Charles M. Vest

Stability of natural convection in a vertical slot

The stability of natural convection of a viscous fluid in a vertical slot having isothermal side walls of different temperatures is investigated analytically. Both the conduction and boundary-layer regimes are found to be unstable with respect to stationary disturbances in the form of multicellular secondary flows. Theoretical predictions of the critical Rayleigh number and of the form of the secondary flow are verified by experimental measurements.

Reconstruction of Three-Dimensional Refractive Index Fields from Multidirectional Interferometric Data

Numerical and analytical techniques are presented that allow three-dimensional, asymmetric, refractive index fields to be reconstructed from optical pathlength measurements, which can be obtained using multidirectional holographic interferometry. Analytical reconstruction techniques that have been used in radioaptronomy and electron microscopy for a number of years, and recently in interferometry, are presented in the context of interferometric applications in the refractionless limit. These techniques require that optical pathlength data be collected over a 180 degrees angle of view. The required pathlength sampling rate is discussed. An efficient numerical procedure is developed for direct inversion of the data. Several numerical techniques are developed that do not require that data be collected over a full 180 degrees angle of view. All such techniques require redundant data to achieve accurate reconstructions. The required degree of redundancy increases as the angle of view decreases. Numerical simulations using six different reconstruction techniques indicate that with a 180 degrees angle of view, all are capable of providing accurate reconstructions. Four of the techniques were used to analyze simulated interferometric data recorded over an angle of view of less than 180 degrees . Examples of reasonably accurate reconstructions using data with angles of view as low as 45 degrees are presented.

Interferometry of strongly refracting axisymmetric phase objects

Inversion of measurements of optical pathlength through strongly refracting, radially symmetric phase objects, such as plasmas, is discussed. An exact inversion scheme, based upon methods originally applied in seismology is developed and applied to interferometry. It is shown that Abel inversion, which assumes that the probing rays are straight lines, yields rather accurate results if the interferogram is formed with appropriate imaging.

Tomographic reconstruction of strongly refracting fields and its application to interferometric measurement of boundary layers

An iterative algorithm for tomographic reconstruction of refractive-index fields from measured values of path integrals along rays which have been bent by refraction is presented. The behavior of the algorithm is studied by applying it to path length data obtained by computer simulation of experiments in which holographic or Mach-Zehnder interferograms of the field are recorded for several different viewing directions. A special form of the algorithm is also used to measure concentration profiles in the boundary layer formed at the cathode of an electrolytic cell containing ZnCl(2). The Appendix contains a discussion of series expansion techniques for reconstructing object fields from measured values of line integrals through the field.

Measurement of three-dimensional temperature fields above heated surfaces by holographic interferometry

Abstract Optical holography can be used to record multi-directional interferometric data, which provides a basis for measuring three-dimensional, asymmetric temperature or density fields in fluids. If continuous optical pathlength data are available over a 180° angle of view, the temperature or density field is shown to be equal to the inverse Radon transform of the data. A procedure for computing limited-resolution reconstructions of the field in terms of discrete data collected over a limited angle of view is presented. The technique of holographic interferometry was used to map isothermal contours in the developing convective plume above heated, horizontal, rectangular surfaces. It was found that the thermal structure of the developing plume is strongly influenced by the partitioning of the flow adjacent to the surface along lines of geometric symmetry.

Tomography for properties of materials that bend rays: a tutorial

When tomography is performed with electromagnetic or acoustical radiation, refraction may cause sufficient bending of the probing rays that ordinary reconstruction algorithms, which are based on the assumption of straight rays, do not yield accurate results. The resulting problem of reconstructing the refractive-index distribution of an object from time of flight or optical path length data is nonlinear. Various approaches to solving this problem approximately have been proposed and subjected to modest numerical studies. These include iterative algorithms and techniques based on linearized inverse scattering theory. One exception is the case of axisymmetric objects for which an exact solution is known.

Refraction correction in holographic interferometry and tomography of transparent objects.

In this paper we review and extend the state of the art in the algorithms that have been developed to tomographically reconstruct 1-D and 2-D refractive-index fields in the presence of significant refraction. A perturbation approach and two iterative procedures were tested and compared in numerical simulation of holographic interferometry experiments. Due to the nonlinearity of the problem, it is very difficult to draw general conclusions with respect to the behavior of the iterative algorithms, which is divergent in the examples presented here. In contrast, the perturbation technique, which is the easiest one to implement and the fastest to run, is shown to be very powerful in reducing refraction errors.

Tomography by iterative convolution - Empirical study and application to interferometry

An algorithm for computer tomography has been developed that is applicable to reconstruction from data having incomplete projections because an opaque object blocks some of the probing radiation as it passes through the object field. The algorithm is based on iteration between the object domain and the projection (Radon transform) domain. Reconstructions are computed during each iteration by the well-known convolution method. Although it is demonstrated that this algorithm does not converge, an empirically justified criterion for terminating the iteration when the most accurate estimate has been computed is presented. The algorithm has been studied by using it to reconstruct several different object fields with several different opaque regions. It also has been used to reconstruct aerodynamic density fields from interferometric data recorded in wind tunnel tests.

Onset of convection near a suddenly heated horizontal wire

THE note deals with the early transient processes which occur in a fluid surrounding a thin horizontal wire which is suddenly heated by passing an electrical current through it. Observation of the resulting temperature field with a Mach-Zehnder interferometer shows that the isotherms in a plane normal to the wire are initially concentric circles. This indicates that heat transfer is by conduction only. After a period of time the isotherms become asymmetrical as those above the wire are convected upward while those below the wire remain nearly stationary. The upward transport accelerates until finally a heated “cap” breaks away and rises to form the familiar mushroom-shaped steady state plume. in this study attention is focused on the “delay time”, t*. between the application of current to the wire and the beginning of observable convection. It is hypothesized that the onset of convection is a manifestation of instability. at least in the senSe that it occurs at a specific critical value of an appropriately defined Rayleigh number. A simple quasisteady analysis predicts the delay time as a function of the rate of energy dissipation in the wire and the transport properties of the fluid. The delay time was also determined experimentally for a wide range of heat transfer rates. The experimental data is in substantial agreement with the theoretical prediction.

Heterodyne holographic interferometry: concentration and temperature measurements in gas mixtures

Heterodyne holographic interferometry is employed to measure refractive-index distributions in transparent media. A system using a He-Ne laser and relatively modest electronic instrumentation is described. The system was used to measure temperature and specie-concentration distribution in natural convection boundary layers in air adjacent to heated surfaces through which a second gas is emitted or injected.