Reference Fringe Research Articles

Mapping of the Decameter Radio Sources of Cassiopeia A Using a 100 km Range Long-Baseline Interferometer: Verification of a New Method of Phase Calibration of Interferometers

Abstract A new method is proposed for detecting the phase difference of cesium frequency standards facilitated at coupling stations of an interferometer of 100 km range baselines for observations of decameter wavelength radio waves. In this method, the Earth’s rotation is utilized. That is, a time-depending variation of the phase differences of arriving radio waves from a given source forms a so-called fringe function due to the Earth’s rotation. By generating a reference fringe function corresponding to the position of a selected radio source, the signals can be detected being selected from widely and continuously distributed radio sources in the sky, when the correlation is analyzed between the generated reference fringe function and the fringe data detected by the interferometer. The feasibility of the proposed method has been verified by applying the method to observations of a 100 km range baseline interferometer for decameter wavelength radio waves at Tohoku University selecting the radio-wave sources in the Cassiopeia A supernova remnant as the objective. The results of the analyzed correlation values averaged for the observation data of 30 hr, at 22.158 MHz, are determined being scattered around average values with a distribution of less than 25%; this distribution corresponds to a phase determination error of $\pm 12^\circ$ for the cesium frequency standards of the interferometer at 10 MHz. That is, we can calibrate the phase shift of the cesium frequency standards facilitated at each member station of the interferometer system with an accuracy of $\pm 12^\circ$, which corresponds to an accuracy of $\pm 1 ''$ for determining the direction of the radio-source position in the sky in the case of 100 km range long baseline interferometer. This accuracy is, however, only possible when an integration time longer than 30 hr is applied for analyses of the fringe correlation values.

A role of fringe pattern catalogue in the course of interferometrically based determination of residual stresses by the hole-drilling method

A further development of the technique for residual stresses determination in thick-walled structures, which is based on a combination of the hole-drilling method and reflection hologram interferometry, is presented. A plane specimen welded from two equal parts of dimensions 130×80 mm 2 in plane and thickness 12 mm is the object of investigation. Weld seam is performed along the shortest side of the specimen. Residual stress field of interest is formed by a superposition of initial welding-induced field and secondary stress field caused by plastic deformation of the specimen. A set of actual fringe patterns, which corresponds to a wide variety of residual stress components both ratio and sign, are reconstructed and presented as illustrations. A series of reference fringe patterns is simulated for the most typical cases inherent in residual stress field under study. It is shown that actual interferograms obtained belong to three main groups depending on a typical form of fringes configuration. On this base the main principles of creating the general catalogue of fringe patterns are established and the first version of this catalogue, which is related to reflection hologram interferometry, is developed. A structure of the catalogue that consists of both actual interferograms and reference fringe patterns is described. Possible ways of further catalogue completing and its direct implementing in the course of quantitative determination of residual stresses are discussed. It is shown that both experimental and numerical data aggregated into the first version of the catalogue can be effectively used for a verification of various coherent optics techniques with respect to a determination of residual stress components by means of hole drilling. An analysis of capabilities of reflection hologram interferometry in the field of residual stresses determination comparing with dual-beam speckle-interferometric techniques is presented. Superimposed residual stress field is quantitatively described in detail for both specimen sides of dimensions 260×80 mm 2. It is shown that fine nuances inherent in residual stress distributions over different specimen faces can be reliably derived from recorded fringe patterns of any type. This study serves as an example of residual stress components determination in real structure with a type of residual stress field to be investigated is unknown before the experiment.

