QUANTITATIVE
HOLOGRAPHIC
INTERFEROMETRY:
MEASUREMENT OF
SOLID OBJECT DEFORMATIONS
R.F.C. KRIENS
QUANTITATIVE HOLOGRAPHIC INTERFEROMETRY:
MEASUREMENT OF
QUANTITATIVE HOLOGRAPHIC INTERFEROMETRY:
MEASUREMENT OF
SOLID OBJECT DEFORMATIONS
PROEFSCHRIFT
ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,
op gezag van de Rector Magnificus,
prof. dr. J. M. Dirken, in het openbaar te verdedigen ten overstaan van een commissie door het College van Dekanen daartoe aangewezen,
op 1 maart 1988 te 16.00 uur.
door
RUDOLF FRANCOIS C0RNELIS KRIENS
Geboren te 's-Gravenhage, Natuurkundig Ingenieur
TR
ó'iss
1613
door de promotor: Prof.dr.ir. H.J. Frankena hoogleraar Theoretische en
STELLINGEN
behorende bij het proefschrift van
R.F.C. Kriens
1 maart 1988
1. Du mogelijkheden van de holografische interferometrie bij de analyse van mechanische vervormingen kunnen in sterke mate worden uitgebreid indien deze meetmethode wordt gecombineerd met het gebruik van eindige - en rand-elementcnmethoden uit de technische mechanica.
2. Hel belang van de in technisch opzicht uitvoerbare interpolatie van de "fringe locus functie" tol op 27T/1000 radialen is twijfelachtig, gezien de benaderingen die moeten worden gemaakt in de vertaling van de interferentie paironcn naar mechanische vervor mingen.
a) R. Diindliker. "Quantitative strain measurement through holographic interferome-try". Proceedings of the International Conference on Applications of Holography and Optical Data Processing. Jerusalem. 1076. Pergamon Press, 1977. biz. 169-181, h) Dit proefschrift. Hoofdstukken 4 en 5.
3. Dynamische dempers reduceren trillingen in een constructie effectiever naarmate ze minder demping bezitten.
4. De gebruikelijke karakterisering van het kabinelawaai in propeller-vliegtuigen in dB( A) is onjuist.
5. Lawaaireductiesdie reeds zijn verkregen in vliegluigen met gesynchroniseerd draaiende propellers kunnen nog aanzienlijk worden vergroot indien wordt overgegaan tot symme trisch draaiende propellers.
6. Een optimaal gebruik van de bijzondere eigenschappen van vezelversterkte materialen ten opzichte van conventionele materialen vereist een nieuwe wijze van ontwerpen waarin een multidisciplinaire aanpak essentieel is.
7. Een groot nadeel van personal computers in grote organisaties is dat naast het gebruik ook hei beheer van programmatuur en gegevensbestanden per persoon plaats vind!. 8. De voorvoegsels "Computer Aided" en "Computer Assisted" zijn bij veel processen al
zo vanzelfsprekend geworden dal hel juisi de niei compuler-ondersteunde processen zijn die een nadere aanduiding behoeven.
9. Boordcomputers in aulomobielen kunnen bijdragen tot de verkeersveiligheid indien daarmee de rijvaardigheid van de bestuurder wordt gelest alvorens het starten van de motor loe ie lalen.
10. De keuze van één kleur en vrijwel dezelfde plaats voor zowel achierlichien. remlichten en mistaehlerlichten bij een aulomobiel is verre van optimaal.
11. Nu bij de wei is geregeld dal een ficis via rclro-reflectic van opzij. en van achteren zicht baar is. is het noodzakelijk zulks ook voor de voorzijde verplicht te stellen.
12. Het is onverantwoord dal het handelen bij ongevallen geen verplicht onderdeel van hel rij-examen is.
Table of contents
TABLE OF CONTENTS
CHAPTER 1. GENERAL INTRODUCTION
1.1 Measurement of solid object deformations 2 1.2 Development of a quantitative holographic interferometer system 3
1.3 Thesis 5 1.4 Conclusions 6 1.5 References 6 CHAPTER 2. HISTORICAL BACKGROUND
2.1 Introduction 10 2.2 Short history of holography 10
2.3 The evolution of holographic interferometry 14
2.4 Problems of a practical nature 17 2.5 Advances in laser technology 18 2.6 Photothermoplastic recording materials 20
2.7 Problems with fringe interpretation 22
2.8 References 26
CHAPTER 3. "OFF-AXIS" REFERENCE BEAM HOLOGRAPHY
3.1 Introduction 38 3.2 A few words on notation 38
3.3 Recording a hologram 42
3.4 The hologram 46 3.5 Object wave reconstruction and the formation of a virtual
image 52 3.6 The f o r m a t i o n of a r e a l image 58
3 . 7 R e f e r e n c e s 60 CHAPTER 4 . HOLOGRAPHIC INTERFEROMETRY
4.1 Introduction 64 4.2 Interferometry with reconstructed wave fronts 64
4.3 Holographic interferometry with diffusely reflecting objects 65
4.4 Generalization of the interferometer configuration 68
4.5 Imaging by the lens system 71 4.6 The object plane fields 74 4.7 The elimination of speckle 77 4.8 Autocorrelation of the complex scattering function 80
4.9 Specular components of the scattered field 81 4.10 Diffuse components of the scattered field 83 4.11 Approximation of the impulse response functions 84 4.12 Approximation of the object illumination wave functions . . 88
4.13 The diffuse image plane field 92
CHAPTER 5. A SIMPLE FRINGE LOCUS FUNCTION
5.1 Introduction d * * d ' * ' ( * " * *>d 1 0°
5.2 Asymptotic expansion for I. , I. and jU. ,0. I . . . . 100
5.3 The fringe locus function B't . . ' . . . . . ' . .'. 107
5.4 Two examples 113 5.5 References 117 CHAPTER 6. BASIC OPERATING MODES FOR HOLOGRAPHIC INTERFEROMETERS
6.1 Introduction 120 6.2 "Real-time" mode 120 6.3 "Double-exposure" mode 127 6.4 "Dual reference beam double-exposure" mode 133
6.5 "Double-pulse" mode 138 6.6 "Time-average" mode 143
6.7 References 156
CHAPTER 7. QUANTITATIVE INTERPRETATION TECHNIQUES
7.1 Introduction 162 7.2 Qualitative interpretation 162
7.3 Quantitative interpretation 164 7.4 The fringe localization technique 165 7.5 The hologram fringe technique 167 7.6 The dynamic interpretation technique 169
7.7 The static interpretation technique 173 7.8 Selection of the best technique for industrial applications 178
7.9 References 179
CHAPTER 8 . MEASUREMENT OF SINGLE DEFORMATION COMPONENTS
8.1 Introduction 186 8.2 Coincident illumination and observation of the object scene 186
8.3 Phase shifted holographic interferometry 191
8.4 Experimental results 196
8.5 References 200
CHAPTER 9. MEASUREMENT OF COMPLETE DEFORMATION VECTORS
9.1 Introduction 204 9.2 Triple interferometer configurations 204
9.3 Calculation of displacement vectors 209 9.4 Simultaneous exposures in the triple interferometer system . 213
9.5 Experimental results 217
9.6 References 225
APPENDIX A. THE IMPULSE RESPONSE FUNCTION OF A THIN LENS
A.l Introduction 228 A.2 The imaging configuration 228
A.3 Imaging of arbitrary object space positions 228
A.4 Imaging of "object plane" positions 230 A.5 Lens with a circular aperture 231
Table of contents
APPENDIX B. A GENERALIZED FORMULA FOR THE OBJECT PLANE FIELD
B.l Introduction 236 B.2 Procedure for derivation of the generalized formula . . . . 236
B.3 "Direct" diffraction and the reference plane field 237 B.4 "Inverse" diffraction and the object plane field 238
B.5 References 239
APPENDIX C. THE STATISTICAL PROPERTIES OF THE COMPLEX SCATTERING FUNCTION
C.l Introduction 242 C.2 The complex scattering function 242
C.3 Gaussian surface roughness distribution 244 C.4 Asymptotic behaviour of the autocorrelation function R(, . . 246
C.5 A Gauss function as normalized autocorrelation function . . 247
C.6 Autospectrum of p 249
C.7 References 251
APPENDIX D. THE SURFACE ELEMENTS ON THE INITIAL AND DEFORMED OBJECT SURFACE
D.l Introduction 254 D.2 The surface elements dS and dS 254
D.3 References 257
APPENDIX E. DERIVATION OF FORMULA (5.16)
E.l Introduction 260 E.2 Mathematical discussion 260
SAMENVATTING 264
ACKNOWLEDGMENT 267
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GENERAL INTRODUCTION 1Chapter 1
1.1 Measurement of solid object deformations
In many branches of scientific and industrial research experimental studies are carried out to determine the deformation of solid objects under mechanical or thermal loads. Traditionally, such experiments
