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Holographic Interferometry: Then and Now

  • Karl A. Stetson
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)

Abstract

In the autumn of 1964, Robert L. Powell and I discovered holographic interferometry while working at the Radar Laboratory of the University of Michigan’s Institute of Science and Technology. I have worked in this field ever since, and I have watched it grow from an unexplored technology to a widespread industrial testing method, and I have contributed to these developments. In this paper, I will trace my history in this field—our discovery and my involvement in its theory and applications. I will conclude with a discussion of digital holography, which is currently replacing photographic holography for most research and industrial applications.

Keywords

Holography Interferometry Holographic interferometry Metrology Digital holography 

35.1 Discovery

35.1.1 Off-Axis Holography

Off-axis holography was invented by Emmett Leith at the Optical Processing Group of the Radar Laboratory of the Institute of Science and Technology at the University of Michigan in the early 1960s. The main function of that group was optical processing of synthetic aperture radar, a new technology that had been invented in the 1950s at that laboratory. Data from a coherent side-looking airborne radar system was recorded on photographic film and optically processed to obtain images. At that time, photographic film was the only material capable of storing massive amounts of data, and the Fourier transform properties of lenses made optical processing of this data very convenient. Leith visualized the process as recording data at radar wavelengths and converting it to optical wavelengths for processing. By this insight, the processing was reformulated as an imaging process, and Emmett Leith found a precedent for this in Denis Gabor’s hologram process which proposed recording electron microscope data as an optical pattern and thus converting it from electron wavelengths to optical wavelengths. Gabor’s application was never put into practice, but synthetic aperture radar was, and it was quickly learned that an angle between the object and reference fields was necessary to avoid the twin image problem that plagued Gabor’s in-line reference process.

I joined the group in September of 1962, just before they bought their first lasers, and I was in the laboratory on Dec. 24th when Emmett and Juris Upatnieks recorded and reconstructed their first laser hologram of a continuous tone optical transparency. Work progressed at a modest pace, and by 1964, laser holograms had progressed from continuous tone transparencies to transparencies illuminated by diffuse light, to three-dimensional objects. In September of that year, Emmett assigned me to work on the problem of the holograms. The diffraction efficiency of holograms with diffused light illuminating a transparency was about half what you got for a transparency without the diffuser. The corresponding diffraction efficiency for a hologram of a three-dimensional object was maybe one tenth of that. They had one hologram, made of a model train, that was far brighter than any of the others, and they were unable to duplicate it. In my memory, that hologram had been recorded during the demonstration of an experimental laser from Spectra Physics that was much more powerful than the 1 mW lasers we were using. That experimental laser eventually became the model 125 that was rated for 50 mW, but normally put out about 90. Around that time, Robert Powell, who had been one of my professors at undergraduate school, joined our group and we began working together. This laboratory had two large granite tables about a foot and a half thick on rubber isolation pads. The photographic material was Kodak 649F, a spectrographic emulsion of very high resolution that was extremely insensitive to light. With the mere 1 mW of power available, our exposures routinely took over a minute, and this, together with the fact that the tables were not on air-suspension vibration isolators and our room was next to the air conditioners, was the real problem of the holograms. We eventually solved this problem, and could consistently make very bright holograms of the model train.

35.1.2 Holographic Interferometry

It can be argued that holographic interferometry is the most wide-spread and successful application of holograms, and it is the only application that makes full use of a hologram’s unique ability to reproduce the optical field reflected or transmitted by an object. It uses two unforeseen properties of off-axis laser holograms. First, a hologram can record fields that are incoherent and reconstruct them coherently so that they interfere. Those fields may come from separate laser modes, they may exist at different times, or they may be incoherent due to motion such as vibration. Second, a hologram can reconstruct the field from an object so precisely that it can interfere with the field from the object itself. Robert L. Powell and I discovered the first of these properties between late October and early December 1964, and the second in April of 1965.

