Young's Fringes Research Articles

Optimization of particle image velocimeters. I. Double pulsed systems

The spatial resolution, detection rate, accuracy and reliability of a particle image velocimeter (PIV) depend critically upon the careful selection of a number of parameters of the PIV system and the fluid motion. An analytical model and a Monte Carlo computer simulation have been developed to analyse the effects of experimental parameters and to optimize the system parameters. A set of six nondimensional parameters that are the most significant in optimizing PIV performance are identified. They are the data validation criterion, the particle image density, the relative in-plane image displacement, the relative out-of-plane displacement, a velocity gradient parameter, and the ratio of the mean image diameter to the interrogation spot diameter. These parameters are studied for the case of interrogation by autocorrelation analysis. By a single transformation, these results can be applied to interrogation by two-dimensional Fourier transform analysis of the Young's fringes.

Measurement of the displacement distribution by speckle photography using a BSO crystal

The use of Bi 12SiO 20 crystal plates for recording media of specklegrams in speckle photography enables one to measure the distribution of in-plane displacement on a rough surface of an object in situ and in quasi real time. For the purpose of measuring the distribution of any in-plane displacement in quasi real time by speckle photography using a BSO crystal plate, the dependence of the visibility of Young's fringes on the readout beam diameter for specklegram and the magnitude of the object displacement has been investigated. The fact is cleared that the visibility of Young's fringes depends on the number of speckles consisting of a Young's fringe, which is decided by the ratio of the displacement magnitude to the readout beam diameter.

Digital direct analysis of a multiexposed photograph in PIV

In Particle Image Velocimetry the analysis of the multi-exposed photographic plate can be carried out either by means of the Young's fringe analysis or by a direct technique. With this second approach the image of each interrogation area, enlarged by a microscope, is recorded by means of a digital image acquisition system. After some preliminary filtering operations the digitized image can be analyzed with numerical tools. In this paper a review of the digital techniques used in the analysis of these images is carried out. Both twodimensional and onedimensional techniques are analyzed and the problems involved in their use are discussed.

High precision retardation measurement using phase detection of Young’s fringes

Phase detection of Young's fringes is applied to a highly precise retardation measurement. A simple common-path polarizing interferometer is used with a birefringent wedge and a polarizer. The birefringent wedge introduces a spatially linear phase difference between orthogonally polarized light and Young's fringes are formed on an image sensor. The phase difference between the orthogonallypolarized components of light is proportional to the phase of Young's fringes. Thus, the retardation is equal to the Young's fringes' phase change before and after insertion of the retarder into the common-path interferometer. The phase of Young's fringes is calculated from the Fourier cosine and sine integrals of the fringe profile. The experimental results for wave plates, a Soleil-Babinet compensator, and a Pockels cell are presented with error estimates. The accuracy of the retardation measurement is experimentally estimated to be greater than lambda/2100.

Digital processing of Young's fringes in speckle photography

A new technique for fully automatic diffraction fringe measurement in pointwise analysis of speckle photographs is presented. The fringe orientation and spacing are initially estimated with the help of a 1 D fast Fourier transform (FFT). A 2-D convolution filter is then applied to enhance the estimated image. A fringe pattern with high signal-to-noise ratio is achieved, which makes feasible precise determination of the displacement components. The halo effect is also optimally eliminated in a new way by a halo-division technique. High reliability and accurate determination of displacement components are achieved over a wide range of fringe densities, with the computation time comparing favorably with those for the 2-D autocorrelation method and the iterative 2-D FFT method.

Fringe positions in double-exposure speckle photography

Double-exposure records in speckle photography or particle image velocimetry are often evaluated by analysis of the system of Young's diffraction fringes. Fringe spacing, necessary to calculate the displacement, is determined from the positions of fringe maxima or minima. These, however, are influenced by the diffraction halo function and by fringe visibility. A generalized theory of the effects is presented, including position dependent visibility and fringe phase. Evaluations are given for disk-shaped particle images in particle image velocimetry, and for coherent and incoherent speckle photography. Fringe shifts are determined numerically for commonly encountered values of fringe density and visibility thus presenting a basis for rapid assessment of accuracy in metrological experiments.

Experimental study of the optical velocimeter using a double-exposure specklegram

An optical velocimeter using a double-exposure specklegram is studied experimentally. In the method, a double-exposure specklegram is used to produce Young's fringes over a probing area, instead of forming the fringes as the result of interference of two beams in the case of a differential-type laser Doppler velocimeter. The method has special advantages over conventional laser Doppler velocimetry such as simplicity in the optical arrangement together with high stability for mechanical shock. In the study, the velocities of the solid object having continuous surfaces as well as the fluid flow or particles in the fluid were measured to show the usefulness of the method. The velocity of the solid object having relatively small variation of the surface brightness was measured with high accuracy in the experiment.