are performed with established measuring techniques from experimental
mechanics using strain gauges and displacement transducers. These techniques provide point-wise data. Extensive experience is required on the part of the investigator to select the proper measuring positions in order to capture the areas of highest interest. Integral measurements over the entire object surface are infeasible. Another disadvantage is that the measuring devices must either be fixed to the object under study or brought into contact with it. This is a time-consuming operation which must be repeated for every measuring location. Moreover, the deformation field may be influenced unacceptably by the measuring devices.
Both disadvantages can be eliminated with the aid of optical measuring techniques. Well-known optical techniques in the field of experimental mechanics are the moiré technique and the use of photo-elasticity . Both techniques, however, suffer from experi mental complexities: the moiré technique is not suited for objects with arbitrary shapes, while photoelasticity requires a photoelastic replica of the object or a special coating on its surface.
Outstanding properties for measuring solid object deformations are offered by a technique known as holographic interferometry. It combines the advantages of the long existing technique of interferometry , of the laser as a coherent light source, and of the holographic process of wave front recording and recon struction. With the aid of holographic interferometry images can be produced of diffusely reflecting objects which are covered with patterns of dark and bright fringes that are indicative of the deformation or rigid-body motion of the object. This is possible since holography allows a light beam scattered by an object to be
recorded and reconstucted with such precision that it shows visible interference with a light beam scattered by the same object at a later time. Alternatively, this second beam can also be a holographic reconstruction. The major advantages of holographic interferometry are that it is contactless, extremely sensitive, and suited for integral measurements across entire object surfaces.
1.2 Development of a Quantitative holographic interferometer
In 1974 the Institute of Applied Physics TNO-TH in Delft together with the Delft University of Technology acquired a contract from FIAT
research laboratories, Turin, Italy, to explore if and how deformation fields could be determined from fringe patterns generated by holographic interferometry. In this particular feasibility study the author demonstrated the possibilities of holographic interferometry for deformation measurements and evaluated the most common techniques used for quantitative interpretation of fringe patterns. Because of its suitability for industrial applications, where fast computerized data acquisition and high accuracy are important, the so-called "static interpretation technique" (see Sections 7.7 and 7.8 of the present thesis) was selected for further development.
As a follow-up to this preliminary study a number of contracts were signed for the actual development of a holographic interferometer enabling the measurement of three-dimensional deformations on solid objects. Major design considerations for this interferometer were:
• the interferometer should be able to accommodate large objects with dimensions up to lm X lm X lm. Such object sizes are common
in the automotive industry.
• the shape of the object may be highly irregular, e.g. as intricate as a combustion engine with its auxiliary equipment.
• the shape of the object and its relative position in the interferometer are unknown a priori. Hence, quantitative interpretation of the fringe patterns must not require explicit data on the object's shape and its position.
Chapter 1
This combination of requirements was beyond the scope of the quantitative holographic interferometers reported in the existing literature , which concerned objects that were either much smaller or had rather simple and well-known geometries. Simplifications that were allowed in the quantitative interpretation procedures of those interferometers could not be adopted in this new interferometer system without Jeopardizing its accuracy.
To eliminate the interpretation problems caused by the large maximal dimensions of the object and the assumed lack of data on its shape and position the author devised a novel interferometer configuration creating coincident illumination and observation of the object. Experiments regarding one-dimensional deformation measurements using
this special configuration were reported in 1977 . At the same occasion the author presented a second innovation permitting the establishment of the signs of measured deformation components and the detection of local extremes in the so-called "fringe locus function", which, if undetected, would lead to severe misinterpretations.
Late 1977, further development resulted In a dual holographic interferometer system with which two-dimensional deformation measurements were performed . In 1978 a complete triple interferometer system was set-up, based upon the previous single and dual interferometer versions. With the aid of this triple system deformation vectors were accurately measured under conditions fully matching the earlier mentioned design requirements. A computer program was developed to calculate the deformation vectors from the fringe patterns generated in the three interferometers. Experimental results obtained with this system were reported at the eleventh Congress of the International Commission for Optics . Later on, an additional improvement was introduced to the system by making the three separate interferometers mutually incoherent, while allowing simultaneous exposures, something previously impossible. Experi mental results with this modified system are reported for the first time in this thesis (see Chapter 9 ) .
Most quantitative interpretation techniques which appeared in the literature on this topic assume small flat objects. The present interferometer, however, was designed to accommodate large objects of
highly irregular shape. The author developed a mathematical formulation which can deal with objects having such characteristics.
1.3 Thesis
This thesis gives a written account of the theory, design considerations, development stages, and experimental try-outs of the holographic interferometer system discussed in the previous section.
Chapter 2 is devoted to the histories of holography and holographic interferometry. It provides a reference frame for the importance of this Interferometer system.
For a proper discussion of holographic interferometry a concise treatment of the theory of holographic wavefront recording and reconstruction is indispensable. This theory is covered by Chapter 3.
Chapters 4 and 5 contain a mathematical formulation for holographic interferometry of large objects with irregular shapes. A rather simple expression is obtained relating the generated fringe patterns to the deformation of the object.
Various recording and reconstruction sequences ("operating modes") can be used to generate the fringe patterns, each having its own range of applications. The most important operating modes are reviewed In Chapter 6.
Chapter 7 describes how the theory of Chapters 4 and 5 can be used to determine deformations. The most prominent interpretation techniques are compared, and the so-called "static" technique is selected.