It is documented [1] that the first observations of phenomena due to holographic interferometry were by Emmett Leith and Juris Upatnieks dating back to December 1963. The first case involved holograms recorded of paper cemented to an aluminum block with a hole in it that showed a black spot in the unsupported area. In another, a sheet of cardboard overlapped the block to which it was cemented and in that area the hologram reconstruction showed what looked like fringes. Upatnieks estimates the latter hologram as recorded in February or March of 1964. These observations, however, were not followed up to determine exactly what was happening. As stated by Upatnieks in an email to me [2], “We observed the effect and noted it, but did not get into any detail. Our main interest was image quality.” The first observation Powell and I made of interference in a hologram reconstruction was the result of an unstable mounting of a holographic plate, which I pressed into a U-shaped frame against some rubber. It moved slightly during the hologram recording, and we saw a set of vague diagonal dark bands in the reconstruction. We abandoned this hologram and the mount and had a more stable one made with which we were able to record good quality holograms.

The Spectra-Physics representative had told me that these lasers emitted typically 3 longitudinal modes, and thus their longitudinal coherence was periodic in twice the cavity length, which was 60 cm. In response to concerns by others about the laser’s coherence, I decided we should demonstrate that, and we set up an experiment where the unexpanded object beam was allowed to strike an object set between two mirrors. We positioned our hologram plate so that we could look through it over one mirror into the other and see a sequence of images, each 10 cm further in path length. We recorded several holograms with the zero path-length point lying at different points in that sequence of dots, and all of these holograms exhibited a periodic variation in image brightness as a function of path length just as we expected.

We noticed in one of these holograms what looked like a horizontal black fringe in the nearest image of the object beam spot. More important, this fringe moved as we raised or lowered our view through the hologram, so it was clearly not something on the object itself. We immediately set up an experiment to contain the entire object beam on a white surface, and capture the entire reference beam on the hologram plate. This recording gave us fringes that moved depending on the vertical position on the hologram plate through which we looked. I checked the laser and found that it was operating in more than one transverse mode. It was a Spectra-Physics/Perkin-Elmer model 110 laser that had a confocal mirror configuration, a spherical output mirror with a flat high reflectance mirror located at its center of curvature. There was a longitudinal adjustment for the flat mirror, and a single TEMoo mode was only obtained when the distance was set correctly. We initially had a combination of a 00 mode and a 20 mode and, after adjusting the laser, we recorded a hologram with a 00 mode and a 10 mode.

The question was: What gave us these fringes? I suggested to Bob that the photographic plate was recording separate holograms for each object and reference beam mode combination. When the hologram was reconstructed, however, both recordings would reconstruct their respective object beams, but since both fields were now being generated by the same reconstruction beam, the two reconstructed fields were coherent and could interfere. The shifting of the fringe positions would be due to phase variations between the two transverse mode recordings. Bob found this very disturbing, because it implied that fields that were incoherent during the recording of a hologram were being made coherent in its reconstruction. At this point that I referred back to the hologram we had made with the plate wedged against the rubber pad as proof of what I was suggesting. Bob was still unconvinced, and I said something like, “look, if we record a double-exposure hologram and give the object a small rotation between the exposures, wouldn’t we expect to see fringes in the reconstruction?” That question spurred immediate action. It took us some time to learn how much rotation to give the object, hologram plate, or reference beam, but we got this to work and showed double-exposure interference patterns in hologram reconstructions.

As with Leith and Upatnieks, our object was a sheet of paper cemented to an aluminum plate, and in one of the reconstructions, we noticed a perturbation of the fringes in a region where there was a bolt hole. In retrospect, I’m sure the paper had statically deformed between the two exposures, but at the time we wondered if the effect could be vibration. We set up an empty can from a reel of 35 mm film with a solenoid mounted under it, and this generated the remarkable set of J0 fringe patterns which we presented at the 1965 spring meeting of the Optical Society of America and published in the December 1965 issue of JOSA [3]. My record books are long gone, but to the best of my memory, we did the coherence function experiments in October 1964, the double-exposure holograms in November 1964, and the vibration holograms in early December 1964. In contrast to Leith and Upatnieks, Robert Powell and I observed a phenomenon, studied it in detail, proposed an explanation, and then tested and confirmed that explanation.

As we submitted our paper to the OSA for the spring meeting of the Optical Society of America at Dallas, TX, in April 1965, I proposed to Emmett that we should also present a paper on the entire set of experiments we had done defining holographic interferometry. He vetoed the idea saying that one paper was adequate, an unfortunate decision, and the reason for it became clear to me in 1970. He and Juris had filed a number of patent disclosures on holographic applications, including one on coherence measurement and one on vibration analysis, and Bob and I had unwittingly walked into these areas. We presented our additional material at the OSA annual meeting in Philadelphia in October 1965, and published it in JOSA in September 1966 [4].

