepared by butt-brazing. The residual stress is estimated based on the stress dependence of thermal expansion coefficient.

A Device for Calibration of Electronic Speckle Pattern Interferometers

A calibration device intended for metrological assurance of instruments used to measure deformations and displacements by methods of electronic speckle interferometry and shearography is developed. The optical methods presented here may be applied to different types of materials possessing rough surfaces. The proposed device reproduces stress-strain states by means of elastic deformation of the surface of a membrane through the use of a rod and leverage. Calibration of the device is performed, its transfer characteristics are investigated, and the nonlinearity of the displacement of the surface of the membrane is estimated. Results of experiments designed to measure the stress-strain state with the use of the noncontact method of shearography are presented. The phase image produced by deformation of the membrane is described and the metrological characteristics of the calibrated device are estimated. It is shown that through the use of the present calibration device it is possible to use optical methods not only for qualitative assessment of the deformation of objects of complex shape, but also for quantitative estimation of the geometric characteristics of these objects.

Relative error in out-of-plane measurement due to the object illumination.

In this work the sensitivity vector is analyzed for collimated and divergent oblique illumination for an out-of-plane arrangement. In the case of collimated illumination, the variation of the sensitivity vector components was considered and a geometric model was proposed for its evaluation. The geometry of the optical setup used allowed us to find sensitivity mostly along the pulling direction; the other two components of the sensitivity vector were relatively small. We measured the displacement induced only along the pulling direction. Errors in the displacement measurement associated with divergent and collimated illumination can be predicted when the sensitivity vector is considered constant. Experimental and theoretical results are presented for the out-of-plane electronic speckle pattern interferometer. The analyzed object was an aluminum plate.

Sub-picometer dynamic measurements of a diffuse surface.

Future space observatory missions are forecasting the need for sensing and controlling wavefront error and system alignment stability to picometer scale. Picometer stability performance demands precision knowledge of the mirror and metering structure materials to the same degree. A high-speed electronic speckle pattern interferometer was designed and built to demonstrate measurements of both static and dynamic responses of picometer amplitudes in materials of diffuse surface subjected to very low energy disturbances. This paper describes the details of a test to impart a dynamic disturbance of picometer scale and measure the response of a composite material. The results of the test are also reported and show conclusively that sub-picometer scale effects can be accurately measured in an open test environment outside a vacuum chamber.

Device for calibration of electronic speckle pattern interferometers

Device for calibration of electronic speckle pattern interferometers

Monitoring of Cytotoxic Induced Cellular Displacements by Utilizing Electronic Speckle Pattern Interferometry

Modern medical science delivers through innovative chemical or mechanical/physical means new strategies to treat patients mildly and fight diseases accurately. In line with this development a screening procedure for tissue samples under usage of the electronic speckle pattern interferometry is developed at the University of Applied Science Wildau. The paper at hand provides the corner stone for such a procedure in form of an incubation system that is adapted to the properties of an electronic speckle pattern interferometer and allows the incubation as well as study of samples over time. As a result the developed system can regulate its own temperature and is constructed for use in an electronic speckle pattern interferometry (ESPI) setup. Its design allows a simple modular approach for further development

Online 3D Displacement Measurement Using Speckle Interferometer with a Single Illumination-Detection Path.

Measurement systems for online nondestructive full-field three-dimensional (3D) displacement based on the single-shot and multiplexing techniques attract more and more interest, especially throughout the manufacturing industries. This paper proposes an accurate and easy-to-implement method based on an electronic speckle pattern interferometer (ESPI) with single illumination-detection path to realize the online nondestructive full-field 3D displacement measurement. The simple and compact optical system generates three different sensitivity vectors to enable the evaluation of the three orthogonal displacement components. By applying the spatial carrier phase-shifting technique, the desired information can be obtained in real time. The theoretical analysis and the measurement results have proven the feasibility of this ESPI system and quantified its relative measurement error.

Quantification of nanoscale deformations using electronic speckle pattern interferometer

Quantification of deformations using electronic speckle pattern interferometer is a well known technique. Usually, deformation size probed by this technique ranges in tens of microns. This paper reports quantification of nanoscale mechanical deformations in metal plates using a low cost optical phase shifter in an electronic speckle pattern interferometer.

A multi-camera speckle interferometer for dynamic full-field 3D displacement measurement: Validation and inflation testing of a human eye sclera

We developed and optimized a custom dynamic Electronic Speckle Pattern Interferometer (d-ESPI) for measuring time-dependent three-dimensional (3D) surface displacements during inflation testing of ocular tissues. The 3D displacement field was resolved under dynamic loading conditions for a simplified test case of a rubber phantom and a real-world test case of the posterior sclera of a human eye. We present the optical layout and calibration procedure of the d-ESPI, and demonstrate how the displacement field can be accurately resolved for specimen deformation rates up to 6 μm/s.

Impact of multiple usages of digital filters on speckle contrast and phase maps

Various digital filters have been use to remove unwanted noise in speckle pattern used in the field of Electronic speckle pattern interferometer (ESPI). However, multiple usages of these digital filters can contribute to significant drop in speckle contrast leading to loss of phase information. This paper reports effect of multiple usages of various digital filters namely, Median, Gaussian and Average on the speckle contrast and ultimately on the phase maps. This study also compares effectiveness of these three digital filters in removing noise from speckle patterns.