Chapter 8 discusses how this technique can be employed in an actual holographic interferometer for the measurement of single components of deformation. It also describes a_ special interferometer configuration with coincident illumination and observation (already mentioned in Section 1.2) allowing the object's shape to be unknown, and a special procedure to determine the proper senses of the measured components by using phase-shifted interferometry. Experimental results are presented.
Chapter 1
The extension of the interferometer system to three-dimensional deformation measurements is the subject of Chapter 9. Feasible interferometer configurations serving this purpose are reviewed in terms of attainable accuracy and ease of operation. A system is selected having three separate illumination sources and three separate viewing ponts. Again, coincident illumination and observation is used to allow the analysis of objects having unknown shapes. A mathematical formulation is presented for the calculation of the displacement vectors from the three fringe patterns using the simple expression of Chapter 5. Furthermore, a technique is proposed allowing simultaneous holographic recordings instead of sequential ones in triple interferometer configurations. Experimental results obtained with this system are discussed.
1.4 Conclusions
A practical holographic interferometer system has been developed together with quantitative interpretation algorithms enabling the precise measurement of three-dimensional deformations on diffusely reflecting objects. The objects under invesigation may be large and have irregular and unknown shapes. The accuracy of the system as presented here is governed by the inaccuracies made in measuring the interferometer geometry (cf. Section 9.5). These can easily be improved by an order of magnitude if dedicated equipment is used to determine this geometry, e.g. theodolites.
Other possible improvements are the replacement of photographic registration of the fringe patterns by video-electronic registration using e.g. CCD (Charged Coupled Device) sensors, and the use of digital image processing techniques to analyze these patterns.
1.5 References
1. F.-P. CHIANG,
"Moiré methods of strain analysis", Chapter VI in: "Manual on experimental stress analysis", Society for Experimental Stress Analysis, Westport, U.S.A., 1978.
2. D.POST,
"Photoelasticity", Chapter IV in: "Manual on experimental stress analysis", Society for Experimental Stress Analysis, Westport, U.S.A., 1978.
3. M.BORN and E.WOLF,
"Principles of optics", Pergamon Press, Oxford, 1970, Chapter VII. 4 . E.J.COLLIER, C.B.BURCKHARDT, and L.H.LIN,
"Optical holography", Academic Press, New York, 1971. 5. R.F.C.KRIENS,
"Een vooronderzoek voor de bouw van een kwantitatieve holografische interferometer" (a feasibility study for the development of a quantitative holographic interferometer), Master's thesis, Delft University of Technology, Department of Physics, 1975 (partly in Dutch).
6 see e.g. References 51 - 62 of Chapter 2. 7 R.F.C.KRIENS,
"Some considerations on the quantitative interpretation of holographic interferograms", Proceedings of the first European Conference on Optics applied to Metrology (October 26-28, 1977, Strasbourg, France), Society of Photo-optical Instrumentation Engineers, Bellingham, U.S.A., Vol. 136, 1978, pp.156-165.
8. R.F.C.KRIENS and M.LODEWIJK,
"Quantitative interpretation of holographic interferograms: a feasibility study", report 805.101, Institute of Applied Physics TNO-TH, Delft, 1978, Chapters V and VI.
9. R.F.C.KRIENS and M.LODEWIJK,
"Measurement of vectorial displacements with the aid of a three fold holographic interferometer", in: "Optica Hoy y Maïlana", Proceedings of the Xlth Congress of the International Commission for Optics, (10-17 September 1978, Madrid, Spain), J.Bescos, A.Hidalgo, and J.Santamaria (Eds.), pp.707-710.
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HISTORICAL BACKGROUND 92.1 Introduction.
The present chapter will briefly describe the evolution of holographic interferometry to its present day state, in order to provide a historical background to the discussions in this thesis. Since holography is an essential part of this technique, its history is treated too.
2.2 Short history of holography
On February 8, 1979 Dennis Gabor passed away . Gabor is known as the father of holography, because of his invention of the process of wave front recording and reconstruction. In his acceptance speech
for the 1971 Nobel Prize in Physics he called himself "one of the few lucky physicists who could see an idea of theirs grow into a sizable chapter of Physics".
It was more than two decades earlier, in 1948, that Gabor2
proposed his idea of a two-step method in an attempt to improve the resolution in images obtained with electron microscopes. Being unable to demonstrate the validity of his principle with electron beams, he reported in a second article in the same year the use of visible light in both stages of the process for the experimental verification of his "new microscopic principle". Gabor presented further developments of his theory in a series of papers ending in 1953. Research carried out to apply Gabor's principle to electron microscopy and to X-ray microscopy has failed to be very successful up to now. Microwave holography and acoustical holography gained more success, but none of these applications could really make Gabor famous.
It was in the field of Optics, that his idea came to flourish. The first to report investigations of applying the process of wave front recording and reconstruction for mere optical purposes, was G.L. Rogers , in 1950. He was also the first to use the word
Historical background
"hologram" for the encoded record of the wavefront. Using high pressure mercury-arc lamps, Rogers and other investigators succeeded in obtaining reconstructed virtual images of small opaque objects on transparent backgrounds; they even conceived at that time techniques which many years later would become important in holography, such as
9 copying of holograms .
Unfortunately, in Gabor's - also called "in-line" - wave front recording configuration (all light beams and components centered around a single straight line), the reconstructed virtual images are plagued from overlap by other, out-of-focus, images. Early, but not very effective attempts were made to eliminate these unwanted images . Other disadvantages of the "in-line" configuration are the limitations put on the nature of the objects which can be recorded holographically, and the low quality and faintness of their holographic recontructions. These drawbacks induced the almost total abandonment of holography by its investigators at the end of the 1950's.
In 1960, an event took place that would have a tremendous impact on many branches of science: the first lasers were brought into operation. This was of vital importance to the survival of
1 3
holography. At the same time Leith and Upatnieks started working on ways to separate the twin holographic images spatially. The methods they used were derived from earlier developed viewpoints in information theory , especially from those related to microwave radar techniques. In 1963 Leith and Upatnieks introduced a holographic configuration in which a separate reference beam is used propagating in a different direction as the beam that is transmitted by the object. With this so-called "off-axis" reference beam configuration they achieved a spatial separation between the reconstructed images . Because of the low intensity and limited coherence properties of their light source, which was a mercury discharge lamp, they still used transparencies as objects. However, in 1964, they coupled their "off-axis" reference beam technique to the growing laser technology and presented results of
j 7 — j o
the imaging of opaque three-dimensional objects . The images reconstructed from holograms taken with this technique are almost life-like. They are bright, undisturbed and they possess all the
properties associated with their three-dimensionality. In this respect, the images cannot be distinguished from the actual objects observed in the same laser-light illumination. These results could be obtained because the laser is a source of light with intensity and coherence properties far superior to those of conventional sources. All these technical improvements formed the breakthrough which let holography experience a great revival. It resulted in an avalanche of scientific papers describing numerous extensions, improvements and applications of the holographic technique. This explosive revival is reflected in a bibliography of more than 180 papers covering the first period of holography starting with Gabor's paper, "Diffraction microscopy", and ending w4th the many
papers published in 1965 and early 1966.