Bob and I searched for prior work using interferometry for vibration analysis and found a paper by Harold Osterberg [5], which identified the fringes we saw in our reconstructions as a zero-order Bessel function of the first kind. It also suggested a method for real-time vibration analysis. Just after the spring meeting of the OSA, it occurred to me that if we could replace a hologram in its holder accurately enough, its reconstruction ought to interfere with the field from the original object. We tried this and it worked, giving us a real-time vibration measurement technique, a method of evaluating the quality of a hologram reconstruction, and measurement of object deformation in real-time. We submitted a letter to the editor in JOSA, which appeared in the same issue as our vibration analysis paper [6].

Kenneth Haines and Percy Hildebrand, who worked in the Willow Run Laboratory, were also thinking about holography in April 1965. They borrowed our real-time holographic interference setup to record the holograms showing deformation of a plate due to bolt tightening. In April 1996, Haines and Hildebrand published a paper [7] presenting real-time holographic interferometry as a “new method” solely attributable to them. The prior work by Robert Powell and me is described by the sentence “A related technique for vibration measurement was used by Powell and Stetson.” Their paper presented an analysis of the fringes and fringe localization, but this paper and a nearly identical one following it [8] were so mathematically dense that neither has been used for that purpose. That year, they also published a theoretical paper [9] describing how object contours could be obtained by changing the laser wavelength. In the following years, I and many others developed comprehensive descriptions of the relationship between object deformations and observed fringes and fringe localization.

A possible contender for discovery prior to ours was Melvin H. Horman [10]. He presented a paper at the same OSA meeting in Dallas where we presented our vibration work, and published in Applied Optics in March of 1965, with a received date of October 1964. His paper was essentially theoretical with no experimental work presented, and it proposed that a hologram could be used to replace an object in an otherwise conventional Mach-Zehnder interferometer. To perceive that theoretically was impressive, but there is no mention in the paper of the key concepts of holographic interferometry—the ability of a hologram to make fields that are incoherent during recording coherent during reconstruction, nor was a hologram proposed as a beamsplitter between the reference and object beams used in its recording.

The year 1965 saw a number of independent discoveries of holographic interferometry. One of the first was by Collier, Doherty, and Pennington [11], who described interference effects within a hologram reconstruction as a moiré effect. Pulsed laser holographic interferometry was reported by Brooks, Heflinger, and Wuerker [12]. Their discovery was a fortunate accident that occurred while they were recording pulsed laser holograms of a bullet in flight. The laser fired two pulses during one of these recordings, one of which occurred with the bullet in the field of view and one without it. The shock waves in the air were clearly visible as an interference pattern. In England, J. M. Burch published a paper in which he described experiments done at the National Physical Laboratory in Teddington that showed both double-exposure and real-time holographic interferometry [13]. In the Soviet Union, holographic interferometry was discovered about this same time by Yu I. Ostrovsky.

