This chapter deals with the apparatus, materials, and experimental details involved in making simple holograms and in performing holographic interferometry to obtain data indicative of shape, deformation, stress, or other phenomena. The practitioner is reminded that, except for stability requirements and restrictions on maximum path length difference, holography is very forgiving. There are some fundamental rules, but a multitude of setups and materials can be made to work. There is much room for inventiveness and resourcefulness. Also, there are many details, and experimenters who want to go beyond the basics should review at least some of the standard literature (Jones and Wykes 1989; Ranson, Sutton, and Peters 1987; Smith 1975; Vest 1979; Waters 1974).

Some basic rules

Before getting into laboratory details, some fundamental requirements for successful holography should be summarized. These are derived from theoretical considerations and from experience.

1. The apparatus must be stable for the duration of the exposure. In interferometry, this stability requirement extends through the viewing of the real-time fringes or for the period of recording both exposures in the frozen-fringe technique. Recall that the process involves recording a grating structure caused by two-beam interference. Motions attaining a fraction of a wavelength of light between any of the optical components will cause the grating to move in space so it cannot be recorded. The setup must be isolated from floor vibrations, air-coupled sound waves that might cause resonance of one of the optical components, and thermal transients.

2. The optical path length differences must not be so large that interference cannot Occur.

The use of television image acquisition and computer image processing has revolutionized optical methods of metrology. A prime example is in the area of speckle correlation interferometry, which is discussed in this chapter. The implications of detector size are discussed, and limitations and advantages are outlined. An understanding of the material in Chapters 18 and 20 is strongly recommended.

Introduction

In spite of their obvious merits, holographic interferometry, speckle photography, and photograph-based speckle interferometry have not seen wide adoption by potential industrial and research users. The main reasons for this lack of acceptance seem to include the stability requirements, the necessity for photoprocessing, the requirements for postprocessing (such as image reconstruction and optical Fourier processing), and difficulties in fringe interpretation by persons not trained in optics. The processing and postprocessing are particularly troublesome, since they increase the time required to complete a cycle of experiments.

For these reasons it is natural to investigate the use of television systems to replace photographic recording materials and to use electronic signal processing and computer techniques to generate interference fringe patterns. This technique is electronic speckle pattern interferometry (ESPI), although it is also called video holography, TV holography, or electronic holography (EH). The basic concepts of ESPI were developed almost simultaneously by Macovski, Ramsey, and Schaefer (1971) in the United States and by Butters and Leendertz (1971) in England. The latter group, especially, vigorously pursued the development of the ESPI technique in both theoretical and practical directions. Later, Lokberg and Hogmoen (1976) and Beidermann and Ek (1975) also undertook successful research and development in ESPI.

One of the oldest and most useful forms of interferometric measurement for engineering purposes is photoelasticity, which involves the observation of fringe patterns for determination of stress-induced birefringence. It is important as a measurement technique. Further, it provides an instructive paradigm of applied interferometry. This chapter presents in some detail the fundamental theory of the photoelastic technique.

Photoelasticity as interferometry

For practical and instructional reasons it is important to recognize photoelasticity as a classic interferometric technique. The path length difference to be measured in the specimen depends on local direction-dependent variations in the refractive index; these variations are usually induced by stress. The surface of the photoelastic model itself acts as the beam splitter because it divides the incident light into orthogonally polarized components. These components travel through the same thickness of material, but the path lengths differ because of the difference of refractive index. Thus, the components exhibit a relative phase difference when they exit the specimen. The phase difference is converted to amplitude information through interference as the two components are recombined at the downstream polarizer, called the analyzer. Because the beam splitting divides a single wave train or a small pencil of waves, photoelasticity is of the amplitude-division class of techniques. It is also a common path interferometer since the two orthogonally polarized waves follow identical geometric paths through the whole instrument. These facts, plus the fact that the path lengths differ by only 20 or so wavelengths, mean that the coherence requirements are not stringent, and ordinary light sources are suitable. Also, vibrations do not have much effect on common path interferometers, so they are easy to use in noisy environments.

