Showing papers on "Displacement (vector) published in 1998"

Submicron deformation field measurements: Part 2. Improved digital image correlation

Abstract: This is the second paper in a series of three devoted to the application of scanning tunneling microscopy (STM) to mechanics problems. In this paper, improvements to the digital image correlation method are outlined, a technique that compares digital images of a specimen surface before and after deformation to deduce its two-dimensional surface displacement field and strains. The necessity of using the framework of large deformation theory for accurately addressing rigid body rotations to reduce associated errors in the strain components is pointed out. In addition, the algorithm is extended to compute the three-dimensional surface displacement field from STM data; also, significant improvements are achieved in the rate as well as the robustness of the convergence. For (STM) topographs, the resolution yields 4.8 nm for the in-plane and 1.5 nm for the out-of-plane displacement components spanning an area of 10 μm×10μm.

Positioning device having two object holders

Abstract: A positioning device has first and second object holders that are guided over a guiding surface extending parallel to an X-direction and parallel to a Y-direction perpendicular to the X-direction and which are displaceable over the guiding surface from a first position into a second position by means of a displacement system. The displacement system includes a first displacement unit and a second displacement unit to which the object holders can be alternately coupled. The first displacement unit is suitable for carrying out a first series of positioning steps of the first object holder in the first position and for displacing the first object holder from the first position into an intermediate position between the first and second positions. The second displacement unit is suitable for carrying out a second series of positioning steps of the second object holder in the second position, simultaneously with and independently of the first displacement unit, and for displacing the second object holder from the second position into the intermediate position. In the intermediate position, the object holders are exchanged, after which the first series of positioning steps can be carried out by the first displacement unit with the second object holder in the first position and the second series of positioning steps can be carried out by the second displacement unit with the first object holder in the second position. The positioning device is suitable for use in a lithographic device to carry out an exposure process with a first semiconductor substrate in an exposure position and, simultaneously therewith and independently thereof, a characterization process with a second semiconductor substrate in a characterization position.

Residual Displacement Response Spectrum

Abstract: Structures subjected to strong earthquake ground shaking may be left in a displaced condition. The amount of this residual or permanent displacement is determined by structural characteristics, including mass and hysteretic behavior, as well as ground motion. Residual displacement is undesirable because it presents problems during repair and reconstruction after an earthquake. This paper describes analyses of many single-degree-of-freedom bilinear oscillators, with different natural periods, damping ratios, ductility factors, bilinear factors, and input ground motions. These analyses were carried out in order to obtain a method of estimating the likely residual displacements of real single-degree-of-freedom structures. The residual displacement was normalized by the maximum possible residual displacement. Although there was scatter in the normalized residual displacement for different earthquake records, trends in behavior were dominated by the slope of post-yielding branch of bilinear loop. A residual di...

The effects of topography on magma chamber deformation models: Application to Mt. Etna and radar interferometry

Abstract: We have used a three-dimensional elastic finite element model to examine the effects of topography on the surface deformation predicted by models of magma chamber deflation. We used the topography of Mt. Etna to control the geometry of our model, and compared the finite element results to those predicted by an analytical solution for a pressurized sphere in an elastic half-space. Topography has a significant effect on the predicted surface deformation for both displacement profiles and synthetic interferograms. Not only are the predicted displacement magnitudes significantly different, but also the map-view patterns of displacement. It is possible to match the predicted displacement magnitudes fairly well by adjusting the elevation of a reference surface; however, the horizontal pattern of deformation is still significantly different. Thus, inversions based on constant-elevation reference surfaces may not properly estimate the horizontal position of a magma chamber. We have investigated an approach where the elevation of the reference surface varies for each computation point, corresponding to topography. For vertical displacements and tilts this method provides a good fit to the finite element results, and thus may form the basis for an inversion scheme. For radial displacements, a constant reference elevation provides a better fit to the numerical results.

