Heterodyne Holographic Interferometry

Publisher Summary Interferometry is an old and very powerful technique to measure the deviation between two wavefields with a sensitivity of a fraction of a wavelength. In holographic interferometry, at least one of the wavefields to be compared interferometrically is stored in a hologram. The hologram is usually recorded experimentally with the help of a reference wave. However, computer-generated holograms constructed theoretically may also be used to supply special, previously not existing wavefields. In most cases, the hologram itself also acts as the beamsplitter for the superposition of the two wavefields. Holographic interferometry has some unique properties, which makes it superior to classical interferometry; wavefields from the same object, but under different conditions and at different times, can be compared. This is an essential prerequisite to compare interferometrically different states of solid objects with opaque, diffusely scattering surfaces. Transient wavefields can be frozen instantaneously by short exposure times. Time averaged wavefields can be recorded and compared afterward. This results in reduction of noise and increase of accuracy and stability.

I Heterodyne Holographic Interferometry

Holographic interferometry is a very powerful technique for the measurement of small deformations and displacements of opaque solid objects. Unfortunately, the quantitative interpretation of the fringe patterns is somewhat involved, and the large number of papers published on this subject in the past 10 years has caused considerable confusion. This review paper is an attempt to rationalize the field by classifying the many different interpretation schemes into four main techniques, and by offering guidelines for the choice of technique for different applications.

The interpretation of holographic interferograms

The general problem of obtaining the derivatives of the displacements in holographic interferometry is analyzed. Expressions for the most general case are derived and a particular solution is suggested. A data-reduction method is proposed. Application examples are given.

The determination of the components of the strain tensor in holographic interferometry

The basic principles of plane strain measurement using speckle pattern interferometry are summarized. In the general case it is shown that the determination of the total plane strain field requires a minimum of two object illumination goemetries. A detailed description of a new design of interferometer which provides the required geometries is presented. Interferograms which demonstrate typical applications of the interferometer are interpreted.

The design and application of a speckle pattern interferometer for total plane strain field measurement

It is re-established, in a suitable form, that live holographic interference patterns are the result of the interference occurring between the wavefronts diffracted from corresponding points in the reconstructed image and the displaced real object. This result is employed to determine the path difference equations for the wavefront forming the interference pattern as observed in three orthogonal directions. A set of linear equations is derived which is shown to relate the components of a small general surface displacement to the fringe spacing and localization plane of the observed interference pattern. The practical application of the theory is then discussed. Numerical equations are derived for various geometries of interferometer and in particular the measurements of rigid-body translations and plane strain are dealt with. In addition it is shown how problems that arise in the measurement of complicated surface displacements may be considerably simplified.

D. Bijl

Papers

A New Theory for the Practical Interpretation of Holographic Interference Patterns Resulting from Static Surface Displacements