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TECHNIQUES by G. Cloud

UNIFYING CONCEPTS IN TEACHINGOPTICAL METHODS

The last four decades have produced many importantadvances in the discovery, understanding, and util-ization of optical phenomena for measurement pur-poses, particularly in the broad field known as ex-

perimental mechanics. Teaching of the basic phenomena andtheir applications to engineering students is important andnecessary, and this knowledge base continues to expand.But, the knowledge in other areas of engineering has alsogrown, and serious conflicts arise as to what should and canbe taught within the limited scope of typical undergraduateand graduate engineering curricula. A complicating factor isthat effective teaching of experimental mechanics demandsinvestment of instructional time and hardware in laborato-ries.

One answer to the conflicting dynamics is to make the teach-ing of experimental mechanics, and optical methods in par-ticular, more efficient. This can be accomplished in two ways,namely, (a) appropriate meshing of theory, study of tech-niques, and laboratory exercises; and (b) maximum exploi-tation of ‘‘transfer of learning’’ by recognizing and emphasiz-ing fundamental concepts that unify the various methods.

BACKGROUNDThe approaches outlined here are drawn from experience indeveloping and teaching several courses involving experi-mental mechanics at Michigan State University and else-where. The first is a laboratory sequence that supports therequired undergraduate course in mechanics of deformablesolids. This lab incorporates experiments that require exten-sive computer-based strain gage data acquisition as well asdemonstrations of photoelasticity and other techniques. Thesecond is an elective senior-level course that covers most ofthe important methods of experimental mechanics, includingstrain gages, motion measurement, and optical methods.This course incorporates some required experiments andseveral demonstrations. The third is a core graduate coursein strain and motion measurement that concentrates onstrain gages, motion measurement with emphasis on seismicsystems, and photoelasticity; with less-deep coverage ofmoire, holography, and speckle methods. The fourth coursegives graduate-level in-depth instruction on optical mea-surement techniques. Both of the graduate courses require

G. Cloud (SEM Fellow) is a Professor in the Materials Science and MechanicsDepartment at Michigan State University.

This paper was presented at the SEM 2001 Annual Conference on Experimentaland Applied Mechanics.

Editor’s Note: ET is launching a new Back to Basics Series for 2002 with a focuson Optical Methods. The Series begins by introducing the nature and descriptionof light and evolves, each month, into topics ranging from diffraction through tophase shifting in interferometries. The intent is to keep the Series educationallyfocused by coupling text with illustrative photos and diagrams that can be usedby practitioners in the classroom as well as in industry. The Series author is Pro-fessor Gary Cloud from Michigan State University who is internationally knownfor his work in optical measurement methods and for his recently published booktitled, Optical Methods of Engineering Analysis. Series Editor: Kristin B. Zim-merman, Ph.D., kristin.b.zimmerman@gm.com.

extensive laboratory involvement. Outlines of these coursesare available on the web at www.egr.msu.edu/�cloud.

Further, the author has offered short courses on opticalmethods of measurement to groups of various interests andbackgrounds. These short courses have varied from 8 to 16hours of instruction, and design of the sequences has re-quired considerable thought about the most efficient ways ofdelivering the material. Typically, they do not involve labo-ratory participation, but portable demonstrations are usedextensively to illustrate the concepts and techniques.

In all these courses, a certain number of case studies areincorporated to emphasize the importance of being familiarwith a battery of techniques, the necessity for choosing ap-propriate techniques, the breadth of problems that can besolved through experimental methods, and the requirementsfor obtaining valid data. The idea that methods must be cho-sen and adapted to fit the measurement problem at hand,as opposed to the common approach of fitting the problem toa method that might be favored by the investigator, is em-phasized.

These approaches have also been employed in teaching thefundamentals of optical methods, with case examples, tohigh school students in only one to three hours.

ORGANIZATION OF THE MATERIALConventional pedagogy typically involves systematic treat-ment of optics and interferometric theory, which might re-quire several weeks of class time. Then, study of specificmethods begins, after which laboratory experience occurs.The problem is that a term or semester might be half overbefore meaningful laboratory work can be performed.

A better approach is to integrate theory as much as possiblewith treatment of the optical techniques. This plan is util-ized, although not to the maximum effective extent, in thebook by the author1 that is used in various ways in thecourses mentioned above. Presented at the beginning arejust enough of the optics concepts and theory to understandlight sources, lenses, and basic interferometry. The conceptsare then utilized in learning about some classic two-beaminterferometry methods including Young’s experiment, New-ton’s rings, and Michelson interferometry. Then, detailedstudy of the classic common path interferometry known asphotoelasticity may be undertaken. The student can begininformed laboratory work as soon as about two weeks intothe course. While the laboratory exercises on basic interfer-ometry and photoelasticity are being completed, the next in-crement of theory can be presented, followed by study of amore advanced technique. This cycle is continued throughthe course. In all cases, the lectures and laboratory work areaugmented by introduction of application examples that un-derline the utility of the techniques in solving practical prob-lems.