Coupled B-snake grids and constrained thin-plate splines for analysis of 2-D tissue deformations from tagged MRI

Abstract: Magnetic resonance imaging (MRI) is unique in its ability to noninvasively and selectively alter tissue magnetization and create tagged patterns within a deforming body such as the heart muscle. The resulting patterns define a time-varying curvilinear coordinate system on the tissue, which the authors track with coupled B-snake grids. B-spline bases provide local control of shape, compact representation, and parametric continuity. Efficient spline warps are proposed which warp an area in the plane such that two embedded snake grids obtained from two tagged frames are brought into registration, interpolating a dense displacement vector field. The reconstructed vector field adheres to the known displacement information at the intersections, forces corresponding snakes to be warped into one another, and for all other points in the plane, where no information is available, a C/sup 1/ continuous vector field is interpolated. The implementation proposed in this paper improves on the authors' previous variational-based implementation and generalizes warp methods to include biologically relevant contiguous open curves, in addition to standard landmark points. The methods are validated with a cardiac motion simulator, in addition to in-vivo tagging data sets.

Analysis and design of an interdigital cantilever as a displacement sensor

Abstract: conventional cantilever used in the atomic force microscope ~AFM!. In this paper we present a detailed analysis of the interdigital cantilever and its use as a sensor for the AFM. In this study, we combine finite element analysis with diffraction theory to simulate the mechanically induced optical response of the ID. This model is used to compare this system with the optical lever detector as used in conventional instruments by analyzing the ratio of signal to noise and overall performance. We find that optical detection of the cantilever motion with interdigital fingers has two advantages. When used in conjunction with arrays of cantilevers it is far easier to align. More importantly, it is immune to laser pointing noise and thermally excited mechanical vibrations and this improves the sensitivity as compared to the optical lever. © 1998 American Institute of Physics. @S0021-8979~98!07112-6#

Long-range AFM profiler used for accurate pitch measurements

Abstract: A long-range atomic force microscope (AFM) profiler system was built based on a commercial metrology AFM and a home-made linear sample displacement stage. The AFM head includes a parallelogram-type scanner with capacitive position sensors for all three axes. A reference cube located close to the tip acts as the counter electrode for the capacitive sensors. Below this metrology AFM head we placed a linear sample displacement stage, consisting of monolithic flexures forming a double parallelogram. This piezo actuated stage provides a highly linear motion over m. Its displacement is simultaneously measured by a capacitive position sensor and a differential double-pass plane mirror interferometer; both measuring systems have subnanometre resolution capability. For the measurement of periodical structures two operating modes are possible: a direct scanning mode, in which the position of the displacement stage is increased point by point while the AFM head measures the height, and a combined scanning mode where the displacement stage produces offsets which are multiples of the pitch to be measured while the AFM head is simultaneously scanning to locate an edge or a line centre position. Construction details, system characteristics and results from first pitch measurements are presented. The estimated relative combined uncertainties for pitch values on different standards are in the range to . Laser diffraction measurements of comparable uncertainty were performed on the same standards and show a very good agreement.

Measurement of in-plane surface strain by hologram interferometry

Abstract: It is shown that the interference fringe patterns obtained by hologram interferometry provide information about surface displacement resolved in one direction only. By recording holograms of the surface from different viewpoints and operating numerically upon the fringe order numbers at corresponding points on the surface, it is possible to measure the displacement in any chosen direction. As an example, the strain in the plane of a stretched metal foil was measured by recording two `frozen-fringe' holograms simultaneously and subtracting one set of fringe contours from the other.

A Unified Approach to Sensitivity Analysis in Equilibrium Displacement Models

Abstract: In this article a unified approach for doing sensitivity analysis in equilibrium displacement models is presented that extends the existing method and overcomes many of its deficiencies. An empirical example from Gardner's seminal article highlights the advantages of the approach presented here.

Catheter simulation device

Abstract: A device for tracking the translational and rotational displacement of an object having two degrees of freedom using a single point of contact with the object. The device is particularly useful in a catheter simulation device for surgery and interventional radiology applications. A spherical contact member is mounted for free rotation about all axes in force-transmitting contact with the surface of the object and a pair of shafts are mounted in tangential engagement with the spherical member to reflect the displacement imparted to the object relative to a reference position. This arrangement provides simultaneous tracking of the combined translational and rotational displacement of the object. Measuring the displacement of the object and a haptic applicator are included such that a load may be applied to the object to precisely control the degree of force required to cause displacement of the object. The actual forces applied to displace the object are also measured such that the device is capable of providing a realistic force reflection to simulate the feel of a surgical procedure, for example. A computerized control system and conventional recording device are employed to provide a programmed procedure which provides realistic "feel" to a user of an actual surgical procedure. The device is readily adaptable for interfacing with a virtual reality type program to simultaneously provide a visual simulation of the surgical procedure.

