Soyoung Stephen Cha

Tomography for reconstructing continuous fields from ill-posed multidirectional interferometric data

A computational tomographic technique has been developed to accurately reconstruct continuous flow fields of a simple shape from severely limited interferometric data. The algorithm is based on iterative reconstruction of the complementary field, the difference between the field to be reconstructed and its estimate. Its advantages lie in the treatment of various ill-posed problems in a unified manner and ease of incorporation of a priori information, even an approximate field shape. In principle it can utilize only available data. Test results demonstrated stable convergence and potential for substantial error reduction with a proper field estimate.

Three-dimensional natural convection flow around two interacting isothermal cubes

Abstract Laminar steady buoyancy-driven flow around two interacting isothermal cubes in an infinite medium is investigated by employing a control-volume finite difference technique and holographic inter-ferometry. The two cubes are positioned along the diagonal direction. Parametric investigations are performed by varying the center-to-center cube spacing and by varying the Rayleigh number while the Prandtl number is kept constant. To validate the numerical solutions, the calculated isothermal contours are qualitatively compared with the isophase lines in pathlength-integrated holographic interferograms. The heat transfer results are presented in terms of the average Nusselt number and the face-average Nusselt numbers at individual walls of each cube.

Interferometric Tomography For Three-Dimensional Flow Fields Via Envelope Function And Orthogonal Series Decomposition

Series-expansion methods for interferometric tomography of continuous flow fields are discussed. The techniques are based on series expansion by orthogonal polynomials and circular harmonics multiplied by an envelope function. These methods employing continuous basis functions are appropriate for reflecting the peculiar characteristics of interferometric tomography of fluid flow fields, namely, continuity, data sparsity, and nonuniform sampling. The high approximating power of the methods allows accurate representation of fields with a small number of series terms. This generates enough redundancy for a given number of data points in setting up a system of linear algebraic equations. The data redundancy thus generated yields accurate reconstruction even under ill-posed conditions including limited view angle, incomplete projections, and high noise level.

Stabilized nonlinear regression for interferogram analysis

A simple but accurate regression method for reducing the conventional single-frame interferograms that primarily arise in flow and heat-transfer measurements is proposed and tested. Phase extraction from the nonlinear interferogram intensity model becomes an ill-posed nonuniqueness problem. Unlike previous regression techniques, the method is based on iterative independent estimation of the individual terms appearing in the model to resolve this problem. Testing demonstrates stable convergence under a wide range of fringe numbers and noise levels. In comparison with the Fourier transform method the regression method provides enhanced accuracy, especially for cases involving few fringes, opaque boundaries, and phase discontinuities. It also allows direct gradient calculation. These features are very attractive for flow measurements despite its slow processing time.

Two-dimensional regression for interferometric phase extraction

An approach based on two-dimensional iterative nonlinear regression for retrieving phase information from single-frame interferograms was formulated and tested for fluid- and heat-flow measurements. Even though an initial crude phase assignment-i.e., fringe-order numbers at limited data points-is needed, the approach does not require complete phase unwrapping as in conventional techniques. Testing of computer-simulated and real interferometric data shows stable convergence and accurate phase extraction. The method works well under a high noise level, including broken fringes or contaminated regions, with a good noise-cleansing capacity. It provides accuracy at image- or opaque-object boundaries and directly offers spatial-gradient values. A weakness, however, can be intensive computation in the iterative estimation. The method is a good candidate for single-frame interferogram reduction.

Holographic interferometric tomography for limited data reconstruction

Holographic interferometric tomography can provide reconstruction of instantaneous three-dimensional gross flowfields. The technique, however, encounters ill-posed reconstruction problems in practical applications, that is, restricted scanning and incomplete projection. A reconstruction algorithm, termed the variable grid method, has been developed to improve the reconstruction under the ill-posed conditions. To test the performance of the developed technique, a three-dimensional gravity-driven flow around two interacting isothermal cubes is investigated experimentally. The flow, while providing challenging reconstruction problems, lends itself to accurate numerical solution for comparison. The refractive-index fields at two horizontal sections of the thermal plume with and without an opaque object, respectively, are reconstructed as a function of view angle varying from the full view to a minimum value of 40 deg. The experimental reconstructions are then compared with those from numerical calculation and thermocouple thermometry.

