Fringe Localization Research Articles

Algebraic ray trace analysis of spatial heterodyne spectrometers.

Algebraic ray traces of various configurations of spatial heterodyne spectrometers are developed to derive general, approximate, formulas for resolving the power, fringe localization plane, and admissible off-axis angle for each configuration. Michelson, all-reflective, and field-widened configurations are considered separately. The derived formulas for each configuration are tested against exact numerical ray traces using optical design software and in general found to be in good agreement.

SNR analysis with speckle noise in interferometry using monochromatic expanded source and fringe localization

As a strongly coherent light source, laser is widely used in various high-precision interferometry techniques. However, the coherence of laser also produces coherence noise. Laser coherence noise degrades the signal-to-noise (SNR) ratio and the interferogram resolution, leading to difficulties in data classification and information restoration. Here, we aim to derive the expressions of laser speckle contrast and SNR of interferograms through the theory of laser speckle noise. The factors affecting the speckle contrast and SNR of images are analyzed theoretically. The problem of fringe localization caused by dynamic scatter is discussed. We verify the relevant expression by using an experimental system and find that it can serve as a basis of laser interferometry to analyze measurement accuracy and suppress speckle noise.

Influence of implant-retained silicone oculo-palpebral prosthesis on stress distribution: a pilot study using a photoelastic model.

The purpose of this pilot study was to evaluate the behavior of stresses surrounding orbital model implants subjected to a load of a silicone oculo-palpebral prosthesis. A photoelastic model was constructed mimicking the orbital cavity of an adult patient who underwent left orbital resection. Two 3.75 × 5-mm extraoral implants with 3.75 × 5.25-mm magnetic connectors were placed in the model to anchor a silicone oculo-palpebral prosthesis. The stress generated by prosthesis retention was evaluated using photoelasticity at 15, 30, and 60 minutes. The polariscope images were analyzed qualitatively at five areas surrounding the implants. These same areas were analyzed quantitatively using Matlab software based on the RGB color pattern. Data were compared with the Wilcoxon test. Using fringe localization, the qualitative analysis demonstrated that the area between the implants had the greatest stress. The quantitative analysis showed that the peri-implant stress increased significantly in proportion to the increase in prosthesis retention time. The oculo-palpebral prosthesis generated stress around the implants, and the stress intensity was directly proportional to the duration of use.

Fringe localization using focus measure

A method for automated evaluation of fringe localization using focus measure is demonstrated experimentally. Dual-illumination digital holographic interferometry is used to generate phase difference maps (PDMs) of a rough test object. Focus measure values of the PDMs along the axial direction (increment: 10λ=6.33 μm) yield an inverted bell-shaped curve which, in turn, facilitates the characterizations of the plane and region of fringe localization. The method can be applied in the distance measurement of rough objects and in the optimization of fringe visibility.

Positioning and localization of two-wavelength interferograms for wavefront reconstruction with volume holographic media

This work studies both theoretically and experimentally the formation of the contour interference patterns generated by a two-wavelength real-time holographic interferometer. The resulting contour interference fringes are due to the intersection of the measured surface with parallel, equally spaced planes of constant elevation. The theoretical analysis describes how the spatial frequency of the elevation planes, their angular position, and the localization of the fringes depend on parameters of the optical setup. A theoretical model for fringe localization is developed and confirmed by the experiments, showing a strong dependence of the interferogram position on the slope of the studied surface. Due to the thick Bi(12)TiO(20) crystal employed as the storage medium the Bragg selectivity of the holographic readout is also considered.

Analysis of the localization of Michelson interferometer fringes using Fourier optics and temporal coherence

Fringes formed in a Michelson interferometer never localize in any plane, in the detector plane and in the localization plane. Instead, the fringes are assumed to localize at infinity. Except for some explanation in Principles of Optics by Born and Wolf (1964 (New York: Macmillan)), the fringe localization phenomena of Michelson's interferometer have never been analysed seriously in any book. Because Michelson's interferometer is one of the important and fundamental optical experiments taught at both undergraduate and graduate levels, it would be appropriate to explain the localization of these fringes. In this paper, we analyse the localization of Michelson interferometer fringes using Fourier optics and temporal coherence, and show that they never localize at any plane even at infinity.