At that time, the public, too, seemed to be ready to appreciate holography. The possibility of forming three-dimensional images
found profound interest from the artistic community and the advertising world . After the rise and fall of a number of non-holographic three-dimensional display techniques , holo graphy was thought to be the final and commercially profitable answer. The famous artist Salvador Dali was one of the first to have a hologram made to order. It is startling to realize that we still can be looking at a lifelike image of Gabor sitting behind his desk, because of the mere fact that a pulsed hologram was taken from him in the early 1970's.
The aforementioned revival faded gradually when it was realized that many futuristic dreams of applications, e.g. holographic movies and television, could not come true with the current state of technology or only at unacceptable costs. Even, things that were thought to be very simple by prospective users, in particular the formation of bright multi-color images with conventional light sources, were not yet within reach of the scientists.
In the mid 1970's the interest in the artistic and commercial applications was at its lowest point since the discovery of holography. And probably, holography would have been abandoned for a second time, had it not been for the progress that was made with scientific and industrial applications. Those applications formed
Historical background
over all these years the incentive for the continuation of the highly specialized research in the field of holography. Without doubt, interferometry with holographically reconstructed wavefronts is the most significant of these applications. In the next section a concise account will be given of the origin and evolution of this kind of interferometry. Other uses of optical holography are found in optical data storage and data retrieval , in optical computing and image processing , in microscopy , and in the manufacturing of optical elements . As an offspring of the research in those fields, techniques emerged that are also quite useful for holographic three-dimensional imagery or "display holography" as it sometimes is called. For instance, the recent
reanimation of the interest in holographic display techniques is largely due to the following two innovative developments:
1. The invention of the so-called "Benton" or "rainbow" type of holograms j in the images reconstructed from these holograms the parallax In one preferably the vertical -direction is sacrificed in favor of the possibility of white-light reconstruction and a brighter image.
2 8
2. The evolution of dichromated gelatin emulsions and appropriate processing techniques through which holograms can be recorded capable of diffracting nearly 100 per cent of the incident light into the virtual image; as yet, these form the brightest holographic images available.
Industry's objective for developing these emulsions is the holographic production of light-weight optical elements with extremely high diffraction efficiencies. Optical elements of this sort can be used in a variety of products such as
2 9
consumer-type movie cameras and head-up displays in aircraft cockpits for imaging important data into the pilot's regular field of view.
The future of display holography is hard to foresee. An attempt to monopolize and control its progress and application by trying to acquire all the vital patents has failed . At present, these patents are owned by the Atari company. The lack of Inexpensive and
simple to use equipment for holographic recordings has hitherto retarded the popularization of display holography. Artistic exploration of holography will undoubtedly stimulate the growth of the number of people actively involved - just as has happened in the early days of photography. Meanwhile, mass reproduced holograms (such as the embossed holograms on the covers of the March 1984 and November 1985 issues of the National Geographic Magazine which were both reproduced in more than 10 million copies) are triggering the fascination of the general public.
2.3 The evolution of holographic interferometrv
Less than 25 years ago, the possibility of interferometry with holographically reconstructed wavefronts was discovered. This novel technique became known as "holographic interferometry". Despite its young age it earned itself an important place among the established non-destructive testing and inspection techniques. Here, a brief account will be given of the discovery of holographic interferometry and the way in which it evolved onto its current state.
Holographic recording of wavefronts is extremely sensitive for mechanical or thermal instabilities of the recording set-up. This characteristic led to the more or less accidental discovery of the possibility of holographic interferometry, only a few years after Leith and Upatnieks had introduced their off-axis reference beam technique. At that time Powell and Stetson, working in Leith's group at the University of Michigan, investigated why certain holographic recordings of opaque threedimensional objects when reconstructed -failed to produce good-quality images, while other recordings yielded flawless images. They discovered that In the low-quality holograms the images were superimposed with dark fringes and - what is more important - that these fringes were caused by tiny vibrations of the objects during the recording. Although, earlier, Horman had used interferometry in conjunction with holography in his wind-tunnel research, Powell and Stetson were first to understand the possibility of interferometry with reconstructed wavefronts to its full extent. They reported on this in April 1965 . In subsequent
Historical background
papers38-*1 it was thoroughly investigated how the fringes in the
holographic images of objects in vibratory motion can be used to determine the modal shapes and amplitudes of these vibrations.
Shortly after Powell and Stetson's first presentation, several other investigators in the U.S.A. and in the United Kingdom discovered independently that holographic interferometry could also be used to analyze static changes in the position or shape of a solid object. These researchers were:
• Brooks, Heflinger, and Wuerker4 2 - 4 3 at TRW in Redondo Beach,
California
• Burch, Archbold, and E n n o s4 4 - 4 5 at the National Physical
Laboratory, Teddington, England
• Collier, Doherty, and Pennington at Bell Telephone Laboratories
• Haines and Hildebrand47-49, who like Powell and Stetson
-were working at the University of Michigan
These pioneers of holographic interferometry shared the opinion that with the discovery of this technique an extensive field of new possibilities was added to the discipline of optical metrology. Major considerations which led to this belief were:
• Through this novel technique it became possible to compare wave fronts of intricate shape which are formed upon diffuse reflection of laser light at unpolished and arbitrarily shaped object surfaces.
• At least one of the interfering beams is a holographic reconstruction of a beam existing at an earlier time (cf. Sections 4.3 and 4.4). Consequently, beams can be compared which do not exist at the same time (e.g. beams reflected by a single object surface under different circumstances). Evidently, such a possibility is not offered by classical interferometry.
• The data of interest are obtained as a pattern of dark and bright interference bands (see e.g. the photographs of Figure 4.2). These patterns are called "holographic interferograms" and the bands in them "fringes". The shape and orientation of the fringes, and the distance between them may vary across the interferogram. This illustrates that most holographic interferograms are not just related to a single point of the object under study, but to a whole region of it: every position in the interferogram corresponds to a different point of the object. A vast amount of information is obtained which with point-to-point measuring techniques (e.g. with strain gauges) would require many successive or simultaneous measurements.
• This is an optical technique and, hence, the measurements performed with it are inherently "contactless". This gives it an advantage over many of the other methods for non-destructive testing and inspection (see e.g. Vink and Versluis50).
At first, interest in holographic interferometry expanded explosively among scientists involved with optics and experimental stress analysis. Since the late 1960's, a great number of scientific meetings have been dedicated to holographic interferometry. At these occasions accounts were given on numerous applications stemming from a wide variety of scientific disciplines. However, despite these devoted efforts, the acceptance of holographic interferometry as a qualified technique did not come before the 1970's. Actually, there is a remarkable parallel in the developments of display holography and holographic interferometry. Both experienced a severe popularity crisis less than a decade after initial periods of enthusiastic response.
The causes for the diminished interest in display holography were already discussed in Section 2.2. In the case of holographic interferometry the reason is that the potential users wanting to invest in its development became disappointed by its slow progress. More problems were encountered in its implementation than were
expected. A number of problems were of a pure practical nature. They were related to the particular environment required for the production of holographic interferograms. Another class of problems
Historical background
concerned the acquisition and analysis of the data contained in the fringe patterns of the holographic interferograms. Fortunately, there was a small number of aficionados who were able to continue the research. Gradually, they solved the most vital problems in holographic interferometry and contributed greatly to its survival.