Metrological justification of reflection hologram interferometry with respect to residual stresses determination by means of blind hole drilling

A description of practical implementing combined technique for residual stress determination in plane thick-walled structures is presented. The main features, which are inherent in a procedure of reconstruction and quantitative interpretation of fringe patterns arising as a result of blind hole drilling in residual stress field, are discussed in detail. Two plane aluminium specimens welded from two equal parts having dimensions 130×80 mm in-plane and thickness of 18 and 12 mm are the objects of investigation. Weld seam is performed along the shortest side of both specimens. A wide set of actual fringe patterns related to both uniform and non-uniform residual stress field is reconstructed. Most of typical fringe patterns are presented as illustrations. A whole set of available interferograms shows that a residual stress field in both thick-walled plane specimens investigated consists of both a uniform and non-uniform part. It is shown that a form of both non-uniform and uniform stress fields remains practically the same along the weld line. Moreover, non-uniform residual stress field at the proximity of weld seam is of similar form for both specimens. Emphasis is made in a choice of the transition model proceeding from a comparison of actual interferograms and reference fringe patterns. For the first time reference fringe patterns are constructed by using data obtained from corresponding actual fringe patterns, which reveal a non-coincidence between specimen's symmetry cross-sections and principal strain directions. It is shown that relations developed for a probe hole drilled in uniform 2-D stress field can be used for deriving residual stress components when fringe patterns obtained reveal a presence of local strain gradients. A good agreement between actual and reference fringe patterns is achieved in a case of local strain gradients existing. Comparing two types of interferograms related to uniform residual stress fields demonstrates their full coincidence. It is shown that the whole set of obtained fringe patterns consists of three main groups. The main evidence, which reveals an interferogram belonging to each specific class, is a typical form of fringes configuration. The main principles of creating the general fringe patterns catalogue are established and initial draft of this catalogue is developed. Distributions of residual stress components are constructed for different surfaces of both specimens under study. Quantitative results have a form that is typical for welded joints of structures bounded by plane surfaces. It is shown that fine nuances inherent in residual stress distributions over different specimen faces can be reliably derived from recorded fringe patterns of any type.

Enhancing sensitivity of a contactless method for measuring profiles and revealing macrodefects in composite periodic structures of the transmission type

Various interference techniques for comparing individual periodic structures incorporated into a transmission-type composite are suggested. All of the techniques are based on the method of interference patterns resulting from superposition of waves diffracted by the elementary periodic structures. It is shown that the sensitivity of measurements can be significantly enhanced and the width and direction of reference fringes can be arbitrarily adjusted. An interference-moire technique allowing a comparative study of elementary periodic structures incorporated into the composite is considered. Efficiency of the technique is confirmed experimentally.

Reflection hologram interferometry combined with hole drilling technique as an effective tool for residual stresses fields investigation in thin-walled structures

A detailed description of unconventional two-step technique of residual stresses determination is presented. This technique has the highest possible sensitivity with respect to plane residual stress components compared with all other destructive mechanical methods. The first step is a high-precision measurement of in-plane displacement components describing a distortion of drilled hole in principal strain directions due to residual stresses redistribution. The second stage is a choice of the most reliable transition model that is capable of deriving accurate residual stresses values from holographic interferometry data. A full metrological justification of both steps is established. Specific approach to a quantitative interpretation of fringe patterns arising near probe hole in terms of absolute fringe order difference is proposed and effectively implemented. Basic relations that allow us a quantitative determination of residual stress components are derived. A wide series of high-quality actual fringe patterns inherent in the procedure involved is obtained. Sophisticated technique for reference fringe patterns constructing is developed and implemented in order to carefully estimate and verify an accuracy of results obtained. A capability of the developed technique is demonstrated in the course of residual stress fields determination at the proximity of welded joints of thin aluminium specimens. Residual stress distributions corresponding to four different welding technologies are presented. An excellent correlation between most of the actual and numerically simulated fringe patterns is demonstrated for different types of residual stress state. It is shown how residual stresses of high level up to 200 MPa in aluminium alloy can be measured by means of the technique developed.

Control of the tuning of reference fringes in the interference pattern of changes in the object state in the optical processing of holograms and photographic images with the same spatial carrier

The condition of obtaining undistorted reference fringes when processing a pair of superimposed holograms or photographic images with a constant carrier frequency of bands due to their relative rotation or tilt is obtained. It is shown that the degree of fringe distortion is determined by the combined action of aberrations and the value of the parameter being measured. The technique of an arbitrary tuning of reference fringes is described, which makes it possible to eliminate the relative shift of holograms or photographic images. Experimental results obtained by the optical processing of photographic images of projected fringes are presented.

