Fringe Vector Research Articles

Two-shot fringe pattern phase-amplitude demodulation using Gram-Schmidt orthonormalization with Hilbert-Huang pre-filtering.

Gram-Schmidt orthonormalization is a very fast and efficient method for the fringe pattern phase demodulation. It requires only two arbitrarily phase-shifted frames. Images are treated as vectors and upon orthogonal projection of one fringe vector onto another the quadrature fringe pattern pair is obtained. Orthonormalization process is very susceptible, however, to noise, uneven background and amplitude modulation fluctuations. The Hilbert-Huang transform based preprocessing is proposed to enhance fringe pattern phase demodulation by filtering out the spurious noise and background illumination and performing fringe normalization. The Gram-Schmidt orthonormalization process error analysis is provided and its filtering-expanded capabilities are corroborated analyzing DSPI fringes and performing amplitude demodulation of Bessel fringes. Synthetic and experimental fringe pattern analyses presented to validate the proposed technique show that it compares favorably with other pre-filtering schemes, i.e., Gaussian filtering and continuous wavelet transform.

Deformed surfaces in holographic interferometry. Similar aspects in general gravitational fields

In the first part some principles of the large deformation analysis in holographic Interferometry are briefly outlined. This may also give a link to the second part here. Modifications of the set-up at the reconstruction should recover the previously invisible fringes. The spacing and the contrast of them are characterized by the fringe and visibility vectors. The relevant derivative of the path difference involves the polar decomposition of the deformation gradient into strain and rotation and the image aberration implies further changes of geodesic curvature and of surface curvatures. In the second part these considerations lead then to similar aspects for hypersurfaces, before all to an interpretation by two virtual deformations for the Schwarzschild-solution of the gravitation. That is further usefull for non-spherical gravitational fields, for the invariants there and for the TOV-relation between pressure and density. The null-geodesics or light rays can also be interpreted by these virtual deformations. An approach towards the Kerr-solution for rotating stars is added. As for the linearisation a connection is outlined which confirms the non-existence of gravitational waves.

Deformation measurement by holographic interferometry. Analysis on curved surfaces. General aspects

Holographic Interferometry is briefly outlined in the case of large deformations. Modifications at the reconstruction are necessary to recover the previously invisible fringes. The spacing and contrast are characterized by the fringe and visibility vectors. The relevant first derivative of the path difference involves the polar decomposition of the deformation gradient and some affine connections. Owing to the modification, one must consider the aberration together with changes of geodesic curvatures and of surface curvatures. This leads to similar aspects for hypersurfaces with remarks concerning the general problem of the gravitational lens.

Laser method for particle size measurement

A method functionally compatible with laser Doppler anemometry is proposed for particle size measurement. This method is based on determination, in real time, of the correlation function of the direct and inverted images of a particle in scattered light. The image is inverted along an axis which is optically conjugate to the direction of the fringe vector of the probe interference field in a laser anemometer.

Fringe localization control in holographic interferometry

The practical use of holographic interferometry in nondestructive testing leads to many situations in which the characteristics of the fringe patterns make the observation and subsequent interpretation of the fringes difficult. Fringe control may then be employed to correct the troublesome parameters, the most commonly treated of which is fringe spacing. To gain more powerful control, a novel method is presented here that also permits one to change the localization of the fringe pattern. General vectorial expressions are derived that relate a tilt in the reference beam to a change in the fringe localization. Moreover the changes introduced into the fringe vector by this tilt can be suppressed by an adequate shift of the illumination beam focus. Some illustrative examples for a plane object are presented.

The magic of carrier fringes in moiré interferometry

Practical applications in which carrier fringes are used with moire interferometry for strain measurements are presented. Examples illustrate how moire carrier fringes are applied to obtain the desired data in complex laminated composite specimens. In many cases, carrier fringes permit extraction of much more detailed information, with procedures that are easier and more accurate than those using loadinduced fringes alone. The fringe vector for carrier fringes is introduced and its application to the interpretation of fringe patterns is explained. In moire interferometry, the carrier fringes are produced easily by adjustments of optical elements that control the virtual reference grating.

Vector representation of Moiré fringes

Moiré fringes are represented as vectors and their characteristics established using vector algebra. It is shown that the Moiré fringe vector of deformation is the vector sum of those due to extension and rotation.>

Determination of sensitivity vectors in hologram interferometry from two known rotations of the object

The fringes generated in holographic interferograms by independent rotations of an object are used to determine the sensitivity vectors of a hologram recording setup. This is done by identifying the fringes observed on the surface of a 3-D object with a fringe vector, which, in turn, equals the vector product of the sensitivity vector with object rotation. These vector relationships are formulated in terms of the projection matrices, and a least square error solution is derived that extracts the sensitivity vectors from the fringe data from two or more known rotations.

Determination of the sensitivity vectors directly from holograms*

New methods for determining the sensitivity vectors directly from holograms are presented. One of these techniques is based on the concept of the fringe vector; the other uses, as the starting point, the definition of the fringe-locus function.

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

Holographic strain analysis: extension of fringe-vector method to include perspective

A method has been published recently that permits determination of complete strain and rotation tensors of homogeneously deformed objects directly from fringes that are observed on their surfaces. However, the illumination and observation directions had to be considered constant over the regions of interest to apply the technique. This paper presents an extension of that theory to include both observation and illumination perspectives. It is shown that bulk translations of an object combine with linear variations in the directions of observation and illumination to generate fringe vectors that add directly to those generated by the object's homogeneous transformations. These linear variations are calculable from illumination and observation geometry.

Homogeneous deformations: determination by fringe vectors in hologram interferometry

When an object undergoes a combination of minute rigid-body motion and homogeneous deformation, its vectorial displacements can be described by a general, 3 x 3 matrix transformation. This same matrix can be used to transform the sensitivity vector of hologram interferometry into a fringe vector that defines the fringes as laminae that are intersected by the surface of the object. When fringes are observable on more than one surface of a three-dimensional object whose shape is known, it is possible to determine the fringe vector from the shape and spacing of the fringes on the object. If three holographic views are available, from which three fringe vectors can be determined for three known sensitivity vectors, it is possible to determine the transformation matrix, and this, in turn, can be decomposed into deformation and rotation matrices. More than three views allow the use of least-square-error theory to minimize errors in data taking.

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.