Showing papers in "SPIE milestone series in 1998"

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

Abstract: A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Digital decoding of in-line holograms

Abstract: Digitally sampled in-line holograms may be linearly filtered to reconstruct a representation of the original object distribution, thereby decoding the information contained in the hologram. The decoding process is performed by digital computation rather than optically. Substitution of digital for optical decoding has several advantages, including selective suppression of the twin-image artifact, elimination of the far-field requirement, and automation of the data reduction and analysis process. The proposed filter is a truncated series expansion of the inverse of that operator that maps object opacity function to hologram intensity. The first term of the expansion is shown to be equivalent to conventional (optical) reconstruction, with successive terms increasingly sup-pressing the twin image. The algorithm is computationally efficient, requiring only a single fast Fourier transform pair.

Multiple-wavelength and multiple-source holography applied to contour generation

Abstract: This paper describes two methods for obtaining three-dimensional holographic images containing superimposed constant-range contours for accurate cross-section tracing or contour mapping. The first and simplest method requires two illuminating sources with identical wavelength but at slightly different positions. This method has the drawback of requiring the hologram to be made at right-angles to the illumination direction. This results in shadowed areas on the object. The second method requires an illuminating source containing two wavelengths. This method also requires precise positioning of two reference sources, one for each wavelength. The positions of the reference sources may be optimized so that contours will appear over a maximum object angle. Experimental results that prove the principle are shown.

Reconstruction of three-dimensional refractive index fields from multidirectional interferometric data

Abstract: Numerical and analytical techniques are presented that allow three-dimensional, asymmetric, refractive index fields to be reconstructed from optical pathlength measurements, which can be obtained using multidirectional holographic interferometry. Analytical reconstruction techniques that have been used in radioaptronomy and electron microscopy for a number of years, and recently in interferometry, are presented in the context of interferometric applications in the refractionless limit. These techniques require that optical pathlength data be collected over a 180 degrees angle of view. The required pathlength sampling rate is discussed. An efficient numerical procedure is developed for direct inversion of the data. Several numerical techniques are developed that do not require that data be collected over a full 180 degrees angle of view. All such techniques require redundant data to achieve accurate reconstructions. The required degree of redundancy increases as the angle of view decreases. Numerical simulations using six different reconstruction techniques indicate that with a 180 degrees angle of view, all are capable of providing accurate reconstructions. Four of the techniques were used to analyze simulated interferometric data recorded over an angle of view of less than 180 degrees . Examples of reasonably accurate reconstructions using data with angles of view as low as 45 degrees are presented.

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.

Time average holographic interferometry with photoconductive electrooptic bi12sio20 crystals

Abstract: Photoconductive eiectrooptic crystals such as Bi12SiO20 (BSO) are attractive materials for read-write volume phase hologram recording. As reported in Ref. 1 the recording and erasure energy (S 1 ) with an external applied field have been found to be equivalent to that of high resolution photographic plates (S ≃ 130 μJ/cm η = 1%; λ = 488 nm). In addition, excellent quality reconstructed images and no fatigue effects to reversibility were reported. Physical mechanisms for ho­ logram recording and erasure are drift and trapping of photoelectrons under fringe illumination with a transverse eiec­ trooptic configuration. This gives rise to a space-charge field which modulates the refractive index via the linear eiec­ trooptic effect. Hologram erasure is achieved by space-charge relaxation under uniform illumination with the reference beam. A typical experimental recording-erasure cycle with a 6-kV applied field is given in Fig. 1. More precise analyses of the space-charge build-up and relaxation in photosensitive

High resolution hologram interferometry by electronic phase measurement

Abstract: The described dual frequency method interpolates the fringe pattern of any kind of hologram interfermetry down to better than 1 100 of a fringe, independent of intensity variations. Experiments with double-exposure holography demonstrate a resolution of 6 × 10−4 fringes at any point of the object. Spatial derivatives of deformations can be measured accurately for mechanical strain analysis.

Sandwich hologram interferometry : a new dimension in holographic comparison

Abstract: New methods are introduced that utilize interferometric comparison of images of diffusely reflecting objects from different hologram plates that are sandwiched together. To make the plate positions optically and mechanically identical during reconstruction and exposure, they are also exposed in sandwiches. If the two sandwiched hologram plates are separated by a small distance a new method of fringe evaluation can be used. Fringes caused by object tilt between two exposures can be eliminated by an analogous, but much larger, tilt of the sandwich hologram during reconstruction. Even the direction of tilt, forward or backward, is found this way.