Herein we describe how to set up a photoelasticity interferometer, calibrate it, manufacture models, obtain fringe patterns, and interpret them to obtain maps of stress directions and stress magnitudes. More can be said on all these topics; some are expanded in Chapter 6. Persons planning extensive experiments using photoelastic interferometry should also become familiar with the excellent treatments in the several available books and handbooks (e.g., Burger 1987; Dally and Riley 1991; Frocht 1941; Jessop and Harris 1949; Post 1989; Wolf 1961).

Polariscope optics

Many different choices of optical elements and systems are possible for conducting model analysis by photoelastic interferometry. The object here will be to describe a few practical basic arrangements for general use. Much confusion is avoided if a systematic approach is adopted. It is apparent that certain basic optical functions must be accomplished in a polariscope. As long as the basic functions are served, there is considerable latitude in the final choice of optical elements. These points are especially important when a polariscope is being built for a special research application.

The optical system can be represented in block diagram form as shown in Figure 5.1. The light source must be capable of providing fairly intense monochromatic radiation as well as white light. For most efficient operation, the radiation must be collimated. These requirements taken together mean that the lamp must be small, intense, and spectrally pure, although the last restriction may be eased if filters are used to separate monochromatic light from multicolor radiation. For most photoelastic investigations, it has proven best to use mercury vapor or sodium vapor discharge lamps.

In this part, a moire method that combines the concepts of the moire effect, diffraction by a grating, and two-beam interference is described. The method is truly interferometric, and it is capable of high sensitivity. This chapter develops the theory.

Concept and approach

The preceding chapters have discussed two approaches for utilizing the moire effect in measurement of displacements, rotations, and strain. There is yet a third approach for performing moire measurements. It utilizes the fundamental concept of the moire effect, the concept of diffraction by a grating, and the phenomenon of two-beam interference to extend the capability and utility of moire measurement far beyond the limitations of geometric moire. It shares some basic ideas with intermediate sensitivity moire, which uses optical processing; but it bypasses the limitations imposed by the necessity to optically image the gratings. The result is a moire technique that is capable of truly interferometric sensitivities. That is, the wavelength of light is the metric, and displacements of fractions of 1 μm can be measured. This technique is finding increasing favor with experimentalists doing research in material characterization, fracture, and other areas for which high sensitivity is needed but other interferometric techniques are not suitable.

Moire interferometry can be modeled as a physical process in two distinct ways, and valuable insights are to be gained from each model. Before getting into the details of this powerful technique, which necessarily involve intricate geometric visualization, let us examine briefly these two physical models.

On the one hand, moire interferometry can be viewed strictly as a process involving two-beam interference and diffraction, and nothing needs to be said about the moire effect.

This chapter describes techniques for using geometric moire to measure out-of-plane displacement and slope, and also for mapping the contours of three-dimensional objects (Chiang 1989; Parks 1987; Theocaris 1964). The ideas are illustrated by an example from biomechanics, which has been a major area of application.

Shadow moire

The shadow method of geometric moire utilizes the superimposition of a master grating and its own shadow (Takasaki 1970; Takasaki 1973). The fringes are loci of points of constant out-of-plane elevation, so they are essentially a contour map of the object being studied. In studies of deformable bodies, the method can be used to measure out-of-plane displacements or changes in displacement. To understand the creation of fringes and to be able to interpret them, consider the optical system shown in the conceptual sketch of Figure 9.1.

A master grating of pitch p is placed in front of an object that has a light-colored nonreflective surface. The combination is illuminated with a collimated beam at incidence angle α. Observation is at normal incidence by means of a field lens that serves to focus the light to a point, where a camera or an eye that is focused on the object is located.