Speckle photography fringe analysis: assessment of current algorithms

The accuracy and reliability of four fringe analysis algorithms have been assessed, using Young's fringe patterns calculated from computer generated speckle patterns. The 1-D integration, 1-D autocorrelation, 2-D Fourier transform, and 2-D Walsh transform methods all estimated the two in-plane displacement components with negligible systematic error; the random errors were found to vary in proportion to sigma(2)/VR (speckle diameter = sigma, fringe visibility = V, and radius of laser probe beam = R), with the lowest errors given by the 2-D Fourier transform method.

Double exposure speckle technique for imaging system analysis and use in rod lens arrays

New double exposure speckle techniques for imaging system analysis are developed and their feasibility is experimentally examined. Using a single convex lens as the test lens, the MTF of the lens is obtained from the measured visibility of Young's fringes which have been produced by Fourier transforming a double exposure specklegram recorded through the test lens. By using conventional optical filtering techniques the spatial variations in the imaging quality are visualized for GRIN rod lens arrays.

Improvement of young's fringes' visibility in speckle photography by use of BSO-PROM device

For real time measurements of small displacements and deformations, dependence of the Young's fringes' visibility on an applied voltage to a BSO-PROM device, which is used as a recording device of the specklegram in the speckle photography, has been investigated. It is experimentally shown that the Young's fringes' visibility is improved by changing the applied voltage to the PROM device in the readout operation. This improvement is useful to accurate measurements of displacements in the speckle photography when the amount of the exposure is small and will be able to shorten cycle times of measurements.

Parallel optical evaluation of double-exposure records in optical metrology

The evaluation of double-exposure records in optical metrology (speckle photography or particle image velocimetry) is simplified by using two-step optical processing that is performed on many interrogation areas simultaneously by a 2-D array of narrow focused light beams. A first application of this procedure to the original record, if dimensioned properly, produces an array of small nonoverlapping Young's fringe systems. The photographic record of these patterns is subjected to the same operation once more, each beam illuminating precisely one pattern. The resulting output is an array of autocorrelation functions that are a direct representation of the displacement field since the spacing of respective side peaks gives the displacement. A single whole-field interrogation of the array of fringe systems produces an optical representation of accumulated displacement values thus rendering the statistics of the displacement field. The required matrix of light beams is generated by holographic optical elements.

Optical velocimeter using the double-exposure specklegram

A new type velocimeter using a double-exposure specklegram is proposed. In the method, a double-exposure specklegram is used to produce Young's fringes over a probing area, instead of forming the fringes as the result of interference of two beams in the case of a differential-type laser Doppler velocimeter. Compared to conventional laser Doppler velocimetry, the present method has special advantages such as simplicity in the optical arrangement and adaptability in the measuring range together with high stability. Preliminary experiments were performed to examine the validity of the method, especially under the existence of speckle noise. The results support the validity of the proposed method.

Optical fiber sensors using a phase detection of Young’s fringes

A method for the phase detection of straight and equidistant fringes is applied to an optical sensor using a highly birefringent fiber. A birefringent wedge introduces a linear phase difference between orthogonally polarized light which emanates from the fiber, and Young's fringes are formed on an image sensor. The phase difference between two orthogonal retardations of the fiber is proportional to the phase of Young's fringes. The phase of Young's fringes is calculated from Fourier cosine and sine integrals of the fringe profile. The experimental results of a fiber extension induced by a PZT expansion are presented with error estimations. The accuracy of a 2-m long fiber sensor is estimated to be higher than lambda/200. A technique to extend the measurement range of the fiber sensor is also presented using two laser wavelengths, in which a new method for calculating the difference between two phases is used. The experimental results are presented with error estimations.

Velocity Measurements In Convective Flows By Particle Image Velocimetry Using A Low Power Laser