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UNIFYING CONCEPTS INOPTICAL METHODS

Fig. 1 Generic inferferometer

UNIFYING CONCEPTSThe purpose here is not to discuss in detail an outline ofwhat might be considered an effective course on optical phe-nomena and measurement techniques. Rather, emphasis ison concepts and processes that are common to the varioustechniques of optical methods of measurement. If these con-cepts are understood thoroughly, as they are needed, muchtime and effort is saved. Available space limits discussion toonly some of the concepts and techniques, but these are suf-ficient to establish the paradigm, which is repeated and ex-tended as the training develops.

As a general principle, emphasis is given to the fundamentalphysical phenomena that are utilized in each technique.With unifying concepts and physical foundations in hand,the student is poised to advance his breadth of knowledgebeyond the limits imposed by course and curriculum bound-aries.

CONCEPTS INVOLVING LIGHTAt the beginning, it is usually necessary to teach the natureof light energy, insofar as it is known; the history and basicideas of Maxwell’s equations; the wave equation for non-conducting media; its simplest solution in the form of aharmonic wave, here considered only in trigonometric nota-tion; the electromagnetic spectrum; polarization; radiationsources; intensity measurement as by square-law detectorsincluding halide films and electronic devices; and, finally, ba-sic lens functions. Some attention is given to the dichotomybetween electromagnetic and quantum theories with the il-lustration that one is used to describe the behavior of lightand the other is used to describe the creation and detectionof light—all within the same optical system.

The ideas mentioned above can be covered effectively in onlyone disciplined hour or so if they are presented as a seriesof rhetorical questions and concepts. For example, ‘‘What islight?’’ Concept 1: One view is that light is energy in the formof electromagnetic waves characterized by an electric vectorand a magnetic vector. . . . Concept 2: An alternate view isthat light is energy in the form of bundles, packets, orquanta that . . . . Concept 3: For many of the processes weare interested in, electromagnetic theory serves. In this ap-proach, the interaction of light with materials can be de-scribed by a set of equations developed by many people overa long time, but which were augmented and made system-atic by Maxwell. And so on.

INTERFERENCEFollowing presentation of the introductory material, the uni-fying concept of interference of waves is presented. This isthe first cornerstone in optics. A simple demonstration ofinterference using a laser and Lloyd’s mirror or Young’sfringes, two optical flats to show Newton’s rings, or a shortphotoelasticity demonstration is useful to set the stage andarouse curiosity. There are two parts to this section on in-terference. In the first, interference of collinear waves is dis-cussed in detail using trigonometric notation. The importantfinding is that interference produces another wave of thesame frequency but whose amplitude is dependent on thephase difference between the interfering waves. That the

phase difference can be determined to some degree by mea-surement of the irradiance of the resulting wave is empha-sized as the most important fundamental idea in interfer-ence techniques. The second part is a phenomenologicaldiscussion of the oblique interference of two plane waves.Sufficient for the moment is the basic concept with emphasison the fact that a grating-like structure is produced, and thatthis type of interference is fundamental in moire and holog-raphy.

THE GENERIC INTERFEROMETERThe next step is the concept of the ‘‘generic interferometer.’’An illustration of such an imaginary device is shown in Fig-ure 1. This model of measurement of path length differenceby two-beam interference is very useful in that it establishesa universal paradigm for all interferometric measurementwithout reference to a particular technique. Emphasis isgiven the fundamental idea that detectors are insensitive tophase, so we convert phase difference to irradiance differ-ence through the process of interference. This is also a goodtime to mention the main problem with interferometry, thatabsolute phase difference cannot be measured without ad-ditional information such as can be obtained by phase step-ping, compensation, or the use of two wavelengths.

DIFFRACTIONAlthough it is not actually needed at this point in the de-velopment, this is a good time to present the second corner-stone in optics, that being the concept of diffraction at anaperture and its implications for modifying optical informa-tion. Only the basic ideas are given at this stage, since thetopic will be studied in detail when it is required for under-standing of optical processing, moire, and holography. Anintroductory demonstration involves passing laser lightthrough gratings and looking at the result on a screen. Ifavailable, a simple optical bench with a laser, a beam ex-pander, two lenses, and a screen can be set up to show thediffraction patterns obtained when a plane wave falls on anaperture containing a transparency.