A new method for generating depth contours holographically

Abstract: Employing holographic techniques, Hildebrand and Haines have demonstrated that a multiple frequency source can be used to generate range contours on or near an image. Supplementing their system with an auxiliary imaging system, we show that contours can be generated over much larger surfaces. With our modified system, it is also very easy to generate contours denoting constant depth rather than constant range. Experimental results are presented that show depth contours representing separations of 9.25 μ over a surface area of about 80 cm2.

Measuring combination mode vibration patterns by hologram interferometry

Abstract: In this paper the authors offer an explanation for the holographic observation of vibration patterns that do not agree with the classical mode theory of vibrating objects. The equations are derived for the formation of hologram vibration interference fringes under the assumption that an object may vibrate in any linear combination of its permissible modes, even while executing forced vibration at a single frequency. The modes appear to combine by phasor addition in these equations to give fringe loci that depend strongly on the relative phase of the combining modes. A set of experiments are reported which demonstrate this behaviour and allow quantitative comparison to the theory. Finally, the equations are derived for combinations of modes vibrating with independent frequencies, and again a set of experiments is reported which demonstrates this behaviour and permits quantitative comparison. Here the resultant fringes appear as the product of the fringe patterns of the component modes.

Holographic moire, an optical tool for the determination of displacements,strains, contours, and slopes of surfaces

Abstract: In conventional holographic interferometry, the observed fringe patterns are determined by the object displacement and deformation, and by the illumination and observation configurations. The obtained information may not be in the most convenient form for further data processing. To overcome this problem, and to create new possibilities, holographic fringe patterns can be changed by modifying the optical setup. As a result of these modifications, well-known procedures of the moire method can be applied to holographic interferometry. Components of displacement and components of the strain tensor can be isolated and measured separately. Surface contours and slopes can also be determined.

Multichannel phase-stepped holographic interferometry

Abstract: A modified holographic interferometer is described which enables automatic fringe pattern analysis to be achieved when recording transient events. The introduction of a phase grating enables the method of phase-stepping fringe analysis to be applied to a wide range of measurement problems. The theory is developed, and an analysis of the sources of error is presented with the aid of computer simulations. Initial experimental results confirm the utility of the method and its potential application in pulsed laser holography. The method can in principle be applied to electronic speckle pattern interferometry.

Comparative holographic moire interferometry in real time

Abstract: A holographic moire technique is developed which allows one to compare the resistance to strength in real time of two nominally identical specimens. The moire interference pattern gives contours of path variations related to the difference in displacements of the two specimens. The method is whole field and noncontacting; it is demonstrated by comparing deflections of two square plates clamped along the edges and subjected to centrally concentrated loads.

Application of holography to photoelasticity

Abstract: This paper discusses the exploratory application of holography to photoelasticity. It is shown that the two-beam holographic method may be used to record the birefringent pattern of a standard two-dimensional photoelastic specimen. A special type of polariscope is required. A discussion is presented of the various arrangements required to produce isochromatic, isoclinic, isopachic and combined isopachic and isochromatic fringe patterns. The three-dimensional nature of the holograph is utilized to separate the principal stresses by means of oblique incidence. Both normal- and oblique-incidence fringe patterns are recorded on a single hologram. A brief discussion of the extension to the dynamic case is presented.

Theory of holographic interferometry

Abstract: A simple theory of three forms of holographic interferometry “time‐average,” multiple‐exposure, and “real‐time” (live) interferometry is presented, based on a new development in holographic “image synthesis” (complex amplitude addition and subtraction), introduced in 1965 by D. Gabor and G. W. Stroke et al. They demonstrated the remarkable property of holography: Interference can occur between two or more light beams that are not superimposed either in time or in space, if the holographic intensities corresponding to the beams are obtained with the aid of a coherent reference‐background beam of the same spatial shape and if these intensities are successively added in the same hologram. Following the independent discovery of holographic interferometry, in 1965, by J. M. Burch; by R. L. Powell and K. A. Stetson; and by L. O. Heflinger, R. F. Wuerker, and R. E. Brooks, among others, it was found that two or more successive photographic additions of the hologram intensities (corresponding to two or more sequential positions or shapes of a given object) would thus indeed permit one to “synthesize,” in the form of an interferogram, the complex sum of the spatial‐electric‐field vectors, corresponding to each object‐point position, as if the different object‐point positions had all existed simultaneously rather than sequentially, as they do during the hologram recording (for instance in the case of multiple holographic‐image recording of a vibrating object). The rigorous equations we present, notably in vector form, for the general cases of practical interest bear out the equations previously derived by a number of authors, for some special cases, frequently in heuristic form.

