Hologram Interferometry Research Articles

The use of normal mode theory in holographic vibration analysis with application to an asymmetrical circular disk

The theory of normal vibration modes is reviewed for transverse vibrations of two-dimensional structures, and its implications are discussed with respect to vibration analysis that is performed by hologram interferometry and laser speckle interferometry. It is concluded that care should be taken to record vibration interferograms of true vibration modes. Experimental results are shown that illustrate how data taken of true vibration modes can be used to compute vibration patterns that result from mode combinations.

Hologram Interferometry of Nonsinusoidal Vibrations Analyzed by Density Functions

The characteristic fringes of hologram interferometry can be analyzed by the use of density functions, i.e., functions that specify what fraction of the exposure time an object point spends in any one place. In many cases, this method of analysis avoids cumbersome series solutions for fringe functions; in this paper the method is applied to nonlinear vibrations and to combinations of sinusoidal oscillations whose frequencies are related by rational numbers. For nonlinear vibrations, results are obtained that allow direct calculation of nonlinear spring functions, without presumption of a solution to the nonlinear differential equation of motion.

Measurement of Three-Dimensional Displacements by Hologram Interferometry

It is possible to determine three-dimensional displacements by recording the three holograms of the surface from three different viewpoints and counting the fringe order numbers at each corresponding point on the surface. The experimental values obtained here follow the theoretical results well.

The Holo-Diagram IV: A Practical Device for Simulating Fringe Patterns in Hologram Interferometry

A new simple moiré equivalence to hologram interferometry has been investigated. We have found this equivalence to be very useful as an educational tool. The analogy to any interference pattern can be projected before a large auditorium using an ordinary overhead projector, and the fringes can be studied directly during formation. The equivalence is rather easily understood as it is only based on the loci of constant pathlength for the light traveling from the light source to the observer via the object. No, or very little, mathematical, optical, or linguistic preknowledge is needed, because the ellipsoids onto which the method is based can be demonstrated using just two nails and a string. The new equivalence method is also being tested in a simple analog computer, which, we hope, will be used as the holographer's sliderule.

Vibrations in Unassembled Violin Plates Compared by an Acoustical Method and Hologram Interferometry

Hologram interferometry is making possible the visualization of transverse waves in the wooden bodies of stringed instruments under vibration. The present study is an attempt to coordinate the information now being obtained from holograms of unassembled violin plates with criteria previously developed in the course of the successful construction of 100 instruments in which the sound radiated from the plates is measured as a function of frequency. Comparisons will be made between holograms and acoustical tests of flat plates versus arched plates, and plates made intentionally “correct” versus “incorrect” according to violin making practice.

Moiré Patterns and Hologram Interferometry

A DOUBLE exposure hologram can be produced if an object (C) is illuminated by a spherical coherent wavefront originating from a point source (A). Observations can be made from another point (B), at a distance L from A and a photographic plate (P) between C and B can be used to record all the optical information from C. P also must be illuminated by a reference beam1–6.

Resonances of a Violin Body Studied by Hologram Interferometry and Acoustical Methods

Hologram interferometry is applied to study resonances of a violin body. A violin is made and after each major step, modes of vibration are studied. The top plate is studied in six steps: without and with f-holes, with f-holes and bass bar, with an artificial sound post, in the assembled instrument without and with strings. The back plate is studied in four steps: without and with artificial sound post, in the assembled instrument without and with strings. Interferograms of the lowest five to seven modes ranging from about 400 to 1 300 Hz are shown. The top plate is shown to be divided into plate and body resonances. The back plate is acting more as a unit together with the ribs thus mainly giving body-resonances. Deformations of the violin are studied when strings are pressed against the fingerboard, by double exposure hologram interferometry. The lowest air resonance of the sounding box and frequency responses are acoustically measured. In playing the unvarnished violin the tone is found powerful and even.

Fringe Localization and Visibility in Classical Hologram Interferometers

A descriptive account of both classical and hologram interferometry shows many common features. In each, the position of fringe localization is found by a similar ray construction and the fringe visibility is derived from the amplitude distribution in a diffraction pattern near focus.

The Holo-Diagram III: A Practical Device for Predicting Fringe Patterns in Hologram Interferometry

The holo-diagram-a map of the setup used during exposure and reconstruction of a hologram-is a practical device for engineering uses of holography. It is designed to simplify the making and evaluating of holograms and to optimize the information retrieval in hologram interferometry. Existing complex interference patterns can, with the use of the holo-diagram, be interpreted with a minimum of calculations. The holo-diagram can also be used to predict fringe patterns caused by simple basic motions, e.g., translation and rotation. Prediction is by a direct method, with no calculations, and very quickly produces an approximate view of the patterns. Patterns predicted in this paper, and verified by experiment, in general correspond with those presented by other workers with some interesting differences due to the generality of the holo-diagram. It is also stated that the theory of the holo-diagram is relevant both for diffuse and specular reflection, and diagrams for pure translation of an object in the plane of the holo-diagram are given. A direct study of the parallax (dynamic method) is compared with a study of the apparent localization in depth (static method).

Effects of Beam Modulation on Fringe Loci and Localization in Time-Average Hologram Interferometry

A comprehensive formulation of hologram interferometry is modified to include the effects of beam modulation in the recording of a hologram. The result is a unified description of fringe loci and fringe localization that is valid for arbitrary object motions and arbitrary beam modulation. This result is used to discuss the effect of beam modulation on fringe loci and localization conditions for a wide variety of cases: where one time function is sufficient to describe the motion of all points on an object surface; where a combination of independent time functions is required; where a combination of dependent time functions is required; where phase modulation proportional to the time function of the object’s motion is introduced; and where an object may execute sinusoidal vibrations that must be added as phase vectors (phasor vibrations). Localization conditions are shown to have potentially useful properties, for example, to permit separate observation of independent object motions when they occur simultaneously.

