This chapter states the goals of the book, traces some reasons for its existence, and describes the best ways to use it. Some of the material that appears here would normally be found in an Author's Preface and would, because of its position of exile outside the main text, suffer the fate of being unread. Given the character of this treatise and its somewhat odd but purposeful organization, it seems best to give this commentary the status of a chapter.

Objectives

The author perceives that a strong need exists for a book about optical methods of experimental engineering analysis, a book that begins from a firm base in the sciences of physics and modern classical optics, proceeds through careful discussion of relevant theory, and continues through descriptions of laboratory techniques and apparatus that are complete enough to help practicing experimental analysts solve their special measurement problems.

This book on optics, interferometry, and optical methods in engineering measurement is primarily a teaching tool, designed to meet that need. It is not intended to be a research monograph, although it contains many examples drawn from research applications. It is not an encyclopedia of results, nor is it a handbook on optical techniques. It grew from lecture notes prepared during the past 25 years for graduate and undergraduate courses in experimental mechanics. These courses are taken by graduate students and seniors who have a variety of educational and professional experiences in several science and engineering disciplines.

This chapter describes some practical applications of geometric moire analysis in the measurement of displacement, deformation, and strain. Questions of sensitivity, some extensions of the method, and laboratory details are also discussed.

Determination of rigid-body motion

The moire phenomenon has been used, but not extensively, to sense the rigid-body rotations and translations of objects relative to a fixed coordinate system or to another object. The devices can give visual readout or serve as a source of an electronic signal that can be used in feedback control. As an illustrative application, consider the problem of developing a simple method for precise angular positioning of a shaft over a small range of motion. The apparatus must have low mass, be portable, and give visual readout. Application possibilities are automatic or manual control of a steering mechanism, directional control of an antenna, measurement of wind direction, and so on.

One way to accomplish the desired result is to utilize two rigid moire grills.

One of the grills is attached to the end of the shaft. The other is placed in close proximity to the first, but rigidly fixed. Figure 8.1 illustrates the general scheme. The two grills are initially aligned so that no moire fringes can be seen. Then, by simply counting the fringes as they form, one can determine N at a given distance y from the shaft center; θ is calculated by equation 7.8. In practical terms, the goal is to establish θ as a function of fringe spacing or the number of fringes that move through a chosen point on the plate. Keep in mind that equation 7.8 is restricted to small θ.

Described here are details of procedures for analysis of displacement and strain in deformable bodies using moire interferometry. Some of these techniques have parallels in other optical methods, but the rest are specific to moire interferometry. The chapter closes with some sample results from various applications of the method.

Specimen gratings

Utilization of the moire effect in experimental measurements depends on the successful forming of line grids (or dots) on the surface of the specimen. The spatial frequencies of the gratings employed in moire interferometry fall in the range of a few hundred to several thousand lines/millimeter (roughly 5,000 to 50,000 lines/in.). If we recollect from the discussion of Fourier optics that the spatial frequency bandpass of a quality lens is limited to about 200 lines/mm, then we understand that no method of optical imaging is adequate for replicating gratings for moire interferometry, even supposing that a master grating is available to begin with.

The problem has three aspects. In the first place, some sort of master grating at the desired frequency must be created. Then, gratings suitable for transfer to the specimen must be manufactured. Finally, the gratings must, indeed, be somehow fastened to the specimen. Only after solving these problems can moire interferometry be undertaken. Walker (1994) outlines the several approaches that have been pursued through recent years. Post, Han, and Ifju (1994) also describe various techniques.

Of course, very fine and precise diffraction gratings have long been made by mechanical means. Such gratings tend to be very expensive and to exist only in small sizes.

This chapter brings together many of the concepts discussed in the preceding five chapters to develop a moire technique that is superior to simple geometric moire but simpler than moire interferometry. The details of the procedures are presented in considerable detail. Many of the techniques described here, including specifics of using pitch mismatch, reproducing gratings, differential processing, and digital fringe reduction apply equally well to geometric moire and moire interferometry. In fact, many of the general ideas are useful in other areas of interferometry.

Introduction

A moire technique that incorporates spatial filtering has several attractive aspects. The fundamental idea is to take advantage of the sensitivity multiplication and noise reduction offered by optical Fourier processing of moire grating photographs, which are recorded for various states of a specimen. Sensitivity of the method can be controlled after the experimental data are recorded, within limits that are between those of geometric and interferometric moire. The method also is very flexible in that any two specimen states can be compared easily. The original data are permanently recorded for leisurely study later. Certain common errrors are automatically eliminated. Fringe visibility is usually much improved over that obtained by any method of direct or optical superimposition. Finally, the method is useful in difficult environments.

For orientation purposes, a short summary of a typical but quite specific procedure is presented first. Recognize that many variations in the procedure are possible, and the method is easily adaptable to whatever resources are at hand.

In the sections following the procedure summary, some specific details of technique are given. These details should be viewed as suggestive examples.

It seems fitting to close this text by discussing a technique that can be used to improve the precision, convenience, and usefulness of all varieties of interferometry. The basic idea is to insert into one of the optical paths a device that will provide known phase shifts. By doing this a few times, the exact phase at a point in the unknown can be deduced from only intensity measurements at that point. There is no need to map fringes and interpolate between them. The origins of the idea seem to date from the early days of photoelastic interferometry when simple compensators were used to improve measurements of birefringence. The approach has gained popularity with the advent of powerful microcomputers and improved electronic imaging technology. It is especially useful in electronic speckle pattern interferometry, so the idea and examples are presented in that context. Keep in mind that existing and potential applications are much broader in scope.

A perspective

When first getting involved in the use of phase shifting to enhance interferometry, whether electronic speckle or any other variety, it is very easy to become mired in the mathematics and the various computer algorithms that are promoted. One then loses sight of the essential simplicity of the concept, its universality, and its utility. Some background is in order, and then the basic concept will be presented in order to efficiently learn about the phase-shifting approach.

First, let us retrace briefly what we have been doing in collecting and interpreting interferometric fringe data. With few exceptions, one being pointwise birefringence measurements using a compensator or polarization (e.g., Cloud 1968), it is usual that a picture of a fringe pattern is created.

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.