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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.

A statistical analysis of the effect of measurement errors on the determination of small vector displacements of diffusely reflecting objects by holographic interferometry is reported. There are two sources of error: inaccurate measurement of fringe-order number and inaccurate measurement of illumination and observation directions. Standard deviations of errors in measured displacements due to these two sources are presented in graphical form for a variety of holographic system geometries. Absolute fringe orders should be measured whenever possible, because fringe readout by scanning leads to very large errors.

A simple formula is given for inverting data in the form of measured integrals Phi(x) of a spherically symmetric density distribution f(r) over planes x = constant. The application of the inversion formula is illustrated by analysis of spatially resolved spectroscopy of x-ray emission from a laser-induced microimplosion of a gas-filled glass sphere.

Fringe formation and localization in holographic interferometry of transparent media are discussed for configurations in which light enters the medium and is scattered back through it by an embedded diffuse object. Fringe order numbers are doubled, and the fringe localization region is translated and compressed by a factor of 2. The results are applicable to tomographic reconstruction of aerodynamic density fields around opaque test objects.

Inversion of measurements of optical path length of rays traversing a strongly refracting, asymmetric-refractiveindex field in a variety of directions is discussed. An initial estimate of the field is made by computing the inverse radon transform of the data. This estimate is then corrected by an iterative process in which computational ray tracing is used to generate optical path lengths that are indirectly compared with the measured values. The method is applicable to interferometric measurements of temperature or density fields and also to related techniques, such as computer-assisted ultrasonic tomography.

The propagation of long thermal waves induced in thin aluminum plates by a slowly modulated heat source was investigated by stroboscopic holographic interferometry. The effect of different modulation frequencies on the visualization of such waves is shown. Experimental results confirm analytical thermoelastic predictions. The application of long thermal waves to holographic nondestructive testing is demonstrated.

Time-average holographic interferometry has been used to observe modal patterns of acoustically excited thin plates and shells having shapes which are schematically related to shapes occurring in the coats of animals. These modal patterns are related by a reaction-diffusion model to animal coat markings found in nature.

Superposition of two double-exposure holographic interferograms creates moiré patterns that can be used to detect flaws. Relative magnification can be used to correct for imprecise replication of loading when the second interferogram is formed; it also can be used to detect flaws when only a single interferogram is used if the basic deformation field is radially symmetric. Digital image processing is a rapid and versatile technique for forming such moiré patterns.

The formation of images of semitransparent spherical particles illuminated with coherent light is described from a diffraction theory viewpoint. Such images are distinctly different from those of opaque particles. The primary optical phenomena involved are illustrated by experimental results, and practical implications for holographic imaging of sprays are noted.

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.

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.

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.

Laser speckle in holographic interferograms of three-dimensional transparent objects is eliminated at the expense of limiting the available viewing directions to a finite number. This is accomplished by using a phase grating to divide the object wave into a number of discrete plane waves propagating in various directions. Experimental results of the application of this technique to the study of natural convection above a heated wire are presented. Fringe resolution obtained by this technique is compared with that obtained using plane wave or diffuse illumination. A brief analysis of fringe localization in holographic interferometry is presented in the discussion.

A full-field, variable sensitivity technique for mapping the vibrational amplitude of a diffuse surface is demonstrated. The surface under study is placed in an optical field consisting of two mutually coherent plane waves which propagate in different angular directions. At any instant of time the interference of these waves causes a fringe pattern to be formed on the surface under study. The time average, over one or more vibrational periods, of the intensity pattern on the surface can be obtained in real time by utilizing visual persistance or by making a time-average recording of an image of the surface. The visibility of the fringe pattern thus obtained is found to be modulated by a function of the local amplitude of vibration. This modulation can be observed directly or a photograph of the pattern can be optically processed to yield fringes that are loci of constant vibrational amplitude.

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.