Desensitized Hologram Interferometry

The possibility of using multiple-wavelength holography to obtain desensitized hologram interferometry is being investigated analytically and experimentally. A simple analysis has been performed, and its conclusions are supported by experimental results. These results indicate that the new techniques will extend by several orders of magnitude the range of displacements amenable to measurement to hologram interferometry.

Combining hypersensitization and rapid in situ processing for time-average observation in real-time hologram interferometry

A rapid in situ processing system for holograms to be used in real-time hologram interferometry is designed. The plates are held in a liquid gate and exposed under immersion in the developer. Interferometric evaluation takes place with fixing bath surrounding the plate. The swelling properties of photographic layers are discussed, and formulae are given for a rapid developer and a fixing bath of the same index of refraction, which are matched to keep the layers of Agfa-Gevaert Scientia 8E70 and 10E70 plates at the same thickness in both solutions. An instruction is given on how to match processing solutions by checking the fulfillment of the Bragg-angle condition. The volume character of these thick holograms suppresses intermodulation noise, making practicable high modulation and a reference source close to the object. Because of hypersensitization, exposure time is reduced by a factor of 2-3. Interferometric evaluation can start 100-180 s after exposure. Fringe-free superposition of the object field and the reconstructed field is obtained, allowing time-average observation of vibrations in real time by visual inspection or photography. Interferograms are shown and compared with the conventional method of making one time-average hologram recording for each vibration mode. The experimental results agree with the theoretical analysis made for fringe formation in real-time hologram interferometry, which shows that, in comparison with time-average hologram recordings, half the number of fringes is obtained and the fringe visibility is lower.

Some Techniques for Hologram Interferometry of String Instruments

While hologram interferometry is proving very useful in determining the plate resonances of string instruments such as guitars, viols, and violins, there are definite technical difficulties involved. Many of these relate to the extreme sensitivity of any interferometer to dimensional changes such as produced by wood expanding with humidity, or seismic noise. Others relate to mode combinations that often occur owing to close spacing in frequency of relatively low Q modes. This paper discussed hologram interferometry from a practical point of view, explaining those techniques which are most helpful in overcoming these difficulties. They include use of liquid gates and in-place development of holograms to speed up real-time measurements, 35-mm film for recording time average holograms rapidly and in large numbers, the positioning of excitation points to separate combining modes, and laser speckle interferometry as an alternate to real-time hologram interferometry. The measurement of Q values for vibration modes via hologram interferometry is also discussed.

Holographic determination of in-plane deformation

The paper describes a method for determining the displacement component in a chosen direction on the surface of a deformed object. The method is based on hologram interferometry and uses two illumination waves. During reconstruction, two families of interference fringes are formed; the moiré fringes formed by the superposition of those two families are loci of equal displacement, measured along a direction perpendicular on the bisector of the two illumination waves. By properly choosing the illuminating directions, it is possible to form a moiré pattern corresponding to the in-plane displacements of a flat specimen. Although in the present state of the art applications of the method are confined to the laboratory, it is thought it will provide a simple tool for research in studying small deformations. Some experimental applications verifying the theory are presented.

Moiré method for determining bending moments from hologram interferometry

Interferograms obtained in hologram interferometry provide the observer with ‘contour maps’ of more or less constant displacement of an object surface. The contours are presented in the form of fringes, often sinusoidal or approximately so. In many applications, however, it is important to determine the bending moments of the surface, which are related to the second partial derivatives of the surface deformation with respect to the surface coordinates. It is shown that bending moments can be evaluated at any point on the interferogram by moiré interference between two transparencies of the interferogram, rotated 180° about the point in question. This method not only yields the bending moments but also indicates the principal axes of bending and the relative sign between the two principal components. One application of the technique is in the design of certain musical instruments, guitars in particular, where analysis of vibration modes of braces is helpful.

The use of fringe loci and localization to measure vectorial surface deformation in hologram interferometry

The use of fringe loci and localization to measure vectorial surface deformation in hologram interferometry

Time-average observation in real-time hologram interferometry by use of rapid in-situ processing

Time-average observation in real-time hologram interferometry by use of rapid in-situ processing

Moire´-Holographic Technique for Three-Dimensional Stress Analysis

The moire´ method is combined with hologram interferometry to obtain the three displacements of an arbitrarily deformed plane in the three-dimensional space. Double beam interference patterns are utilized. The interfering beams are obtained from the diffraction patterns of a grating printed in the analyzed plane. The in-plane and the out-of-plane displacements are measured in separate steps and yield separate patterns. The patterns are generated by double exposure and observed by a wave front reconstruction process. The experimental results included in the paper show a good agreement with theoretical results, proving the feasibility of the proposed technique.

Geometrical optics treatment of fringe localization in two-beam hologram interferometry

Geometrical optics treatment of fringe localization in two-beam hologram interferometry

Fringe visibility and localization in hologram interferometry with parallel displacement

The geometrical optics treatment of hologram interferometry is extended to all kinds of fringes to show that in general there is no unique localization. The limiting aperture for observing fringes with good contrast is obtained. It is shown that these results lead to a partial solution to the problem of determining the three components of displacement.