To date, powerful lasers such as argon or ruby lasers have been used in most applications of particle image velocimetry. We present an analysis of the ability of this technique when a low power (5 mW He-Ne) laser is used. As a practical example we apply it to the Rayleigh-Benard convective flow, where velocities ranging up to several mm/s have been measured with about 100µJ energy pulses. The parameters that allow us to obtain good quality photographs with such low light power are analyzed. Several examples of pictures taken from different flow planes at different Rayleigh numbers are shown. The data reduction is made by fringe analysis. The digital image of the Young's fringes is recorded with a videocamera at each point of the photograph and is then processed with the 1-D averaging technique. This technique is the fastest but has the drawback of needing an external operator to select the fringe direction. To avoid this problem, we implement an algorithm whose practical performance is analyzed here. Another improvement proposed for this technique is the pedestal removal from the signal by digital high pass filtering. In this way, automatic detection of the first peak in the Fourier transform of the 1-D averaged signal is reached more easily. Thus, full automation of the 1-D averaging technique is obtained. The spatial filtering technique is also used. Several examples of whole-field velocity maps obtained from the photographs are shown, allowing a quick analysis of the velocity field. Finally, results obtained from postprocessing of the velocity measurements are shown. They include velocity, vorticity, and streamline maps. Isovelocity contour maps are also generated with the computer from the velocity field to compare with the maps obtained from the spatial filtering technique.

Full-field laser metrology for fluid velocity measurement

This paper reviews the development of full-field laser metrology from its inception as a dynamic extension of scattered light speckle photography, a voherent optical technique originally developed to make full-field measurements of quasi-static displacements in transparent solids, to its present applications in fluid dynamic studies. The full-field laser velocimetry technique, including both double exposure and multiple exposure recording methods, is discussed in detail, and comparison is made of their advantages and disadvantages in applications to steady and unsteady flows. Both the coherent light speckle and the particle image modes of operation are defined and evaluated. Computer aided ‘point-wise’ (Young's fringe) and ‘global’ (Fourier filtering) methods of optically analyzing the specklegrams are also discussed. Finally, experiments in which full-field laser velocimetry has been applied to a study of convective flow in a liquid are described, thus illustrating the potential of this new, non-onvasive optical technique.

Flow field analysis by large-area interrogation in particle image velocimetry

The evaluation of flow records obtained by particle image velocimetry (PIV) employs the interrogation of certain regions in the flow image. Basic relations are derived for the case that the velocity is not constant within the region of interrogation. The influence of a distribution of velocities on the Young's fringe system and its Fourier transform, the autocorrelation of the flow record, are discussed. The considerations show that there is an easy access to statistical parameters of the flow by carrying out large-field interrogation. The autocorrelation function will reproduce the probability density function of the velocity, and there is no need for a large number of time-consuming small-area interrogations. Furthermore, the effects of velocity variations in ordinary fringe analysis are discussed. Examples are given from synthetic PIV records and measurements in a wind tunnel.

Boundary element method and speckle photography for the investigation of the solidification of filled polymers

Some results on the boundary element method and speckle photography application for an investigation of the solidification of filled polymers are presented. With a correspondence between the composition of the reaction composite and its mechanical properties at hand the integral equation of the three dimensional thermoelasticity problem with non isothermal conditions are derived. The system viscosity variation is followed according to the contrast of the Young fringes determined experimentally. Furthermore, the displacement fields in separate areas are measured. These two approaches are compared and combined which give us a possibility to follow the modification of the state of the system during the solidification. Since qualitative and quantitative correspondence between the modification of the fringes contrast is obtained some mechanical characteristics of the polymer system are determined.

Speakle measurements of convection in a liquid cooled from above

Buoyancy-driven recirculation in a liquid-filled rectangular cavity cooled from above is shown to be locally modulated by an unstable thermal layer at the surface. Interferometric observations suggest that fluctuations that occur in a plume descending through the upper liquid layers are of the type described by Howard (1964) and by Krishnamurti & Howard (1981). Temperature measurements across the surface layer are in reasonable agreement with the diffusive heat-conduction model, but indicate that near the plume the fluid is cooler than elsewhere. Quasi-steady measurements of the velocity distribution in the upper regions of the cavity were made using multiple-exposure laser speckle velocimetry. Interrogation of the specklegrams with a Young's fringe technique yields a velocity-vector field of about two thousand elements. These data are used to calculate the corresponding velocity components and estimates of the vorticity distribution. The results compare favourably with measurements recorded directly from Fourier filtering methods.

Automated fringe measurement in speckle photography

An automated Young's fringe processor for point filtering of speckle photographs is described. It automatically measures the magnitude and direction of displacements from fringe densities of less than twenty with good accuracies. Microcomputer-based, requiring <64K of memory, the system provides full automation by employing computer-controlled scanning.

Second-order Statistics of a Partially Developed Speckle Pattern in the Far Field

The space amplitude and intensity correlations of a partially developed laser speckle pattern produced in the far-field region have been theoretically studied. The statistical properties are analysed for speckle amplitude of Gaussian statistics. It is shown that the non-circularity of the speckle statistics exhibits the difference in spatial behaviour of space correlation of the real and imaginary parts of amplitude. The non-circularity of the speckle statistics does not influence the visibility of Young's fringes but is evident in the spatial intensity correlation.