Zero fringe visibility in the classical localization plane of a two-beam interferometer.

In 1987 we published "Fringe localization depth" [Appl. Opt. 26, 5125 (1987)], where, with first principles, we generalized the van Cittert-Zernike theorem for two-beam amplitude-division interferometers illuminated by extended sources. In this generalization the complex degree of coherence between the interfering beams is equivalent to the Fraunhofer diffraction pattern of an aberrated optical system. In 1989 Hariharan and Steel [Appl. Opt. 28, 29 (1989)] commented on this paper and pointed out that the fringe visibility can be zero in the localization plane determined by the conventional pair-of-rays method. Now, we numerically and experimentally show a situation where the equivalent aberrations are such that this finding is verified and that the localization region splits in two, one ahead of and the other behind the classical localization plane.

Fringe localization in wavefront division interferometers

Abstract When an amplitude division interferometer is illuminated by an extended incoherent source the fringes are localized. If the incoherent source is a periodic array of sources or if it continuous, there is a fundamental difference at the observation space and this is the appearance of several (more than one) localization surfaces. In the present paper it is stated that localized fringes can also be obtained in wavefront division interferometers provided the source is incoherent and periodic. As an example, the multiple localization planes in Fresnel's biprism are shown and experimental results are compared to the theoretical ones.

Development of a phase-displacement equation for panoramic interferometry

We developed the parametric equations that are needed to quantify the modulations in the sensitivity vector that occur when the phase-displacement equation is applied to make panoramic interferometric measurements. The measurement system relies on two collinear panoramic annular lenses, one to illuminate and the other to image their surroundings. When a coherent light source is used and a reference beam is added, interference occurs over the region of interest defined by the illuminating and viewing lenses. A holographic system is used to demonstrate the approach and quantify the analysis. We obtained interference fringes in real time by comparing holograms recorded before and after a section of cylindrical pipe is displaced relative to the measurement system. The annular images and the holographic fringes are acquired and stored digitally in a computer system, and image transformation algorithms are applied to remove optical distortions in the holographic patterns. Excellent agreement is obtained when the fringe loci are compared with those predicted on the basis of theory.

Multilocalization and the van Cittert-Zernike theorem. 2. Application to the Wollaston prism

The van Cittert-Zernike theorem can be used to evaluate visibility at the exit of an amplitude-division interferometer with two-beam interferences. If the source illuminating the interferometer is a periodic array of slits, at the exit there is a sequence of localization surfaces. The formulas for the position and fringe spacing of the principal localization surfaces are applied to a Wollaston quartz prism, and there is good agreement between theoretical and experimental results. Moreover, the fringe localization depth and the intermediate localization surfaces obtained experimentally coincide with those predicted by theory.

Multilocalization and the van Cittert-Zernike theorem. 1. Theory

The complex degree of coherence and the resulting van Cittert-Zernike theorem are employed to analyze the exit of an arbitrary amplitude-division interferometer with two-beam interferences. Considering that the source is a periodic array of spatially incoherent slits and assuming negligible equivalent aberrations and no vignetting, an expression for the complex degree of coherence as a function of the position of an exit point is derived. Formulas for the location, fringe spacing, and fringe localization depth of the multilocalized fringes are given.

1999 William M. Murray lecture

The history of holographic interferometry is one of problems. It has progressed from a novel discovery to a recognized technology only by the systematic pursuit of explanations for the puzzling phenomena it presents: unusual fringe patterns, fringe localization phenomena and bizarre fringe parallax. How to use the fringes to find three-dimensional deformation patterns is also a problem. Furthermore, the problem of how to handle high-volume testing spurred the evolution from photographic plates to fiexible roll film for all electronic media. Finally, the use of CCD television cameras and digital video processing has made phase-step interferometry the dominant method of fringe analysis but presents a major problem in the form of the phase-unwrapping quandary. This paper will attempt to trace the history of this technology in terms of the problems it has presented and their solutions.