The following three sections will deal in more detail with the problems of a practical nature. The difficulties related to the data acquisition and interpretation of the interferograms will be discussed in Section 2.7.
2.4 Problems of a practical nature
In the early days of holography the only photosensitive materials suitable for recording holograms were silver-halide emulsions . These emulsions allowed an acceptable trade-off between the contradictory requirements on the resolution and the photosensitivity of a holographic recording material. Since the resolution requirement is the most stringent of the two, the trade-off resulted in photosensitivities lower than that of the usual photographic silver-halide emulsions (exposure energies needed to obtain processed emulsions with densities around D = 1 are typically 0.02-0.8 J/m
2
for holographic, and 0.1-1.0 mJ/m for photographic materials). The laser sources available in the later 1960's had powers not exceeding 10 mW. Consequently, the exposure times of holographic recordings ran into scores of seconds, and even into minutes, depending on the characteristics of the particular object and on the recording configuration.
During the recording of holographic interferograms, path length variations in the beams which are not contributed by the phenomenon under investigation should be avoided. Even variations as small as a tenth of a wavelength can lead to deterioration of the desired fringe pattern. These unwanted variations may occur as a result of mechanical vibrations or thermal expansions in the holographic set-up. Another cause are refractive index changes in the air trajectories traversed by the laser beams induced by flow and turbulences in the air. Considering the long exposure times, the early investigators decided that it was imperative to carry out their
experiments with rigid set-ups mounted on massive vibration-isolated tables which were shielded from air-flows and fluctuations in the environmental temperature. Furthermore, they were forced by the broad spectral sensitivities of the silver-halide materials to take the holographic recordings in absolute darkness. Other less acceptable consequences of the use of silver-halides are:
• A photochemical process is required involving immersion of the exposed emulsion in at least one liquid agent to turn it into a hologram. This proces often takes five minutes or more, and is
usually carried out in a processing facility located outside the actual holographic set-up. It is easily understood that this inhibits the application of holographic interferometry in situations demanding high through-put rates of holographic interferograms (e.g. in non-destructive inspection of products manufactured in large volumes).
• The photochemical process leads to inhomogeneous shrinkage of the emulsion and to a significant change in its refractive index. Accordingly, the reconstructed wavefronts are not fully identical to the recorded ones: spurious fringes are added to the fringe patterns of the interferograms. Ideally, no fringe should be present at all in cases where the actual wavefront is compared against its own reconstructed replica (cf. Section 6.2: "Real-time mode"). In practice, however, spurious fringes are pratically always visible. Frequently, accurate quantitative interpretation of the fringe patterns from this kind of interferograms is hampered considerably by these unwanted fringes.
After this summary of practical problems the following two sections will discuss how progress in laser technology and development of a revolutionary recording material helped to solve them.
2.5 Advances in laser technology
Soon after the first lasers emerged from the laboratory a multitude of scientific and industrial applications was discovered. This caused a huge demand for laser sources and created perfect economical conditions for the rapid development of the most popular types. The
Historical background
kind of laser mostly used for holography was the Helium-Neon (He-Ne) gas laser. Through continuous development it became a very simple and extremely reliable source. Unfortunately, its potential output power appeared to be rather limited (the most powerful models have output powers in the order of 0.1 W ) .
At the end of the 1960's Argon-ion and Krypton-ion gas lasers became commercially available. These lasers had output powers which were one to two orders of magnitude larger than that of the He-Ne lasers. Present day Argon-ion lasers are capable of a so-called "single-line" output power in excess of 4 W. Evidently, the exposure times required for taking holograms are reduced substantially with such lasers. Hence, mechanical and thermal instabilities as well as background light have less influence on the hologram quality. If, on the other hand, long exposure times can still be tolerated, larger objects can be recorded. It is this type of laser that has enabled holographic interferometry with objects of the size encountered in industrial practice (e.g. with automobile engines and aircraft wing-sections).
Even the exposure times that can be attained with the most powerful continuous-wave lasers are not short enough to eliminate the need for a rigid vibration-isolated table to support both the object and the holographic set-up (including the laser source). Unsteady objects
like people or operating machinery are in too much motion or vibration to be holographed with continuous-wave lasers. However, with a class of lasers known as pulse-lasers one can generate very short light pulses with sufficient energy for holographic exposures. The duration of these pulses is typically about 30 nanoseconds, short enough to permit holographic recording of the aforementioned objects. With advanced systems the pulses can be emitted in pairs with short, controllable, separation times. This enables holographic interferometry of very fast motions and vibrations (cf. Section 6.5).
The use of pulse-lasers has extended the range of applications for holographic interferometry to situations where high levels of vibration and ambient illumination necessitate very short exposure times. It has been shown , that holographic interferograms can be recorded in industrial environments if the exposure of the
recording material Is limited to the minimal interval containing the pulse pair and if the undesired ambient light is blocked with optical filters. Illustrative of the present-day state of the art in holographic interferometry are the recordings taken of the vibrations
of spinning fan blades in a jet engine running at an outdoor test stand as reported by Stetson and Elkins . Pulsed holographic intererometry has also opened the possibility of dynamic object-loading for holographic non-destructive testing and inspection
(cf. Section 6.5). For instance, cracks can be detected with bending waves generated by impact excitation
2.6 Photothermoplastlc recording materials
Materials suitable for recording the holograms have been studied widely since the very beginning of holography . Many results of this work have been accumulated in Reference 74. Continued research carried out on silver-halide emulsions was rather disappointing. The improvements made on the photosensitivity of these materials and on their dimensional stability during processing were small and could only be made at the expense of their resolution potential. It is therefore easily understood that much research effort was directed into the quest for other photosensitive materials that would permit holograms of acceptable to good quality, in short processing times and at low cost.
Since the mid 1970's, a new and very promising photosensitive material has entered the field of holography. This particular material doesn't require any chemical processing. Its operation combines the physical phenomena of photoconductivity and thermoplasticity. Materials of this type are given the name "photothermoplastics". Initially, their potential was Investigated for xerographic applications. Later, it was realized that these materials are particularly suitable for the in-situ recording of holograms.
A standard piece of photothermoplastlc recording material consists of a substrate covered with a photoconductive layer, and a thermoplastic layer on top. Other arrangements are possible, too . After being positioned into the holographic set-up, the material is made
Historical background
photosensitive by electrostatic charging of the photoconductive layer. Exposure of the sensitized photothermoplastic yields a spatial modulation of its conductivity in a pattern which follows that of the incident light distribution. In a holographic recording this pattern is formed by the interference between the reference beam and the object beam. The result of the exposure is that an electrostatic force field is exerted on the thermoplastic layer which is modulated in the same pattern. One can process the recording material by bringing the thermoplastic to its softening temperature. At this stage a relief is formed by thickness modulation of the thermoplastic layer. In this way the light distribution incident during the exposure is stored in a hologram by spatial modulation of the optical path length across the photothermoplastic.