Emphasis is given the fact that when light passes throughany aperture, whether or not there is a lens in place, theirradiance pattern downstream is proportional to the Fouriertransform of the aperture. Analogies with audio signal proc-essing are useful here, given that students know something

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of that subject. In the optics form, spatial frequency in theinput plane is converted to distance in the transform plane.That the frequency content of the information in the aper-ture can be modified in the transform plane and that a mod-ified inverse transform can be created are discussed withsome examples. For some reason, examples related to intel-ligence gathering seem quite effective. Bandwidth limit im-plications catch the imaginations of some, particularly pho-tographers. ‘‘Do you really want to use the smallest possibleaperture for landscape photography?’’

BASIC INTERFEROMETRIESWith the concepts mentioned above delivered, one can passto some specific techniques that illustrate applications of theconcepts, that are useful measuring methods, and that es-tablish additional concepts. One approach is to use Newton’srings to develop the idea of interferometry based on ampli-tude division, and Young’s fringes to illustrate wavefront di-vision. Both of these interferometries are easily demon-strated in the classroom or laboratory, it being most effectiveto do the demonstration before any explanation is offered.Optical flats and a penlight serve to illustrate Newton’srings. A laser and a piece of aluminum foil with two smallholes very close together will illustrate Young’s fringes.

A useful goal can be accomplished by developing clearly forboth these methods the relationships between interferencefringe order, path length difference, and the parameter ofinterest, namely surface profile differences in the one caseand pinhole separation in the other. These calculations arevery simple in the context of these two interferometries, andthe principles carry over to more complex methods. It is alsoworth mentioning that Young’s fringes are used directly inthe method of speckle photography to be studied later.

PHOTOELASTICITY AS A PARADIGMWhether or not Newton’s and Young’s interferometries arestudied, it is appropriate but not necessary to study photo-elasticity next. Photoelasticity serves as a useful instruc-tional paradigm for two-beam common-path interferometryas well as being an important measurement tool. The im-portant possibilities of photoelasticity for determining stressdirections and magnitudes are shown using a couple of po-larizers, a model, and an overhead projector. Also, the po-tential for obtaining accurate data in a quick and simple waynear stress concentrations and singularities can be empha-sized during this demonstration by using a model with somenotches or section changes. Before getting into the subjectas a measurement technique, some more unifying conceptsare presented, including refraction, retardation, birefrin-gence, and relative retardation. Once these ideas are under-stood, photoelasticity theory can be developed quickly, sinceall the required concepts have already been presented, andmaximum attention can be given to the calculation of pathdifference as a function of principal refractive indices. Thatthe birefringence in materials might be dependent on stresscan be saved for later. The idea of photoelastic compensationcan be presented as a precursor to what are now called phasestepping methods.

HOLOGRAPHY AND HOLOGRAMINTERFEROMETRYAn important point is that with the concepts and tools inhand, instruction in any of the optical techniques can be pur-sued with little additional development. For example, sup-pose that photoelasticity is not of high priority, maybe be-cause it is considered old-fashioned, but there is specialinterest in holographic methods. First, a white-light holo-gram and penlight can be passed around to arouse curiosity.One need only introduce complex notation and complex am-plitude (actually, this is not necessary, it just makes the cal-culations easier) and a more complete discussion of obliqueinterference of two beams; then the development of holog-raphy theory can be finished in a half-hour or so, dependingon the detail needed and the time available.

Here, the process of holography is presented as one involvinginterference to store the information and diffraction to re-trieve it. All the rest is technical detail that can be discussedas time permits, and the students can begin lab experimentsin holography right away. After presentation of the basic ho-lographic process, hologram interferometry is considered asanother application of the concept of two-beam interference.In its simplest form, this interferometry is only another visitwith Newton’s rings.

SPECKLE PHOTOGRAPHYThe treatment of speckle methods is similar except that noadditional concepts are necessary. A speckle pattern is firstcreated in the classroom on a screen or the wall using a laserand simple beam expander. The students are asked to ob-serve the changes in the speckle caused by: (a) slow smallmotions of the head; (b) changing the eye aperture by bring-ing the eyelids nearly closed. These demonstrate the rela-tionships between speckle size and aperture, and that move-ment of either the observer or the specimen produce changesin the speckle pattern.