Fringe localization in interferometers illuminated by a succession of incoherent line sources

It is well known that interference fringes formed by an interferometer that is illuminated with a point source are non-localized and, when it is done with an extended source, they are localized. Nevertheless, when the interferometer is illuminated with a discrete succession of points or lines, the localization of the fringes presents some characteristics that are different from those obtained with the former, for example the discrete number of localization surfaces. In this work we obtain the conditions to find the position of the surfaces of localization of these planes for an arbitrary interferometer. Then we apply this method to a wedge interferometer and compare the experimental and theoretical results.

Fringe localization in interferometers illuminated by a succession of incoherent line sources

Fringe localization in interferometers illuminated by a succession of incoherent line sources

Advances in the development of the interferometric otoscope.

Present measurement techniques for middle ear function have inherent limitations because they are either spatially insensitive (acoustic immittance) or descriptive and qualitative in nature (otoscopy). By integrating advances in electrooptic technology (fiber optics, miniature diode lasers, solid-state detector arrays) and digital processing, further advances are possible. On the basis of measurements taken with electronic speckle-pattern interferometry on human temporal bones and models, we demonstrate quantitative static and dynamic vibration/displacement characteristics of the tympanic membrane with high spatial resolution. Our presentation emphasizes advantages of optically based methods and demonstrates computerized signal processing capable of fringe localization, enhancement, and counting. Miniaturization and real-time digital image processing in the clinical setting is the goal of this research.

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.

Fringe localization depth: a comment

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 P. Hariharan and W. H. Steel, "Fringe localization depth: a comment," Appl. Opt. 28, 29-29 (1989) Export Citation BibTex Endnote (RIS) HTML Plain Text Citation alert Save article

A new formula for fringe localization in holographic interferometry

Holographic interferometry generally involves the interference of two or more speckle fields reflected from or transmitted through a diffused object. The visibility of the resulting fringes depends on the degree of coherence of the interfering speckle fields. Through a statistical analysis it is found that the degree of coherence of speckle fields is essentially a function of the relative speckle displacement and average speckle size. The analysis leads to a new physical model for holographic interferometry. With this model the problem of fringe formation and localization may be analyzed and formulated in terms of speckle movement. A new formula for ideal fringe localization is then derived from the analysis. Furthermore, a localization factor V c, i.e. the visibility of the holographic fringes, is introduced to analyze the partial fringe localization in holographic interferometry, which is of practical interest to most researchers.

Infrared holographic interferometry

Infrared (10.6-μm) dynamic holograms are obtained on a recording medium consisting of a thin oil film on a glass substrate. Reconstruction with visible light (0.63 μm) permits copying the initial hologram on a photographic plate. Any subsequent displacement of the object modifies the corresponding reconstructed wave at the recording medium, thereby creating a characteristic visible interferogram. Analysis of the double image in copy holograms together with fringe localization and visibility did not show stringent setup conditions. Experimental results are well related to various objects and displacements while the long wavelength (≃ 10 μm) used offers the advantage of large displacements or wavefronts deformation measurability and considerably decreases the setup sensitivity to vibrations.

Moiré interferometry at VPI & SU

A relatively easy technique for producing high-frequency gratings on specimens extends moire techniques into the high-sensitivity domain. Whole-field patterns of inplane displacement components are obtained with grating frequencies of 1200, 2400 and 4000 l/mm (30,480, 60,960 and 101,600 l/in.). Moire interferometry is a case of two-beam interference, characterized by extensive range, excellent fringe contrast and fringe localization on the specimen surface. It is a reflection technique, compatible with opaque specimens and live observation of deformation.