The incident illumination creates a shadow of the grating on the surface of the specimen. The grating shadows are elongated on the specimen by a factor that depends on the inclination of the surface, and they are shifted laterally by an amount that depends on the incidence angle and the distance w from the master grating to the specimen.

This chapter describes a way of using speckles that seems more elegant than speckle photography. A reference beam or a second speckle pattern is coherently mixed with the object speckle. The brightnesses of the resulting speckles are very sensitive to object motion. Comparison of two such patterns through superimposition or digital processing yields fringes indicative of displacement. The photograph-based version of the method is not used as much as speckle photography owing to experimental difficulties. Study of the method is worthwhile since it is the basis of electronic speckle pattern interferometry, which is becoming increasingly important.

Introduction

We turn now to what might be considered a more sophisticated use of speckle information in measurement. Rather than use a speckle merely as a marker on the specimen surface, we utilize to some extent the phase information within a speckle and the coherent combination of speckle fields as the basis of measurement. Such an approach is properly interferometric in concept and execution, so the techniques in this class are usually lumped together under the terms “speckle interferometry” or “speckle correlation interferometry” as distinct from “speckle photography.”

The somewhat confusing early history of these related but quite different techniques was presented in Chapter 19, so it will not be recapitulated here. The tutorial writings of Vest (1979), Ennos (1975), and Jones and Wykes (1983) are extremely useful from both the technical and historical viewpoints, as is the review by Stetson (1975).

One aspect of these techniques deserves special comment to preclude possible misunderstandings.

This part of the book deals with geometrical moire, an optical effect that is useful, interesting, and, to many minds, esthetically pleasing. It is also the only optical approach discussed here that does not rely on optical wave interference and diffraction. Rather, the geometrical moire fringe patterns are created entirely by mechanical occlusion of light by superimposed gratings. There are other moire techniques, to be examined in Parts IV and V of this text, that do utilize interference and diffraction. The fundamental concepts supporting those more exotic methods are to be found in the basic theory of geometrical moire, to be discussed here.

The moire effect

The moire effect is the mechanical interference of light by superimposed networks of lines. The pattern of broad dark lines that is observed is called a moire (or Moiré) pattern. Such a pattern is formed whenever a repetitive structure, such as a mesh, is overlaid with another such structure. The two structures need not be identical. The effect was evidently noted in ancient times. Modern examples easily observed include the effect when two layers of coarse textile are brought together, the bars observed on television when the scene includes a striped shirt or a building with regular joinings at the proper distance, and the pattern seen through two rows of mesh or picket fence from a distance.

Only a little study of the moire effect uncovers a very striking and useful characteristic: a very large shift in moire pattern is obtained from only a small relative motion between the superimposed networks.

The interference phenomenon and its place in optical measurement have, to this point, been the dominant themes. This chapter introduces and develops in detail the second anchor point in optics, diffraction by an aperture. After discussion of diffraction theory, several simple but important examples are presented; then the idea of optical spatial filtering is explained. These concepts are important in the remainder of the book.

Overview and problem identification

One of the oldest and most fundamentally important problems in optics is to predict the nature of the light field at any distance and direction from an illuminated aperture having arbitrary shape and perhaps containing certain optic elements in the form of a lens, a grating, or some kind of a filter. This problem is important because it provides an understanding of the formation of images by optical components, and it leads to ways of predicting, specifying, and measuring the performance of optical systems. Diffraction theory also leads to a conception of certain optical components as Fourier transforming devices, and it gives us the theoretical basis of whole-field optical data processing. The recording and analysis of moire gratings, the process of holography and holographic interferometry, and the methods of speckle interferometry and speckle photography all can be understood as diffraction processes.

The diffraction problem is complex and has not yet been solved in generality. The classic solutions rest on some severe assumptions that are not altogether realistic and logical. Even with the simplified solutions, the calculation of the optical field for arbitrary or complex apertures is forbidding. It testifies to the brilliance of the devisers of these solutions that their results describe and predict with considerable accuracy what is observed.