A tracking fringe method for measuring the shape and position of a swimming fish

A novel tracking fringe projection method is developed to simultaneously measure variations in both the position and the shape of a moving object. The method combines a commonly used fringe pattern projection method and a laser tracking technique into one optical system. In this new system, two tracking fringes are used to track the object, while one fringe is used for reference fringe. The order of conventional fringes can be determined by measuring the angle of reference fringe. The method enables us to simultaneously measure the position and shape of a moving object, such as a swimming fish.

Measuring velocity of speckle fields with digital speckle pattern interferometry

We investigate a digital method for detecting the velocity of a diffusing object. The technique is based on Digital Speckle Pattern Interferometry (DSPI). A set of reference fringes is generated externally through the reference beam in a digital interferometer. As the object moves, subsequent frames are acquired and subtracted according to the normal DSPI procedure and stored. By means of the theory of first order speckle statistics applied to speckle intensity correlation, we relate the visibility variations in the reference fringes with the object velocity. Thus, by measuring the fringe visibility variation in the resulting DSPI stored frames the mean object velocity can be obtained. The theoretical results are experimentally verified.

Simultaneous measurement of the position and shape of a swimming fish by combining a fringe pattern projection method with a laser scanning technique

A novel scanning fringe projection method is developed to simultaneously measure the variations in both position and shape of a swimming fish. This method combines the commonly used fringe pattern projection method and a laser scanning technique into one optical system. In this new system, one or more reference fringes are generated by an acousto-optic deflector, and laser triangulation is used to determine the order of the reference fringe. These reference fringes are then combined with the conventional fringe pattern, and the fringe order is determined from the reference fringes. The method enables us to simultaneously measure the position and shape of a moving object. We successfully apply the method to a swimming fish.

Multireference fringe-pattern projection method for measuring the shape of an object with spatially isolated surfaces

A multireference fringe-pattern projection (MRFP) method is developed for rapid measurement of the shape of an object that has spatially isolated surfaces. The method combines the commonly used fringe-pattern projection method and an acousto-optic deflector (AOD) scanner in one optical system. The AOD scanner generates reference fringes, whose positions can be conveniently adjusted to suit the respective object by changing the control signal to the AOD. We determined the accuracy of this MRFP method by measuring the displacement of a plastic plate and comparing the results with those obtained using a linear gauge. We find the relative accuracy to be 0.3%. To demonstrate the capability of this method to measure objects that have isolated surfaces, we use it to measure a vertical translation stage. Finally, we use it to measure the variations in position and shape of a fish while it is swimming. Such variation measurements are useful for studying the fluid dynamics of a swimming fish.

Method of investigating phenomena in liquids by holographic interferometry

A method based on holographic interferometry in real time with reference fringes for the determination of liquid parameters in cells with one inclined wall is presented. By studying the interferograms one gets a graphical recording of the spatial distribution of the refraction index of the liquid at a given time.

Laser holographic interferometry for investigations of cylindrical transparent tubes

A new double differential refractometer for student laboratories, based on holographic interferometry in real time with reference hologram and reference fringes, is presented. By studying the interferograms one gets a graphical record of the radial, axial, and temporal distribution of the refraction index in cylindrical tubes. This method permits the determination of the experimental parameters for cases when the relationship between these parameters and the refraction index is known. The paper presents experimental results for gas-discharge parameters.

3D Reconstruction of Large-Depth Objects Using Fresnel Diffraction of a Ronchi Grating and Simultaneous Recording of Reference and Object Fringes

We propose an active triangulation based range-finding system that, besides its simplicity, has two advantages over similar existing systems. First, the system can acquire range data for large-depth objects since it generates an illumination pattern with large-depth of focus using Fresnel diffraction from a Ronchi grating projected over the entire object surface. Secondly, the system does not need preliminary recording of reference fringes since it displays simultaneously, on a single image, both reference and object deformed fringes. This system offers other properties: it is mechanically simple, uses everyday optical components, is low cost, can be operated via a PC and uses relatively simple image analysis software. Three dimensional reconstructions are illustrated for various objects having 10 cm maximum depth variations. The depth accuracy (typically 0.5 mm for an object located at 350 mm from the camera) is comparable with other systems, but a certain compromise has to be accepted in acquisition time (typically 1 minute). This system can find applications in research laboratories as a tool to provide range data with relatively good depth accuracy.