The photosensitivity of photothermoplastics (typically 0.05 J/m ) is comparable to that of silver-halide holographic ' recording materials. Hence, the exposure times are in the same range. Processing times, on the contrary, are orders of magnitude shorter than that needed with silver-halide materials: often, a few milliseconds are sufficient. Photothermoplastic materials can easily be processed "in-situ", i.e. in the set-up itself without removing them. The only condition is, that all illumination is stopped during this processing. The processing is dry, and it may be carried out by heat produced from an electric current. Since the sensitization of the photoconductor is also carried out by an electric process, the whole holographic recording can be controlled by electric and electronic circuits.
Another asset of photothermoplastic materials is the fact, that because of their special processing, they are not subject to shrinkage, nor do they exhibit refractive index changes. Hence, in "real-time" holographic interferometry (cf. Section 6.2) where an actual wavefront is compared with its reconstructed replica, no spurious fringes are developed that are due to the processing.
A property which cuts down on the quality of the reconstructions is the band-pass characteristic of the material's spatial resolution. On the other hand, the low-frequency cut-off of photothermoplastics
allows some incoherent background illumination to be present during the holographic recordings. This is useful, for instance, for recordings in the presence of burning candles and incandescent lamps.
Until now, two photothermoplastic holographic recording systems have become commercially available. A first system with a photothermoplastic film was introduced in 1975 . The film and a prototype system were developed by the German firm Kalle. A stripped-down version of it was put on the market by Rottenkolber Holosystems. In 1980 the Newport Research Corporation from California announced a commercial adaptation of a system developed by Honeywell. In this particular system the photothermoplastic material is supported by glass substrates. More importantly, the processing unit (and the material) also permits erasure of the information from the photothermoplastic material, after which it can be reused for recording. This repeated recording and reconstruction can be carried out hundreds of times without noticeable deterioration of hologram quality. In the first-mentioned system a motorized film transport is utilized to allow high through-put rates of holograms. With the approach used in the second system, even higher rates are possible. Neither system is available with automatic exchange of the recording material or a rapid refill capability.
Research on photothermoplastic materials and their processing is continued in many research laboratories of universities and industry. The huge potential of photothermoplastic materials for industrial applications of holographic interferometry, has been proven already by Ineichen and others . The number of applications is steadily growing.
2.7 Problems with fringe interpretation
Most people who see holographic interferograms for the first time,
are caught by their eye-pleasing fringe patterns. However, the
interpretation of these patterns in terms of the physical parameters of the phenomenon under investigation, e.g. a vectorial displacement field, is extremely difficult.
Historical background
When the first holographic interferograms were made, it turned out that the fringe patterns encountered were quite different from those found in classical interferometry. The common methods for data acquisition and fringe-evaluation were not directly applicable to those fringe patterns.
It was soon recognized that the lack of an adequate theory with algorithms for fringe interpretation inhibited the expansion of the technique and, thereby, limited the number of potential applications. With great effort studies were initiated to investigate how and where fringes are formed, and in what way they are related to the phenomenon under study.
At first, this research was aimed at finding criteria for the
* 7 JQ 7 9 — g n
localization of the fringes. Many papers deal with this subject. All this research, however, did not lead to a reliable method for the acquisition of accurate numerical data from a holographic interferogram. Later, the investigation of the fringe
B 9 — 9 2
localization was continued for its own sake
Other methods were devised in order to obtain quantitative results from the interferograms. Initially, quantitative interpretation of interferograms taken from solid objects was confined to pure rigid-body motions . With the experience gained from this, attempts were made to analyze not just rigid-body motions, but the general case of an object undergoing a deformation as well. To this aim the interferograms were divided in sections small enough to be considered as taken from parts of the object having homogeneous deformations. Information gained in this way appeared to have little
9 4 9 8
quantitative value. This activated other investigators to devise and propose techniques, with the aid of which both rigid-body motions and general deformations could be determined quantitatively. Numerous variations of these basic techniques for fringe
interpretation can be found in the relevant literature from the period 1966-1975. An overview and classification of the basic interpretation techniques was given by Briers in 1976.
In most literature published before 1975 the experimental verifications concerned objects of simple and well-known geometries, and single components of displacement. Obviously, the determination of vectorial displacement and deformation fields of arbitrarily shaped objects requires more elaborate interferometer systems and interpretation techniques. In the mid 1970's several research groups started the development of holographic interferometer systems capable of vectorial displacement measurements. Two different approaches can be discerned among the most promising of the proposed systems:
1. Systems using the so-called "dynamic" interpretation technique for acquisition of the desired data. In this particular technique - introduced by the Russian scientists Aleksandrov and Bonch-Bruevich - the observation is focussed on a fixed point located on the virtual image of the object's surface. If the direction of observation is changed continuously from one viewing angle to another, interference fringes will appear to shift and pass this point. The number of these fringes is proportional to the displacement component along the perpendicular bisector of the directions under which the point is observed at the beginning and the end of the change in viewing angle (this will be explained in more detail in Section 7.6). Additional components can be measured if the viewing direction is also varied along other pathes. Holographic interferometers for vectorial displacement measurements based on this concept were developed by Fossati Bellani and S o n a1 0 0 - 1 0 2 and Ek and _ . 1 0 3 - 1 0 5
Blederman
2. Systems in which the so-called "static" interpretation technique is employed. In this technique the entire image is observed from a static viewing point. The pattern of interference fringes is evaluated numerically by the following operation: it is assumed that a point can be identified on the object surface which has an accurately known displacement (e.g. a point with zero displacement). This will serve as a point of reference. The reconstructed image of the object surface is scanned along a line starting in the reference point and ending in the point of actual interest. There, the displacement component along the perpendicular bisector of the local illumination and observation
Historical background
directions can then be determined from the number of fringes that are passed along this line (cf. Section 7.7). This technique was introduced by Ennos . Measurement of additional components requires a set-up with multiple object illumination beams or multiple observation systems.
One of the proposed holographic interferometers that matured into a practical system is the interferometer presented in this thesis. Its development was initiated in 1974 with a feasibility study by the Institute of Applied Physics TNO-TH in Delft, the Netherlands, and the Delft University of Technology, under contract of FIAT automobile industries from Turin, Italy. In an early stage of this development the "static" and "dynamic" interpretation techniques were evaluated and compared (to be discussed in Section 7.8). In this comparison the "static" technique turned out to be the best choice for applications where accurate and efficient data acquisition is very important. Therefore, this technique was selected as a basis for the quantitative holographic interferometer. A configuration enabling the measurement of vectorial displacement fields was proposed in 1977 . This particular configuration consisted of three separate holographic interferometers each having its own object illumination beam and observation system. The orientation of the interferometers was arranged in such a way that for object surface points visible in all the corresponding interferograms, three independent displacement components could be obtained. Others have proposed similar configurations. Their systems, however, were restricted to deformation measurements of objects with simple and numerically determined shapes. An important asset of the configuration designed by the author Is, that vectorial measurements can be performed on objects with arbitrary and undetermined shapes. This is accomplished by the incorporation of coincident object
illumination and observation. This and other advantages of the system will be discussed in Chapters 8 and 9. The suitability of this system was well-demonstrated in practice with objects having shapes as intricate as that of a human skull and having sizes as large as that of the head of a big diesel engine . A special technique, unpublished as yet, was developed for this interferometer system in order to allow the simultaneous recording of the holographic interferograms in spite of the illumination of the
object from multiple directions (without it, such illuminations lead to intersecting fringe patterns in the various interferograms). This technique will be discussed in Section 9.4.
