Fringe Localization Research Articles

Holographic contour generation by spatial frequency modulation

A contouring method by spatial frequency modulation using hologram interferometry is presented. The principle is that Young's fringes produced by tilting the illumination ray are modulated by the object shape and demodulated by tilting the observation ray to generate depth contours. The problems of fringe localization and visibility in the arrangements of Fresnel holography and Fourier transform holography are studied. This method has the advantages that the sensitivity and the standard plane orientation are continuously variable, and high sensitivity and large measurable depth can be achieved for diffuse surface objects.

Holographic interferometry of transparent media using light scattered by embedded test objects

Fringe formation and localization in holographic interferometry of transparent media are discussed for configurations in which light enters the medium and is scattered back through it by an embedded diffuse object. Fringe order numbers are doubled, and the fringe localization region is translated and compressed by a factor of 2. The results are applicable to tomographic reconstruction of aerodynamic density fields around opaque test objects.

Fringe localization in holographic interferometry in the case of a transparent object with a nonuniformly varying index of refraction

Fringe localization, fringe interspace, and the normality theorem are investigated in the case of a transparent object with a nonuniformly varying index of refraction.

Geometrical Theory of Fringe Localization in Holographic Interferometry

A new definition of fringe localization in holographic interferometry has been proposed, and a new geometrical theory has been developed. The basic condition is that the total differential of path difference with respect to the coordinates of the object surface and the aperture for observation becomes zero. The developed theory can be applied to arbitrary deformation and shape of objects, and removes the perplexity of the theories based on the Michelson localization condition. It was verified by numerical calculations and experiments for some special cases.

Localization of fringes produced by rotation of the recording plate in focused-image holography

The equations determining the localization of interference fringes produced by rotation of the photographic plate in ‘focused-image holography’ are derived for an arbitrary cylindrical surface. The important properties of fringe localization are discussed and are experimentally verified.

A New Method of Frozen-fringe Holographic Interferometry Using Thermoplastic Recording Media

Abstract A new technique is described which confers the advantage of a permanent holographic frozen fringe record on live fringe holographic interferometry. The exact form of the frozen fringe record is known in advance and all information about fringe localization is retained. Some of the applications and implications of such a technique are discussed.

Fringe localization

Get PDF Email Share Share with Facebook Tweet This Post on reddit Share with LinkedIn Add to CiteULike Add to Mendeley Add to BibSonomy Get Citation Copy Citation Text James C. Wyant, "Fringe localization," Appl. Opt. 17, 1853-1853 (1978) Export Citation BibTex Endnote (RIS) HTML Plain Text Citation alert Save article

Fringe Loci and Visibility in Holographic Interferometry with Diffuse Objects

We investigate the three-dimensional distributions of loci and visibility of the fringes observed in the image region of a diffuse object in double-exposure holographic interferometry. The loci are shown to represent the contour lines of surface displacement in a certain direction and have the local spatial frequency proportional to the amounts of rotation and strain of the object, while the visibility is a function of the ratio of the amount of the speckle movement caused by the object deformation to the mean speckle size, depending on aperture size. The results of the computer calculation based on the analytical relations are graphically exhibited for typical cases.

Fringe Loci and Visibility in Holographic Interferometry with Diffuse Objects

Fringe formation in double-exposure holographic interferometry applied to diffuse objects has been investigated. For fringes observed in the region conjugate to the source of object illumination (fringes of equal inclination), relations giving the three-dimensional distributions of the fringe loci and visibility have been derived in the case of an arbitrary combination of object translation, rotation and strain as well as optical set-up. The role of speckle in the fringe formation is explained. Results of computer calculation for several examples are shown graphically.

A Practical Method for Holographic Interference Fringe Assessment

A semi-quantitative method for the assessment of optical holographic interference fringes is developed. It is found that the fringe loci caused by a general three-dimensional translation of a flat object can be approximately described by a quadratic equation. The equation represents off-centered concentric circles with the location of the center determined by the displacements and the geometry of the holographic system. The location of the center is shifted opposite to the direction of the in-plane component of the displacement with an amount increasing with the amplitude of that component. The radii of the circular fringes decrease as the out-of-plane component of the displacement increases.

