Some examples of so-called classical interferometric techniques are described in this brief chapter. Also included is a discussion of laser Doppler interferometry, which is fundamentally different from the other methods discussed in this book, but which has matured into an extremely useful approach for dynamic measurement.

Newton's rings

One of the oldest and most easily observed of interferometric phenomena is the formation of interference fringes in thin films. Apparently, they were first described scientifically by Boyle and Hooke, but they are named after Newton because he first analyzed their properties. This type of interference is responsible for the colors observed in an oil slick. It causes troublesome spurious fringes when one photoplate is contact copied onto another and when glass cover plates are used to protect your favorite 35-mm slide. On the other hand, Newton's rings provide an easy way of checking for full contact between two surfaces, as when an optical flat is used to check the flatness of a finely lapped surface. A similar process accounts for the functioning of dielectric interference filters that are used to isolate a narrow band of wavelengths from a beam of light. In fracture mechanics research, Newton's rings have been used for measuring the opening of cracks in transparent materials.

Analysis of the formation of Newton's rings in the general case (Born and Wolf 1975; Tolansky 1973) is not as simple as might be thought. Only the most basic case is discussed here, as the purpose is primarily one of example.

This type of interferometry is classed as amplitude division because each wave train of light is divided into two parts that are subsequently recombined.

General considerations relevant to the design of moire interferometry apparatus are presented, followed by a description of the construction and adjustment of a particular 6-beam 3-axis device.

Approaches to design

There are three general design steps in the physical realization of a device for performing interferometry, including the moire variety. First, the needed special capabilities and tolerable limitations must be listed. Second, an optical arrangement that will satisfy the requirements must be designed. Finally, optical components must be obtained and arranged to perform the desired tasks.

Various optical arrangements for moire interferometry have been employed (Cloud and Herrera Franco 1986; Herrera Franco 1985; McDonach, McKelvie, and Walker 1980; Post 1980; Post 1987; Post and Baracat 1981; Post, Han, and Ifju 1994). Discussion of all the possibilities would be somewhat tedious and could be counterproductive in that the reader's attention might be distracted from the development process. Once the process is understood, the practitioner can review literature on the designs that have been employed and can then modify these designs or create new ones to fit the problems and resources at hand. For that reason, attention here is focused on the design and construction of a general-purpose 6-beam instrument with useful capabilities for experiments that require full knowledge of the surface strain fields in different types of specimens (Cloud, et al. 1987; Cloud, Herrera Franco, and Bayer 1989; Herrera Franco 1985).

In this chapter, diffraction and spatial filtering theory are put to good use in moire measurement of displacements, with significant gains in sensitivity and flexibility. Before we describe the method, some additional development of diffraction by superimposed gratings is necessary. Improvement of moire results by performing spatial filtering during the grating photography is also explored.

The basic idea

Although useful moire fringe patterns can be obtained by direct superposition of the grating photographs with one another or with a submaster grating, as is discussed in Chapter 8, such a simple procedure does not yield the best results, nor does it exploit the full potential of the information that is stored in a photograph of a deformed specimen grating. Increased sensitivity, improved fringe visibility, and control of the measurement process can be had by utilizing some of the basic procedures of optical data processing.

Three related physical phenomena are important in developing an understanding of moire fringe formation and multiplication by superimposing grating photographs in a coherent optical analyzer. The first of these phenomena is the diffraction of light by a grating, or more accurately, by superimposed pairs of gratings having slightly different spatial frequencies. The second is the interference fringe patterns that are produced in the diffraction orders by interference of two beams that come together at small relative inclination. The third important phenomenon is that a simple lens acts as a Fourier transformer or spectrum analyzer and offers the possibility of performing filtering operations on space-dependent optical signals in a manner analogous to the treatment of time-dependent vibration and electrical signals. Actually, these concepts are not independent from each other; they are manifestations of fundamental interference and diffraction processes.

This chapter treats several topics that are important not only in photoelasticity but also in other areas of interferometry. For example, many engineering experiments require good knowledge of the viscoelastic properties of materials and how to measure them. The transfer of experimental results from model to prototype is important to anyone contemplating experiments that might involve models, and such experiments are very common. Measurement of exact fractional fringe orders is useful in many applications of interferometry, and the methods used in photoelasticity provide a basis for similar methods in other areas, such as phase shifting in electronic speckle pattern interferometry.

Even so, inclusion of all the material that should appear in a chapter on applied photoelastic interferometry has been problematical because of space limitations and possible perceived distortion of emphasis. A factor is that many optical methods courses still spend a good deal of time on applied photoelasticity, and rightly so because it is an important engineering tool. Industrial users of the book probably need more on the subject than is given in Chapter 5. The coverage, in the end, represents a compromise among utility, educational value, length limitations, and the overall balance of the book; and it should be viewed in that light.

Finally, many of the references cited in the preceding two chapters are relevant to this one, even though they might not be mentioned specifically. The literature on techniques of photoelasticity is very large, and practitioners of the art will need to examine a good deal of it. Burger (1987) provides a particularly extensive and valuable list of references along with a wealth of technical detail.

This chapter begins the study of a topic that is very interesting for many reasons, technical and otherwise. Holography is a method for creating three-dimensional images without a lens, and it offers many intriguing possibilities. Holographic images are precise enough to be used in interferometry, and this idea leads to several powerful techniques for measurement in a broad range of application areas.

Orientation

Holography is a unique method of storing and regenerating all the amplitude and phase information contained in the light that is scattered from an illuminated body. Because all the information is reproduced, the regenerated object beam is, in the ideal case, indistinguishable from the original. Here is a technology that offers the possibility of perfect three-dimensional photography. Since it is possible to record the exact shape and position of a body in two different states, then it is also possible to compare the two records to obtain a precise measure of the movement or deformation. This measurement technique is called holographic interferometry.

Holography was invented by Dennis Gabor in about 1948 as a method for improving the usefulness of microscopy. It did not work very well, partly because the two beams created in holographic reconstruction, which form what are commonly thought of as the real and virtual images, ended up in line with one another in the arrangement necessitated by the apparatus then available. His theory was not, apparently, limited in this way; but the potential beauty and utility of the technique were masked by the problem with the two images.

This chapter presents a remarkably simple and effective way to use the speckle effect in the measurement of displacements and deformations. It can give point-by-point or whole-field data, and the sensitivity can be made variable. The method can be extended to use noncoherent illumination, and an example of such an application is described. Certain versions of the technique are closely tied to moire and shearographic techniques. These parallels are noted because they provide valuable unifying insight.

Introduction

A direct and simple exploitation of speckle for engineering measurement is to use it as a microscopic marker of points on the surface of the object being studied. A single speckle is a unique signature derived from the local characteristics of a small area of the object surface and dependent on the geometry of the optical system and the numerical aperture of the illumination or viewing system. If a speckled image is created, then the speckle near a point in the image is uniquely identified with the corresponding point on the object. If the point on the object moves within certain limits, and if the optical system is not changed, then the speckle moves with the point, and the motion is apparent in the image. The speckle is not lost or reformed. If the speckle is recorded for two states of the specimen, then the displacement of the speckle corresponds to the local displacement of the surface.

Suggestions for the direct use of coherent light speckle in displacement metrology and contour mapping first began to appear in about 1968. Subsequent development was quite rapid and somewhat complicated with several different researchers working simultaneously but independently on differing approaches to similar problems.

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.