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Interference-optical Methods of Solid Mechanics (Foundations of Engineering Mechanics)

Added to Your Shopping Cart. This is a dummy description. Unique within the field for being written in a tutorial style, this textbook adopts a step-by-step approach to the background needed for understanding a wide range of full-field optical measurement techniques in solid mechanics. This method familiarizes readers with the essentials of imaging and full-field optical measurement techniques, helping them to identify the appropriate techniques and in assessing measurement systems.

In addition, readers learn the appropriate rules of thumb as a guide to better experimental performance from the applied techniques. Rather than presenting an exhaustive overview on the subject, each chapter provides a concise introduction to the concepts and principles, integrates solved problems within the text, summarizes the essence at the end, and includes unsolved problems.

With its coverage of topics also relevant for industry, this text is aimed at graduate students, researchers, and engineers involved in non-destructive testing for acoustics, mechanics, medicine, diagnosis on artwork and construction, and civil engineering. About the Author Pramod Rastogi received his M. He is the author or coauthor of many scientific papers and the author of book chapters and Encyclopedia articles, and has edited several books in the field of optical metrology.

Erwin Hack holds a diploma in theoretical physics and a Ph. His research interest is in full-field optical measurement techniques including speckle interferometry and thermography. He coordinated and participated in European research projects on optical techniques.

ISBN 13: 9783642112218

Hack regularly publishes in peer-reviewed journals and conferences. He lectures at ETH Zurich on optical methods in experimental mechanics. Permissions Request permission to reuse content from this site. Table of contents 1. The surface in the left photo is nearly flat, indicated by a pattern of straight parallel interference fringes at equal intervals. The surface in the right photo is uneven, resulting in a pattern of curved fringes.

Each pair of adjacent fringes represents a difference in surface elevation of half a wavelength of the light used, so differences in elevation can be measured by counting the fringes. The flatness of the surfaces can be measured to millionths of an inch by this method. To determine whether the surface being tested is concave or convex with respect to the reference optical flat, any of several procedures may be adopted.

One can observe how the fringes are displaced when one presses gently on the top flat. If one observes the fringes in white light, the sequence of colors becomes familiar with experience and aids in interpretation. Finally one may compare the appearance of the fringes as one moves ones head from a normal to an oblique viewing position. When the flats are ready for sale, they will typically be mounted in a Fizeau interferometer for formal testing and certification. Dichroic filters are multiple layer thin-film etalons. In telecommunications, wavelength-division multiplexing , the technology that enables the use of multiple wavelengths of light through a single optical fiber, depends on filtering devices that are thin-film etalons.

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Single-mode lasers employ etalons to suppress all optical cavity modes except the single one of interest. The Twyman—Green interferometer, invented by Twyman and Green in , is a variant of the Michelson interferometer widely used to test optical components. Michelson criticized the Twyman—Green configuration as being unsuitable for the testing of large optical components, since the light sources available at the time had limited coherence length.

Michelson pointed out that constraints on geometry forced by limited coherence length required the use of a reference mirror of equal size to the test mirror, making the Twyman—Green impractical for many purposes. Light from a monochromatic point source is expanded by a diverging lens not shown , then is collimated into a parallel beam. A convex spherical mirror is positioned so that its center of curvature coincides with the focus of the lens being tested.

The emergent beam is recorded by an imaging system for analysis.

Interferometry - Wikipedia

Mach—Zehnder interferometers are being used in integrated optical circuits , in which light interferes between two branches of a waveguide that are externally modulated to vary their relative phase. A slight tilt of one of the beam splitters will result in a path difference and a change in the interference pattern. Mach—Zehnder interferometers are the basis of a wide variety of devices, from RF modulators to sensors [55] [56] to optical switches.

The latest proposed extremely large astronomical telescopes , such as the Thirty Meter Telescope and the Extremely Large Telescope , will be of segmented design. Their primary mirrors will be built from hundreds of hexagonal mirror segments. Polishing and figuring these highly aspheric and non-rotationally symmetric mirror segments presents a major challenge. Traditional means of optical testing compares a surface against a spherical reference with the aid of a null corrector.