35.1.3 Characteristic Fringe Functions and Separable Object Motions

The function that describes the fringes observed in a time-average hologram reconstruction is the time average of the phase generated by the object motion. This can be expressed as
$$ \mathrm{M}\left(\Omega \right)=\left(1/\mathrm{T}\right){\int}_0^{\mathrm{T}}\exp \left(\mathrm{i}\Omega \kern0.5em \mathrm{f}\left(\mathrm{t}\right)\right)\kern0.5em \mathrm{dt}, $$
(35.1)
where M is the fringe function, Ω is the fringe locus function, T is the exposure time, f(t) is the function of time describing the object motion, and t is time. The fringe locus function can be described in terms of the object displacement vector, L, and propagation vectors describing light propagation from the object to the hologram, K2, and from the illumination to the object, K1, as
$$ \Omega =\left({\mathbf{K}}_2\hbox{--} {\mathbf{K}}_1\right)\cdotp \mathbf{L}=\mathbf{K}\cdotp \mathbf{L}, $$
(35.2)
where K is called the sensitivity vector. Implicit in this formula is the idea that the object motion is separable, i.e., that it can be expressed as the product of a single object deformation vector, L, times a single function of time, f(t). This means that all points on the object move with the same time function. With vibrating objects, this is not always the case.
Adam Kozma, one of the major figures at the Optical Processing Group, made a significant contribution to the theory of holographic interferometry very shortly after our demonstration of holograms of vibrating objects. He sought to describe hologram reconstructions for random object motions. He observed that for object motions are stationary and ergodic in a statistical sense, the values it would assume could be described by a probability density function, p(f), describing the percentage of the exposure time at which it assumed each value. Thus, we could rewrite Eq. (35.1) as
$$ \mathrm{M}\left(\Omega \right)={\int}_{-\infty}^{+\infty}\mathrm{p}\left(\mathrm{f}\right)\kern0.5em \exp \left(\mathrm{i}\Omega \kern0.5em \mathrm{f}\right)\kern0.5em \mathrm{df}={\mathrm{\mathcal{F}}}_{\Omega}\left[\mathrm{p}\left(\mathrm{f}\right)\right], $$
(35.3)
where \( {\mathrm{\mathcal{F}}}_{\Omega} \) [p(f)] indicates the Fourier transform of p(f) with respect to the variable Ω. This formulation makes it quite easy to tabulate fringe functions, and, for Gaussian motion in particular, the fringe function becomes itself a Gaussian function. This formulation also stresses the fact that the fringe function is not determined by the exact motion of the object but rather by how much of the exposure time it spends in each position.

35.2 The Search for Applications

Robert Powell and I were not mechanical engineers. For example, one of the vibration patterns we recorded of our film can bottom showed a five-lobed pattern that was an impossible vibration mode for a circular vibrating structure. In retrospect, it was a combination of a five-diameter mode and a two-ring circumferential mode and not a mode by itself, but we did not understand that at the time. I communicated information about our discovery quite freely, and one of the people I told was Ralph Grant, a professor of acoustics at the University. I also came in contact with Donald Gillespie, who was very interested in finding a way to exploit holograms financially. Don worked in a laser laboratory and was able to make his own lasers. I helped him set up a holography laboratory in his basement in which he made holograms for demonstration purposes. Eventually he and his brother John Gillespie formed the first company to make equipment specifically designed for holography laboratories, Jodon Engineering. Ralph Grant had teamed up with a lawyer, Joseph Crafton to form Grant-Crafton Optronics, aka GCO. They were fortunate to find that this new interferometry could make bonding flaws visible on laminated structures, such as pneumatic tires, when subjected to changes in pressure, and this became a major business. Around 1973 or so, GCO ended and was replaced by Industrial Holographics, Inc., which, in turn, was replaced by Grant Engineering, Inc. around 1986. Approximately 1997, this business was obtained by another company who sold systems under the trade name, L-Ray.

The aircraft industry became a major user of holographic interferometry. Holographic testing required a significant initial investment which added considerable cost to products, and this was practical for items like airplanes which cost a lot to make and for which failures are very serious. In jet engines, high cycle fatigue due to vibration is a major source of failure for the blades, and they are designed to have resonances that are not excited at the rotation speeds of operation. Holography offered a way to visualize the mode shapes and confirm mathematical analyses. This was used very early on by Pratt & Whitney, GE, and Rolls-Royce, and also by Westinghouse for analysis of vibration modes for steam turbine blades. Aircraft structures made of honeycomb cores and metal or composite skins were also inspected by holography for delaminations. Another major area of application has been analysis of air flow and analysis of plasmas, which generally required use of pulsed lasers. A wide survey of techniques can be found in the book, Holographic Nondestructive Testing, edited by R. K. Erf [14], and a detailed discussion of holographic interferometry can be obtained in the book Holographic Interferometry, by C. M. Vest [15].