Vibration analysis by stroboscopic holography

Abstract: THIS communication describes a method for vibration analysis in which fringes are directly related to the amplitude of the vibrating object. This is achieved by combining the frozen fringes technique with stroboscopy.

Direct phase determination in hologram interferometry with use of digitally recorded holograms

Abstract: A new method of phase determination in hologram interferometry is described. The Fresnel holograms, which represent the undeformed and the deformed states of the object, are generated on a CCD target and stored electronically. No lens or other imaging device is used. The reconstruction is done from the digitally stored holograms with mathematical methods. It is shown that the intensity as well as the phase can be calculated from the digitally sampled holograms. A comparison of the phases of the undeformed and the deformed states permits direct determination of the interference phase.

Characteristic functions for time-average holography

Abstract: This paper presents an analysis of the fringes obtained by time-average holographic interferometry of a generalized time-dependent optical phase function. The generalized optical phase function considered is the sum of a series of sinusoidal functions of time having arbitrary amplitudes, frequencies, and relative phases. Characteristic functions are determined for various optical phase functions of interest in time-average holography. In general, the characteristic functions are sums of products of Bessel functions (zero order and higher orders) and exponential phase factors. Rationally and irrationally related frequencies are included in this analysis. An example of vibrating string is considered, to illustrate the application of the results of this paper to objects vibrating at a multitude of frequencies.

Real-time metrology with bso crystals

Abstract: Electro-optical crystals are used for real-time holography, optical data storage, optical information processing and more recently for speckle applications. Many ferro-electric materials were investigated, the Bi12 SiO20 (BSO), a cubic, para-electric and electro-optic material was found to be very useful for real-time holographic interferometry and speckle applications. For the application of the BSO in real-time metrology, the crystals is usually biased with a transverse electric field in the 110 or 100 crystallographic direction. Illuminating the crystal with spatially structured information in the 110 direction as a result of a hologram or speckle pattern, a space charge field is built up, leading to a refractive index variation in the crystal. Double-exposure techniques and time average exposure will be presented for real-time deformation displacement and vibration analysis and for contour line holography using a two-wavelengths method. Young's fringes of double-exposed, or in the time-average recorde...

Use of sensitivity vector variations to determine absolute displacements in double exposure hologram interferometry

Abstract: Two solutions are presented to the problem of unknown absolute fringe order in double exposure hologram interferometry, a problem that confronts systems that require a single view of an object. One solution determines the vectorial object displacements relative to one reference point on the object. The other employs variations of the sensitivity vectors to provide absolute displacement analysis. For absolute displacements, a minimum of four illuminations is required.

Measuring accuracy of three-dimensional displacements in holographic interferometry

Abstract: In order to establish a quantitative method of measuring the distribution of three-dimensional displacements by holographic interferometry, measuring errors caused by the following two factors are analyzed quantitatively: (i) reading error of fringe order, (ii) setting error of observing and illuminating directions. As an application of the result, these two factors are calculated for a typical optical arrangement and three-dimensional displacements in the deflection of a cantilever model measured quantitatively. On the basis of the results of the analysis, some optical arrangements were evaluated.

Heterodyne holography applications in studies of small components

Abstract: Heterodyne hologram interferometry was used to study load-deformation characteristics of computer microcomponents that were surface mounted on a printed circuit board. The board was assembled as a cantilever plate and subjected to cyclic flexure loading according to industry standards. The flexure loading was sinusoidal at 0.1 cps with an amplitude of 1.25 mm (0.050 in.) at the tip of the board. Double-exposure heterodyne holograms were recorded under a number of conditions specified by the magnitude of deflection at the board's tip and the number of accumulated flexure cycles. Data obtained during reconstruction of heterodyne holograms were used to compute displacements and strains along the leads connecting the component to the printed circuit board. The experimental results show that lead displacements were on the order of 1.2 um, while strains were up to 0.054%. The results obtained in this study will be used as input to finite element models of computer microcomponents.

Some considerations on the statistical error analysis in holographic interferometry with application to an optimized interferometer

Abstract: A statistical analysis of errors is performed by consideration of fringe number and geometrical errors. The results of the analysis are applied to an optimized interferometer for the fringe-counting method, and simple relations for the calculation of the condition number and standard deviation are discussed, taking into account overdetermined equation systems.