Problem of defocusing in speckle photography, its connection to hologram interferometry, and its solutions

The movements, in three-dimensional space, of laser speckles observed from diffusely reflecting objects are described. The description connects these motions to relationships between fringe vectors and fringe localization in hologram interferometry. The results indicate the conditions under which defocusing leads to false measurements with conventional techniques, and methods are suggested that could solve the problem encountered due to defocusing when small displacements are to be measured on highly three-dimensional objects.

Use of fringe vectors in hologram interferometry to determine fringe localization

Use of fringe vectors in hologram interferometry to determine fringe localization

A holographic-moiré technique to obtain separate patterns for components of displacement

A symmetrical double-beam illumination is used in conjunction with a fictitious fringe system to obtain a moire pattern which represents the projection of the displacement vector into a single plane. The fictitious system of fringes is generated by a rotation of the photographic plate. This additional degree of freedom makes it possible to optically superimpose holograms, to apply spatial filtering techniques, and to control fringe localization. The method is applicable for displacement determination throughout the entire holographic range. A disk subjected to diametral compression is used to demonstrate that displacements and strains on the order of magnitude of those found in real engineering problems can be determined very accurately.

Fringe localization in holographic interferometry

The paper describes a method which allows the accurate prediction of the fringe localization in holographic interferometry, in the case of objects moving as a whole. The method uses the optical path concept; it is valid either in the case of spherical illumination or in the case of plane illumination.

Space-invariant achromatic grating interferometers: theory

A general analysis of an n-grating interferometer under various conditions of illumination is presented, where n = 1,...,4. Conditions for fringe localization and effects of misalignment are given. The lesser known phenomenon of the imaging of a grating by a second grating is described from which the fringe forming capacity of multiple-grating interferometers stems; this can occur regardless of the coherence of the source.

Localization of Interference Fringes in Holographic Interferometry

For the case of holographic interferometry when one measures changes in position and shape of diffusely reflecting surfaces new, quite general relations determining the localization of interference fringes are derived. The important properties of fringe localization are also discussed and a useful practical solution is drawn.

A New Theory for the Practical Interpretation of Holographic Interference Patterns Resulting from Static Surface Displacements

It is re-established, in a suitable form, that live holographic interference patterns are the result of the interference occurring between the wavefronts diffracted from corresponding points in the reconstructed image and the displaced real object. This result is employed to determine the path difference equations for the wavefront forming the interference pattern as observed in three orthogonal directions. A set of linear equations is derived which is shown to relate the components of a small general surface displacement to the fringe spacing and localization plane of the observed interference pattern. The practical application of the theory is then discussed. Numerical equations are derived for various geometries of interferometer and in particular the measurements of rigid-body translations and plane strain are dealt with. In addition it is shown how problems that arise in the measurement of complicated surface displacements may be considerably simplified.

Fringe interpretation for hologram interferometry of rigid-body motions and homogeneous deformations

Previous theoretical work on hologram interferometry is reduced, in this paper, to a number of guide lines for fringe interpretation. One of the most helpful is that, for any combination of rigid-body motion and homogeneous deformation, fringes appear on the object as though it intersected a set of equally spaced lamina perpendicular to a specific fringe vector. This elucidates the role that object shape plays in determining fringe patterns. Fringe localization for slit-apertured optical systems and fringe parallax are compared and the conditions for their equivalence are presented. The line of fringe localization that results from observation with a large two-dimensional aperture in an optical system is shown to have a simple geometrical relationship to the axis of the helical motion that may characterize any rigid-body motion. The orientation of fringes in their region of localization can be used to differentiate between rigid-body motions and some homogeneous deformations.

Fringe localization and visibility in hologram and classical broad source interferometry

The concepts of fringe localization and visibility in classical broad source and hologram interferometry are discussed and a distinction is drawn between them. Experimental results are used to demonstrate that in general there is no unique region of localization in hologram interferometry. The expression for the maximum viewing aperture for observation of fringes of good contrast at the surface under study is verified.

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.