2.8 References
1. ANONYMOUS,
"Ich kenne diesen Zwang, um jeden Preis etwas erfinden zu mussen" (I know this urge to invent something at any price), Laser + Elektro-Optik, (1979, no.2), pp.26-28 (in German).
2. D.GABOR,
"Diffraction microscopy", J. Appl. Phys., 12 (1948), p.1191. 3. D.GABOR,
"A new microscopic principle", Nature, 1£1 (1948), pp.771-778. 4. M.E.HAINE and J.DYSON,
"A modification to Gabor's proposed diffraction microscope", Nature, 16_6_ (1950), pp. 315-316.
5. H.M.A.EL-SUM,
"Reconstructed wavefront microscopy", Ph.D. Thesis, Stanford University, 1952 (available from Univ. Microfilm Inc., Ann Arbor, Michigan, U.S.A.).
6. w.E.KOCK,
"Microwave holography", Chapter 9 in "Holographic nondestructive testing", R.K.Erf (Ed.), Academic Press, New York, 1974, pp.373-403.
7. A.F.METHERELL, H.M.A.EL-SUM, and L.LARMORE (Eds.), "Acoustical holography", Vol.1, Plenum, New York, 1969. 8. G.L.ROGERS,
"Gabor diffraction microscopy: the hologram as a generalized zone plate", Nature, 16_6_ (1950), p.237.
9. G.L.ROGERS,
"Experiments in d i f f r a c t i o n microscopy", Proc. Roy. Soc.
(Edinburgh), 6JA (1952), pp.193-221.
10. W.L.BRAGG and G.L.ROGERS,
"Elimination of the unwanted image in diffraction microscopy", Nature, 1£Z (1951), pp.190-191.
11. H.M.A.EL-SUM and P.KIRKPATRICK,
"Microscopy by reconstructed wavefronts", Phys. Rev., 8_5_ (1952), p.763.
Historical background
12. A.LOHMANN,
"Optische Einseitenbandübertragung aufgewandt auf das Gabor-Mikroskop" (optical single side-band transmission applied to the Gabor-microscope), Opt. Acta, 3 (1956), pp.97-99 (in German).
13. E.N.LEITH and J.UPATNIEKS,
"New techniques in wavefront reconstruction", J. Opt. Soc. Am., 51 (1961), p.1469.
1 4 . E.N.LEITH and J.UPATNIEKS,
"Reconstructed wavefronts and communication theory", J. Opt. Soc. Am., 52 (1962), pp.1123-1130.
15. E.N.LEITH and J.UPATNIEKS,
"Wavefront reconstruction with continuous-tone transparencies", J. Opt. Soc. Am., 55 (1963), p.522.
16. E.N.LEITH and J.UPATNIEKS,
"Wavefront reconstruction with continuous-tone objects", J. Opt. Soc. Am., 55 (1963), pp.1377-1381.
17. J.UPATNIEKS and E.N.LEITH,
"Lensless, three-dimensional photography by wavefront recon struction", J. Opt. Soc. Am., 54 (1964), pp.579-580.
1 8 . E.N.LEITH and J.UPATNIEKS,
"Wavefront reconstruction with diffused illumination and three-dimensional objects", J. Opt. Soc. Am., 54 (1964), pp.1295-1301.
19. R.P.CHAMBERS and J.S.COURTNEY-PRATT,
"Bibliography on holograms", Journal of the SMPTE, 25 (1966), pp.373-435.
20. Only recently, holographic advertisements have become a reality, see e.g.:
ANONYMOUS,
"Holografie, futuristische techniek in een advertentie" (holo graphy, futuristic technology in an advertisement), MAN, 14 (1986, nr.2), in Dutch.
21. T.0K0SHI,
"Three-dimensional imaging techniques", Academic Press, New York, 1976, pp.8-40.
22. A.VANDER LUGT,
"Holographic memories", in "Optical Information Processing", Nesteriklin, Stroke, and Kock (Eds.), Plenum, New York, 1976, pp.347-368.
23. S.H.LEE,
"Image processing", Section 10.6 in "Handbook of Optical Holography", H.J.Caulfield (Ed.), Academic Press, New York, 1979, pp.537-560.
24. R.V.VANLIGTEN and H.OSTERBERG,
"Holographic microscopy", Nature, 211 (1966), p.282. 25. R.A.BRIONES, L.O.HEFLINGER, and R.F.WUERKER,
"Holographic microscopy", Appl. Opt., 12 (1978), pp.944-950. 26. J.N.LATTA,
"Holograms as optical elements", Proceedings of the Symposium on the Engineering Uses of Holography (February 16-17, 1972, Los Angeles, California, U.S.A.), Society of Photo-optical Instrumentation Engineers, Redondo Beach, California, 1972, pp.345-359
27. S.A.BENTON,
"White-light transmission/reflection holographic imaging", Proceedings of the International Conference on Applications of Holography and Optical Data Processing (August 23-26, 1976, Jerusalem, Israel), Friesem and Wiener-Avnear (Eds.), Pergamon Press, Oxford, 1977, pp.402-409.
2 8 . D.MEYERHOFER,
"Dichromated gelatin", in "Holographic Recording Materials", H.M.Smith (Ed.), Springer Verlag, Berlin, 1977, pp.75-99.
29. ANONYMOUS,
"Holographic data display in super 8 camera viewfinder developed by Canon engineers", Holosphere, 2 (1980, no.1), pp.1-2.
30. Holographic "head-up displays (HUD's)" for application in fighter aircraft have been shown in:
a) A.GRAUBE,
"Mechanisms of image formation in holographic dichromated gelatin", paper presented at 32n d Annual Conference of the
Society of Photographic Scientists and Engineers (May 13-17, 1979, Boston, Mass., U.S.A.),
and,
b) ANONYMOUS,
"LANTIRN Head Up Display", brochure by MARCONI AVIONICS, Rochester, Kent, England, 1981
A similar system for civil aircraft has been advertised by FLIGHT DYNAMICS, INC., Hlllsboro, Oregon, U.S.A., 1982.
31. ANONYMOUS,
"Holosonics seeks court protection from creditors", Holosphere, g (1979, no.7), pp.1-2; see also Holosphere 2 (1978, no.9), pp.1-2 and Holosphere g (1979, no.7), pp.1-2.
32. K.B0D0 D0RRA,
"Hologramme, L i c h t p l a s t i k e n des 2 1 . Jahrhunderts" (holograms,
l i g h t s c u l p t u r e s of the 2 1
s tc e n t u r y ) , DU die
Historical background
33. ANONYMOUS,
"Museum voor holografie" (museum of holography), Kunstecho's, 10.
(1981, n o . 6 ) , pp.18-19, ( i n Dutch).