A theoretical analysis of the bifurcated fiber bundle displacement sensor

Abstract: An optical displacement sensor using bifurcated fiber bundle technology is investigated here from a theoretical perspective. A purely geometrical approach and an electromagnetic Gaussian beam approach are developed for determining the transfer function of the sensor. A sensitivity analysis is also presented and discussed.

Thermoelastic Interactions without Energy Dissipation Due to a Point Heat Source

Abstract: The linear theory of thermoelasticity without energy dissipation is employed to study thermoelastic interactions due to a continuous point heat source in a homogeneous and isotropic unbounded solid. The Laplace transform method is employed to solve the problem. Exact expressions, in closed form, for the displacement, temperature and stress fields are obtained. Numerical results for a copper-like material are presented.

Theory of speckle displacement and decorrelation: application in mechanics

Abstract: This paper describes the theory of determination of small deformation tensor by means of the method, availing of statistical properties of the speckle field in an optically free space geometry or in a near image field. The small deformation tensor and a correlation function are briefly mentioned, and the main emphasis is aimed on theoretical derivation of the relationship between the correlation function of two speckle intensities, being recorded before and after deformation. This results in the relationship theoretically enabling a determination of all components of the small deformation tensor by means of a relatively simple optical arrangement in connection with computer and linear CCD detectors. Further, a compilation of all completed experimental results are briefly mentioned. An accuracy and sensitivity of this measurement methods are analyzed by theory of errors. As it flows from theory, the exact results at stress deformation, body displacement and rotation depend in crucially upon the geometrical arrangement of the optical system. The emphasis on the analysis of accuracy and sensitivity of individual geometrical parameters of assembly are given, with the aim to find an optimized geometry of experimental arrangement. The feasibility of an easy realization in practice and most importantly achieving satisfactory results of measurements are the important criteria. The conclusion presents some results obtained at concrete measurement with proposed experimental assembly.

A nonlinear model for analysis of slug-test data

Abstract: While doing slug tests in high-permeability aquifers, we have consistently seen deviations from the expected response of linear theoretical models. Normalized curves do not coincide for various initial heads, as would be predicted by linear theories, and are shifted to larger times for higher initial heads. We have developed a general nonlinear model based on the Navier-Stokes equation, nonlinear frictional loss, non-Darcian flow, acceleration effects, radius changes in the well bore, and a Hvorslev model for the aquifer, which explains these data features. The model produces a very good fit for both oscillatory and nonoscillatory field data, using a single set of physical parameters to predict the field data for various initial displacements at a given well. This is in contrast to linear models which have a systematic lack of fit and indicate that hydraulic conductivity varies with the initial displacement. We recommend multiple slug tests with a considerable variation in initial head displacement to evaluate the possible presence of nonlinear effects. Our conclusion is that the nonlinear model presented here is an excellent tool to analyze slug tests, covering the range from the underdamped region to the overdamped region.

Moving loads on a plate on elastic foundation

Abstract: A number of studies have been conducted recently to find the dynamic response of multilayered media as models of pavement systems to moving loads. The dynamic response of an infinite plate on an elastic foundation subjected to constant amplitude or harmonic moving loads was investigated. The advance velocity was assumed to be constant. Formulations were developed in the transformed field domain using a double Fourier transform in space and moving space for moving constant loads; a triple Fourier transform in time, space, and moving space to include the initial application of the load for moving harmonic loads; and a double Fourier transform in space and moving space for the steady-state response to moving harmonic loads. The effects of velocity, load frequency, and damping on the deflected shape, and the maximum displacement were investigated. The critical (resonant) velocities and frequencies were obtained by analyses, and expressions to find them were suggested. The effect of multiple loads on the maximum displacement was also investigated. The variation of the maximum dynamic displacement was affected by the distances and the differences in phase between the loads.

Flows and Horizontal Displacements from Ring Diagrams

Abstract: A new algorithm for analyzing ring diagrams from helioseismic data is presented. This method is applied to two months of Solar and Heliospheric Observatory/Michelson Doppler Imager data from 1996 May 24 through July 24 to study flows and to measure the ratio of the horizontal displacement to the vertical displacement for the oscillations. We find that (1) the rotation rate agrees well with that measured from global modes, extending the measurements closer to the surface; (2) there is a 20 m s-1 poleward meridional flow; (3) there are medium-scale velocity features persisting for several days; (4) the radial gradient of the near surface rotation rate decreases with latitude; and (5) meridional flow decreases with depth. The measured horizontal-to-vertical displacement ratio is in agreement with that expected from theoretical considerations.