35.3 Recording Materials

35.3.1 Photographic Film

In 1967, I joined the Institute for Optical Research at the Royal Institute of Technology in Stockholm to work on a doctoral degree. They were already working with holograms, and to my surprise and delight, they had new photographic materials from Agfa Gaevert for recording holograms that were much faster than the Kodak 649F. As I recall, there were a total of four materials: 8E70, 8E75, 10E70, and 10E75. The 8E series were higher resolution and slower than the 10E series, and were suitable for recording standing waves such as in Lippmann holograms. The 70 series were red sensitive and had a band of low sensitivity to blue-green light, which allowed them to be used under a blue-green safe light. That series was eventually eliminated. When I moved to England in 1969, to join James Burch’s group at the National Physical Laboratory, I found that Ilford had also brought out a high speed holographic material. I returned to the United States in 1971, and within a couple of years Kodak came out with a material they called SO-253 which was the fastest holographic material made. All of these materials were available as either photographic emulsions on glass plates or as reels of film at typically 35 mm width. Jodon Engineering eventually came out with a unit for recording holograms on photographic film. It held a supply reel and a take-up reel, and the film threaded through an open area that was slightly curved for higher stability. A matching fixture was supplied for holding the film in the same position for reconstruction. It was typical to record image-plane holograms on photographic film because warping of the film would affect the quality of reconstructions if the light had to propagate much distance to form an image.

35.3.2 Thermoplastic Holograms

The first thermoplastic recording of holograms was reported in 1966 by Urbach and Meier [16]. A thin photo-conducting layer is covered by a transparent layer of thermoplastic material. The thermoplastic material was charged, the photo-conductor was exposed, the layer was charged a second time, and the outer layer heated. The charge pattern caused the thermoplastic to deform, and after it is cooled it diffracted light to form a hologram reconstruction. The advantage of this was that the hologram was exposed and developed without being moved. In-situ processing of photographic plates was developed in 1970 [17], but the process involved holding a plate within a liquid gate. Typically, the exposure would be with water in the gate, followed by developer, followed by a fixing bath, and often returned to water for the reconstruction phase. By comparison, thermoplastic holograms were completely dry, and required less time between exposure and reconstruction. Both of these techniques were a boon to real-time holography, because nearly perfect, fringe-free, interferograms could be obtained. Hans Rottenkolber, of Rottenkolber Holo-Systems, marketed a thermoplastic recording system in the 1970s and eventually Newport Research Corp. produced a system of this sort as well. The Rottenkolber system used a movable strip of thermoplastic which was advanced for each hologram recording whereas the Newport system reused the same thermoplastic layer which was bonded to the photoconductor.

35.4 The Speckle Interferometer

One result of world-wide interest in holographic interferometry was that it prompted people to think about laser speckles. One of the first innovations was the speckle interferometer [18], a device invented at the National Physical Laboratory (NPL) in 1969. This was an optical instrument that allowed a person to look at an object through an aperture small enough that speckles were clearly visible on its surface. This image was combined with a smooth reference beam to create speckles that would blur if the object vibrated but which would remain of high contrast at the vibration nodes. I was fortunate to spend 2 years at NPL starting in September 1969, and I had the opportunity to make substantial improvements to this instrument [19]. Television cameras were eventually used to observe and process these images, and Electronic Speckle Pattern Interferometry (ESPI) was born. About the same time, John Leendertz at Loughborough University published work demonstrating the use of speckles for measuring displacements and strains of objects [20], and this gave rise to an independent field of measurement called speckle metrology [21].

35.5 Heterodyne Interferometry

Heterodyne readout of interference fringes in holographic interferometry was introduced by Dändliker, et al., in 1973 [22], and this introduced a new level of precision and flexibility. By recording two exposures of a double-exposure hologram with separate reference beams, it became possible to introduce a frequency shift between the two reconstructing beams and convert the fringes into sinusoidal irradiance fluctuations. These could be converted to electrical signals by a photodetector, and these could be analyzed by an electronic phase meter with a phase resolution of 0.1°. The fringes could be evaluated anywhere within the interferogram and to a much higher level of accuracy than by locating fringe centers.

35.6 Phase Stepping and Digital Holography

An alternative to heterodyne readout of interference fringes is to step the phase of a fringe pattern through a set of discrete values and record the irradiance values at each step. If the phase steps are known, and three or more steps are used, it is possible to calculate the phase from the irradiance values. This method is well suited to array detectors such as solid-state TV cameras which can measure irradiance values for an array of picture elements, or pixels, and this technique was introduced into holographic interferometry by P. Hariharan, et al. [23] in 1982 and further developed by K. Creath [24]. Solid-state cameras are an essential enabling factor for this, for unlike the vidicons and orthicons that proceeded them, solid-state cameras provide accurate irradiance measurements and are much more tolerant of overexposure. In addition, their fabrication via photolithography results in a pixel arrays that have essentially no distortion.