Application of Neural Networks to Stereoscopic Imaging Velocimetry

Stereoscopic imaging velocimetry is an optical nonintrusive method for measuring three-dimensional three-component gross-field fluid flows, which is based on the image capture by two CCD sensors from different vantage points. In this approach, part of the individual particle images or equivalently data points are likely to be lost when a flow field with a highparticle density is captured by the imaging system. The data loss mostly occurs during the process of overlap decomposition of superimposed particle images and during the phase of particle tracking. In order to maximize the data point-recovery and to enhance the measurement accuracy, neural networks are implemented in the two phases of stereoscopic imaging velocimetry. For the phase of particle overlap decomposition, the Back Propagation neural network is utilized because of its ability in pattern recognition and classification. For the phase of particle tracking, the Hopfield neural network is employed to attain a globally-optimal solution in finding appropriate particle tracks. Our investigation indicates that the neural networks offer very good potential for performance enhancement and has proven to be very useful for stereoscopic imaging velocimetry.

Automated interferogram analysis based on an integrated expert system

Interferometric data, either from single-frame fringe-tracking and Fourier-transform techniques or from multiframe phase-shifting techniques, pose a problem of 2π ambiguity, that is, wrapped-phase information. As the degree of noise level increases, especially in high-speed aerodynamics, these techniques encounter difficulties in phase extraction to provide continuous unwrapped-phase information. Here, a new hybrid approach, called the integrated expert system, which is developed primarily for aerodynamic interferogram evaluation, is presented. The integrated expert system utilizes interferometric-specific knowledge rules to compensate for the limitations associated with conventional techniques. It integrates in a single structure an expert system and algorithmic programming to provide, as much as possible, a unified approach for all the interferogram evaluation techniques. This initial attempt may provide a useful groundwork for future development in intelligent interferogram processing.

Improvement of a series expansion approach to interferometric tomography via natural pixel decomposition

Interferometric reconstruction of three-dimensional flow fields, that is, interferometric tomography, can be a very useful diagnostic tool. It is noninvasive and can capture gross fields; however, it frequently confronts a challenging problem of reconstructing fields from insufficient data. In most cases, flow-field interferometric data are sparse, nonuniform, noisy, and incomplete in projection and scanning because of opaque objects present either inside or outside the field. Recently, a new method has been developed in an effort to improve reconstruction under these ill-posed conditions. The method is appropriate for reconstructing flow fields with the distinct data characteristics, being based on natural pixel decomposition of the field. It employs rectangular grid elements of different sizes and aspect ratios. It thus reflects intrinsic spatial resolution information contained in the data and allows better resolution and accuracy in the region with more probing rays. Computer simulation of experiments has demonstrated superiority of the method to the conventional one. In simulation, the temperature field of a gravity-driven flow of two interacting heat sources, produced by a numerical code, are tested. Both the maximum and average reconstruction errors are reduced appreciably. Especially, the reconstruction demonstrates substantial improvement in the region with dense scanning by probing rays.

Three-dimensional natural convection flow around an isothermal cube

Abstract Laminar steady gravity-driven flow around a single isothermal cube in an infinite medium is investigated by employing a control-volume finite difference technique and holographic interferometry. The Rayleigh number is varied in a wide range while the Prandtl number is fixed at a specific value. To validate the numerical solutions the calculated isothermal contours are qualitatively compared with the isophase lines in multidirectional interferograms. The heat transfer results are presented in terms of the average Nusselt number and the face-average Nusselt numbers at the top, bottom, and side walls of the cube. Some heat transfer results are also compared with those previously reported. Maximum heat transfer occurs at the bottom at a low Rayleigh number. However, as the Rayleigh number increases it shifts to the side walls. The heat transfer rate at the top wall is approximately one-third of the maximum value for the range of Rayleigh number investigated.