A holographic method for determination of the refraction index of a gas in electric discharge tubes

A new method based on holographic interferometry in real time with reference fringes for the determination of gas parameters in cylindrical tubes is presented. By studying the interferograms one gets a graphical recording of the radial distribution of the refraction index of the gas in any region of the tube at a given time, as well as its axial distribution.

Three-dimensional temperature measurements in enclosures by using multiview interferometric tomography

Optical tomography using interferometric data is applied in this study to measure three-dimensional flow and heat transfer phenomena in a differentially heated cubic enclosure. The interferometric recording and reconstruction system, associated fringe readout and tomographic reconstruction procedures, and the results from this analysis are described, highlighting the specific challenges facing application of the technique to enclosure flows. The features unique to the investigation of enclosure flows using interferometric tomography include limited view angle, refraction effects and the lack of a visible reference fringe. The experimental results are verified by comparison with independent temperature measurements. The comparisons indicate that this experimental technique can yield three-dimensional perspectives of complex flows having sufficient spatial resolution to verify detailed three-dimensional direct numerical simulations.

紫外・可視レーザ干渉による加工表面吸着物の評価

For determining the presence of adsorbed material on surfaces of processed materials, an interferometer is developed using 325-nm He-Cd and 633-nm He-Ne laser sources. A measurement resolution of 0.5 nm is realized by scanning the interference fringes with a translator and taking the correlation between the probe fringes and the reference fringes. From experiments with many types of materials, it is found that the interferometer can detect adsorbed material on the surfaces of materials such as metals.

Sequential bidirectional differential interferometer

A new type of differential interferometer based on holographic optical elements is developed which allows a refractive index gradient field to be determined in two orthogonal directions obtained sequentially with a PLZT electrooptic modulator. The sign of the gradient is unequivocally determined by using a reference fringe pattern added to the interferogram. The sensitivity of the device is easily adjustable by changing the position of only one optical component.

Grating shearing interferometer with variable shear and fringe orientation

A lateral shear interferometer using Ronchi rulings, spatial filtering, and moire technique is described. Two gratings of different spatial frequency are placed on opposite sides of the focus of the beam under test. First diffraction orders of the first grid after being diffracted at the second grating and subsequent spatial filtering form the carrier frequency lateral shear interferogram. It is visualized using the moire fringe technique which simultaneously provides arbitrary reference fringe orientation and number. The experimental verification of principles is given.

A far-infrared Michelson interferometer for Tokamak electron density measurements using computer-generated reference fringes

A simple far-infrared interferometer which uses the 394 mu m laser line from optically-pumped formic acid vapour to measure tokamak electron density is described. This interferometer is unusual in requiring only one detector and a single probing beam since reference fringes during the plasma shot are obtained by computer interpolation between the fringes observed immediately before and after the shot. Phase modulation is provided by a rotating mirror modulator. Electron density has been measured with a phase resolution corresponding to +or-1/20 wavelength fringe shift, which is equivalent to a central density resolution of +or-0.1*1019 m-3 for an assumed parabolic density distribution in a plasma of diameter of 0.2 m, and with a time resolution of 0.2 ms.

Delay compensation: its effect in reducing sampling errors in Fourier spectroscopy

An approximate formula is derived for the spectrum ghosts caused by periodic drive speed variations in a Michelson interferometer. The solution represents the case of fringe-controlled sampling and is applicable when the reference fringes are delayed to compensate for the delay introduced by the electrical filter in the signal channel. Numerical results are worked out for several common low-pass filters. It is shown that the maximum relative ghost amplitude over the range of frequencies corresponding to the lower half of the filter band is typically 20 times smaller than the relative zero-to-peak velocity error, when delayed sampling is used. In the lowest quarter of the filter band it is more than 100 times smaller than the relative velocity error. These values are ten and forty times smaller, respectively, than they would be without delay compensation if the filter is a 6-pole Butterworth.