Large in-plane displacement measurement in dual-beam speckle interferometry using temporal phase measurement

Abstract: Measurement of in-plane displacements of a diffuse object by observing the temporal fluctuation of the speckle pattern in a dual-beam illumination speckle interferometer is illustrated. To conceive the temporal changes the object is displaced in its plane continuously. A high-speed camera is used to acquire a number of frames of the image of the object motion sequentially. Through Fourier transformation and inverse Fourier transformation of the frames stacked together, the total phase is determined. Finally, the magnitude of the in-plane displacement of the object motion is extracted. The range of displacement that can be measured using this novel method lies between few microns and over 100 μm on the upper end. Theory together with experimental results are presented in this paper.

Three dimensional single-particle tracking with nanometer resolution

Abstract: We have developed a method for three dimensional (3D) tracking of polystyrene spheres with nanometer resolution. The detection technique is based on measuring the displacement of a polystyrene sphere positioned in the center of a laser beam just behind the focus. A change in the lateral position of the sphere causes a deflection of the beam which can be measured using a position sensitive detector. A change in the axial position of the sphere causes a shift in the axial position of the focus behind another lens, which can be measured using an overfilled photodiode. A feedback system is used to keep the sphere in the center of the laser beam to avoid the influence of lateral displacements on the detection of the axial position. Spatial resolution for a 0.92 μm polystyrene sphere was better than 1 nm in three dimensions using a sampling rate of 1 kHz. This method was applied to track spheres bound to adhesion molecules LFA-1 expressed at the surface of living cells. It turned out to be a useful method to accurately measure the 3D trajectory of biological molecules on cells in real time.

System for determination of a location in three dimensional space

Abstract: An optical improvement for angular position sensors, which may be used to determine the spatial coordinates of a small source of light (or other energy) in a 3-dimensional volume. Such sensors normally include a linear photosensitive image detector such as a photodiode array or a charge-coupled device (CCD). An irregular pattern of parallel slits is described which increases the amount of light gathered while avoiding the undesirable characteristics of lens optics for this application. One optimal type of irregular pattern is the uniformly redundant array. A mathematical correlation function together with a polynomial interpolation function can determine the displacement of the image on the detector and thereby the location of the source relative to one angular dimension. Given the locations and orientations of several sensors in a 3-dimensional coordinate system and given the angles measured by each, the location of the point source can be computed.

Electronic device for processing image-data, for simulating the behaviour of a deformable object

Abstract: The invention concerns an electronic device comprising a user interface with force feedback (4) corresponding to a tool reactions, a 'collision' module (18) for estimating a point of intersection between a straight line embodying a displacement derived from the action of the tool and the surface mesh generation of a given object, and an internal forces module (16) which elaborates an internal forces field of between nodes of at least a part at least of the object volume mesh generation from the displacement applied on the nodes pertaining to the surface mesh generation containing the point of intersection, limit conditions, and node tensors and link tensors derived respectively for each node and each link of said part at least, matrices of rigidity, and a reaction module (20) for determining the reaction force of the object corresponding to its deformation estimated on the basis of the internal forces, such that the force generated by the user interface (4) is balanced by said reaction force.

Crack tip interpolation, revisited

Abstract: It is well known that the near tip displacement eld on a crack surface can be represented in a power series in the variable p r, where r is the distance to the tip. It is shown herein that the coecients of the linear terms on the two sides of the crack are equal. Equivalently, the linear term in the crack opening displacement vanishes. The proof is a completely general argument, valid for an arbitrary (e.g., multiple, nonplanar) crack conguration and applied boundary conditions. Moreover, the argument holds for other equations, such as Laplace. A limit procedure for calculating the surface stress in the form of a hypersingular boundary integral equation is employed to enforce the boundary conditions along the crack faces. Evaluation of the nite surface stress and examination of potentially singular terms lead to the result. Inclusion of this constraint in numerical calculations should result in a more accurate approximation of the displacement and stress elds in the tip region, and thus a more accurate evaluation of stress intensity factors.