34. H.J.CAULFIELD,
"The wonder of holography", Nat. Geogr. Magazine, 115 (1984), pp.364-377 and front cover.
35. K.F.WEAVER,
"The search for our ancestors", Nat. Geogr. Magazine, IM (1985),
front and inside back covers. 36. M.H.HORMAN,
"An application of wavefront reconstruction to interferometry", Appl. Opt., 4 (1965), pp.333-336.
37. R.L.POWELL and K.A.STETSON,
Spring Meeting of the Optical Society of America (1965), paper FA16 and "Interferometric vibration analysis by wavefront reconstruction", J. Opt. Soc. Am., 5_5_ (1965), pp.1593-1598
38. K.A.STETSON and R.L.POWELL,
Annual meeting of the Optical Society of America (1965), paper WF13 and "Hologram interferometry", J. Opt. Soc. Am., 5.6. (1966), pp.1161-1166.
39. K.A.STETSON and R.L.POWELL,
"Interferometric hologram evaluation and real-time vibration
analysis of diffuse objects", J. Opt. Soc. Am., 5_5_ (1965),
pp.1694-1695. 40. K.A.STETSON
"Hologram interferometry of nonsinusoidal vibrations analyzed by density functions", J. Opt. Soc. Am., 6J. (1971), pp.1359-1362. 41. K.A.STETSON
"Method of stationary phase for analysis of fringe functions in hologram interferometry", Appl. Opt., 11 (1972), pp.1725-1731. 42. R.E.BROOKS, L.O.HEFLINGER, and R.F.WUERKER,
"Interferometry with a holograph!cally reconstructed comparison beam", Appl. Phys. Lett., Z (1965), pp.248-249.
43. L.O.HEFLINGER, R.F.WUERKER, and R.E.BROOKS,
"Holographic interferometry", J. Appl. Phys., 3_Z (1966), pp.642-649.
44. J.M.BURCH,
"The application of lasers in production engineering", Prod. Eng., 44 (1965), pp.431-442.
45. E.ARCHBOLD, J.M.BURCH, and A.E.ENNOS,
"The application of holography to the comparison of cylinder bores", J. Sci. Instrum., 44 (1967), pp.489-494.
46. R.J.COLLIER, E.T.DOHERTY, and K.S.PENNINGTON,
"Application of moiré techniques to holography", Appl. Phys. Lett., Z (1965), pp.223-225.
4 7 . B.P.HILDEBRAND and K.A.HAINES,
"Interferometrlc measurements using the wavefront reconstruction technique", Appl. Opt., 5. (1966), pp.172-173.
4 8 . K.A.HAINES and B.P.HILDEBRAND,
"Surface-deformation measurement using the wavefront reconstruction technique", Appl. Opt., 5_ (1966), pp.595-602.
49. K.A.HAINES,
"The analysis and application of hologram interferometry", Ph.D. Thesis, University of Michigan, 1966.
50. W.J.P.VINK and N.H.R.VERSLUIS,
"Niet-destructief onderzoek" (non-destructive testing and inspection), Delftse Uitgevers Maatschappij, Delft, Netherlands, 1980 (in Dutch)
51. E.R.ROBERTSON and J.H.HARVEY (Eds.),
"The engineering uses of holography", Proceedings of the Symposium (September 1968, Strathclyde, Scotland), Cambridge University Press, Cambridge, 1970.
52. ANONYMOUS,
"Holography", Proceedings of the Seminar-in-Depth (May 23, 1968, San Fransisco, U.S.A.), Society of Photo-Optical Instrumentation Engineers, Volume 15, 1968.
53. B.RAGENT and R.M.BROWN,
"Holographic instrumentation applications", Papers of Conference at Ames Research Center (January 13-14, 1970, Moffett Field, California, U.S.A.), NASA Special Publication SP-248, NASA, Washington, D.C., 1970.
54. J.CH.VIéNOT, J.BULAB0IS, and J.PASTEUR (Eds.),
"Applications of holography", Proceedings of the International Symposium on Holography (July 6-11, 1970, Besancon, France), University of Besancon, 1970.
55. B.J.THOMPSON and J.B.DEVELIS (Eds.),
"Developments in holography", Proceedings of the Seminar-in-Depth (April, 1971, Boston, U.S.A.), Society of Photo-Optical Instrumentation Engineers, Volume 25, Redondo Beach, California, 1971.
56. E.CAMATINI (Ed.),
"Optical and acoustical holography", Proceedings of the NATO Advanced Study Institute on Optical and Acoustical Holography (May 24 - June 4, 1971, Milan, Italy), Plenum Press, New York, 1972.
57. ANONYMOUS,
"Proceedings of the Symposium on Applications of Holography in Mechanics" (August 23-25, 1971, Los Angeles, U.S.A.), The American Society of Mechanical Engineers, New York, 1971.
Historical background
58. ANONYMOUS,
"Proceedings of the Symposium on Engineering Applications of Holography" (February 16-17, 1972, Los Angeles, U.S.A.). Society of Photo-Optical Instrumentation Engineers, Redondo Beach, California, 1972.
59. ANONYMOUS,
"Optical methods in scientific and industrial measurements", Preprints of papers for Conference of International Commission for Optics (Tokyo, August 25-30, 1974), Science Council of Japan,
1974.
"Aktuelle Probleme der holografischen Interferometrie in der zerstörungsfreien Werkstoffuntersuchung" (current problems of holographic interferometry in nondestructive materials testing),
Symposium of Deutsche Gesellschaft für angewandte Optik (September 1973, Meersburg, Germany).
"Frühjahrsschule für holografische Interferometrie", Spring Course on Holographic Interferometry (March 1975, Hannover, Germany).
62. E.ROBERTSON (Ed.),
"The engineering uses of coherent optics", Proceedings of the Symposium (Strathclyde, Scotland, 1975), Cambridge University Press, Cambridge, 1976.
63. ANONYMOUS,
"Optische Holografie" (optical holography) papers given at the meeting for special methods of the German Society for Nondestructive Testing, (February 25, 1976, Hannover, Germany), Deutsche Gesellschaft für Zerstörungsfreie Prüfung e.V., Berlin, 1977 (in German).
64. E.MAROM, A.A.FRIESEM, and E.WIENER-AVNEAR (Eds.),
"Applications of holography and optical data processing", Proceedings of International Conference (August 23-26, 1976, Jerusalem, Israel), Pergamon Press, Oxford, 1977.
65. M.GROSMANN and P.MEYRUEIS (Eds.),
"Proceedings of the first european conference on optics applied to metrology", (October 26-28, 1977, Strasbourg, France), Society of Photo-Optical Instrumentation Engineers, Bellingham, U.S.A., Volume 136, 1978.
66. H.KREITLOW and W.JÜPTNER (Eds.),
"Friihrjahrsschule 78: holografische Interferometrie in Technik und Medizin", Spring course 78: Holographic Interferometry in the Technical and Medical Sciences (April 4-7, 1978, Hannover, Germany), University of Technology, Hannover, 1978 (in German).
f
"Workshop on holography in medicine and biology" (March 14-15, 1979, University of Munster, Germany).