At this point, the concept of speckle photography can be de-veloped and demonstrated in only a few minutes. The onlyimportant concepts are the formation of speckle, the factthat the speckle moves with the specimen, Young’s fringes,and, in the case of whole-field processing, the modificationof frequency content of a doubly-exposed speckle pattern byFourier optical processing (diffraction). It is easy to demon-strate the use of Young’s fringes to obtain surface dis-placements by passing around a double-exposure specklephotograph and a penlight. A basic speckle photographyexperiment is easy to set up, since it requires only an ex-panded laser beam, a specimen whose motion can be con-trolled, and a camera.2

This is also a good time to introduce the concept of white-light speckle photography, since no new ideas are required.Applications to geophysical problems seem to capture theimaginations of students.3

SPECKLE INTERFEROMETRIESThe difference between speckle interferometries and specklephotography must be clearly established, both as to the fun-

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damental ideas and the applications, which augment one an-other.

In speckle interferometry, interference of multiple waves cre-ates a certain irradiance within each subjective speckle, withthis irradiance changing as movement of the specimencauses path length changes within each speckle. Diffractionconcepts are important because the bandwidth of the lensaffects speckle size.

The author finds that speckle interferometry is best ex-plained by use of a thought experiment. Suppose a film isexposed to a speckle pattern from a cantilever beam so as toform a row of only 10 or so coarse speckles having randomirradiances. The film is then developed, causing the darkspeckles to form a hole in the emulsion (unexposed emul-sion), the light speckles form opaque spots in the emulsion,and so on. The developed film is then placed exactly in itsoriginal location. It is easy to show that no light comesthrough the film, because the illuminated spots coincide withthe opaque areas, and the holes in the emulsion have nolight falling on them. But, what if the cantilever beam isdeformed? The irradiances of the individual speckles change,so that now some illuminated speckles coincide with theholes in the emulsion. Imagine passing to a limit wherethere is a large number of small speckles. One can see thatsome sort of fringe pattern will form, but there will be manysmall gaps that reduce fringe visibility because of all thosespeckles that were originally light.

The reason for use of this thought experiment is that it em-phasizes a unique aspect of speckle interferometry that isdifficult to keep in mind, specifically that this interferometryuses only changes of irradiance in individual speckles. Thefringe pattern formed is not, properly speaking, an interfer-ence fringe pattern at all. Experience suggests that referringto speckle correlation phase maps as ‘‘fringes’’ impedes fullunderstanding of these methods. A corollary is that thespeckle size is not fundamentally important as long as thetwo patterns are registered so as to facilitate direct subtrac-tion of one irradiance from the other.

Once the fundamental concept is understood, one observesthat, since speckle size need not be small, electronic /digitalimaging devices can be used to record the irradiances in in-

dividual speckles for each state of the specimen, and the sub-traction of irradiances can be performed in a computer. So,here we have an interferometry method that is compatiblewith electronic imaging and data processing. Experiments todemonstrate simple subtraction electronic speckle interfer-ometry are simple and inexpensive to set up and run.4

As these ideas are developed, the limitation of interferome-tries in determining absolute path length changes will beobvious. Phase stepping can be introduced as a method toobtain absolute path length changes; it can be introduced asan extension of the compensation techniques studied withphotoelasticity.

CONCLUDING REMARKSThe purpose of this paper is to outline a workable flexibleapproach to the teaching of optical methods of experimentalmechanics. Specific techniques were chosen for illustration.There is no intent to slight or diminish other importantmethods such as geometric moire, moire interferometry,shearography, laser doppler, caustics, and so on.

The examples cited above establish a paradigm for teachingat different levels and under serious time constraints. Max-imum use is made of unifying concepts and sequential or-ganization of the material to exploit transfer of learning.

The approaches were developed by trial and error over manyyears. They will certainly evolve further with time and prac-tice. A long-term goal is to teach the physics and the tech-niques with maximum efficiency so that they need not bedropped from crowded engineering curricula.

References1. Cloud, G.L., Optical Methods of Engineering Analysis, Lon-

don, Cambridge University Press, (1995, 1998).2. Cloud, G.L., Practical Speckle Interferometry for Measuring

In-Plane Deformations, Applied Optics 14, 4, 878–84 (1975).3. Conley E. and Cloud, G., Whole-field Measurement of Ice Dis-

placement and Strain Rates, Journal of Offshore Mechanics andArctic Engineering, 110, 169–171, (1988).

4. Cloud, G.L., Speckle Interferometries Made Simple andCheap, Proc. 2000 International Congress on Experimental, Theo-retical and Experimental Mechanics, Society for Experimental Me-chanics, Bethel, Connecticut, June 2000. �