In the late 1980s, I combined phase stepping with the speckle pattern interferometer to create the first system to record and display in real time what are now called digital holograms [25]. The origin of digital holography is generally taken to be the work of Schnars and Jüptner [26] where a charge-coupled device (CCD) TV camera was used directly to replace film in an off-axis hologram recording system. The image of the object was obtained from the recorded data by a numerical calculation that duplicates optical propagation. In our system, the image of the object was focused on the TV camera, so there was no incentive to explore the possibility of focal plane shift via numerical calculation. The data recorded by our system, however, always allowed for this possibility, as was eventually shown in 2009 [27].

The main advantage digital holography has over photographic holograms is that it is possible to calculate the phase of the object image, and, correspondingly, the phase of holographic interference fringes. With double-exposure holograms, this is most easily done by calculating the random image phase of the object before and after deformation, and subtracting these two random functions. The phase calculations generally result in eight-bit pixel values, and subtraction of two such numbers creates a nine-bit number, which also exhibits a phenomenon I call random wrapping. For example, if a larger number is subtracted from a smaller one, the result is a negative number, which will be represented as a positive number in the upper range of the nine-bit numbers. This problem can be eliminated by wrapping the nine-bit numbers into eight bits. The result of this is a wrapped phase map of the object deformation which then has to be unwrapped to obtain a continuous map of the object deformation. Numerous methods for phase unwrapping are discussed in a book by Ghiglia and Pritt [28]. I introduced a method not included in their book, which makes use of calculated phase unwrap regions [29].

The ability to obtain phase maps via phase stepping suggested a way to apply this method to vibration fringes. Because the zero-order Bessel function is nearly periodic, it is possible, approximately, to phase step J0 fringes by introducing a bias vibration into the holographic reference beam. The bias vibration has to be at the same frequency as the object vibration and has to match its phase. Under these conditions, the bias vibration simply adds a scalar number to the argument of the fringe function, and by setting its amplitude correctly, it can be set to yield the equivalent of a 120° phase shift. Data recorded with ±120 and 0° can be used to calculate the resulting argument of the J0 function under the assumption that it were actually a cosine function. The error resulting from this calculation can be precalculated and a table constructed to correct the results to obtain the actual argument of the J0 function [30].

Deformation and vibration analyses of objects important in engineering applications, such as turbine blades and structural components, are probably most easily analyzed by the phase-stepped, image-plane digital holography system we developed 25 years ago. Digital holography, generally, has found extensive applications in microscopy where the focusing capabilities are more important. Details of these applications are found in numerous books, such as those by Schnars and Jüptner [31] and Kim [32].

35.7 Conclusion

Looking back over the past 54 years is an interesting experience. It has given me the opportunity to recall the state of science and technology as it was back then and compare it to what we have available now. Of course, a major factor has been the remarkable rise of personal computers, one of which I am using to write this document and which I am using to listen, simultaneously, to my local classical music station. Fifty years ago, I would have given nearly anything to have the technical capabilities I have now, and had we had them back then, history would have been very different. Optical processing of synthetic radar data would probably not have been developed. Correspondingly, the entire subject of Fourier Optics might not have been pursued either. The development of lasers back in the 1960s, however, would still have galvanized the scientific and engineering community, and many of the things that they have brought to light would still have occurred.

I would like to close with my favorite “what if” story. While I was at NPL, we were visited by Samuel Tolansky a couple of years before his death. He was well known for his work in multiple-beam interferometry and was a major figure in the optics community. He told of having done experiments back in the 1930s with a Fabry-Perot interferometer, an instrument that consists of two parallel mirrors between which light reflects back and forth many times as it does in a laser cavity. He was investigating the phenomenon, predicted by Einstein, of stimulated emission using a neon discharge, and I remember his comment to this day. “I wouldn’t have felt half so bad if I hadn’t had helium on the bench, but I never thought of mixing the two.” Had he decided to see what might happen with a mixture of helium and neon, he might have happened upon the He-Ne laser 30 years before it was discovered. Who can say how much history would have been changed had this happened?

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Copyright information

© The Society for Experimental Mechanics, Inc. 2019

Authors and Affiliations

  1. 1.Karl Stetson Associates, LLCCoventryUSA

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