In recent years, computer-generated holograms CGHs have begun to supplement null correctors in test setups for complex aspheric surfaces. When laser light is passed through the CGH, the zero-order diffracted beam experiences no wavefront modification. The wavefront of the first-order diffracted beam, however, is modified to match the desired shape of the test surface. In the illustrated Fizeau interferometer test setup, the zero-order diffracted beam is directed towards the spherical reference surface, and the first-order diffracted beam is directed towards the test surface in such a way that the two reflected beams combine to form interference fringes.

The same test setup can be used for the innermost mirrors as for the outermost, with only the CGH needing to be exchanged. They operate on the principle of the Sagnac effect. The distinction between RLGs and FOGs is that in a RLG, the entire ring is part of the laser while in a FOG, an external laser injects counter-propagating beams into an optical fiber ring, and rotation of the system then causes a relative phase shift between those beams.

In a RLG, the observed phase shift is proportional to the accumulated rotation, while in a FOG, the observed phase shift is proportional to the angular velocity. In telecommunication networks, heterodyning is used to move frequencies of individual signals to different channels which may share a single physical transmission line.

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This is called frequency division multiplexing FDM. For example, a coaxial cable used by a cable television system can carry television channels at the same time because each one is given a different frequency, so they don't interfere with one another. Continuous wave CW doppler radar detectors are basically heterodyne detection devices that compare transmitted and reflected beams. Optical heterodyne detection is used for coherent Doppler lidar measurements capable of detecting very weak light scattered in the atmosphere and monitoring wind speeds with high accuracy.

It has application in optical fiber communications , in various high resolution spectroscopic techniques, and the self-heterodyne method can be used to measure the linewidth of a laser. Optical heterodyne detection is an essential technique used in high-accuracy measurements of the frequencies of optical sources, as well as in the stabilization of their frequencies.

Until a relatively few years ago, lengthy frequency chains were needed to connect the microwave frequency of a cesium or other atomic time source to optical frequencies. At each step of the chain, a frequency multiplier would be used to produce a harmonic of the frequency of that step, which would be compared by heterodyne detection with the next step the output of a microwave source, far infrared laser, infrared laser, or visible laser. Each measurement of a single spectral line required several years of effort in the construction of a custom frequency chain.

Currently, optical frequency combs have provided a much simpler method of measuring optical frequencies. If a mode-locked laser is modulated to form a train of pulses, its spectrum is seen to consist of the carrier frequency surrounded by a closely spaced comb of optical sideband frequencies with a spacing equal to the pulse repetition frequency Fig. The pulse repetition frequency is locked to that of the frequency standard , and the frequencies of the comb elements at the red end of the spectrum are doubled and heterodyned with the frequencies of the comb elements at the blue end of the spectrum, thus allowing the comb to serve as its own reference.

In this manner, locking of the frequency comb output to an atomic standard can be performed in a single step. To measure an unknown frequency, the frequency comb output is dispersed into a spectrum. The unknown frequency is overlapped with the appropriate spectral segment of the comb and the frequency of the resultant heterodyne beats is measured. One of the most common industrial applications of optical interferometry is as a versatile measurement tool for the high precision examination of surface topography.

PSI uses monochromatic light and provides very precise measurements; however it is only usable for surfaces that are very smooth. CSI often uses white light and high numerical apertures, and rather than looking at the phase of the fringes, as does PSI, looks for best position of maximum fringe contrast or some other feature of the overall fringe pattern.

Phase Shifting Interferometry addresses several issues associated with the classical analysis of static interferograms. Classically, one measures the positions of the fringe centers. Errors in determining the location of the fringe centers provide the inherent limit to precision of the classical analysis, and any intensity variations across the interferogram will also introduce error. There is a trade-off between precision and number of data points: closely spaced fringes provide many data points of low precision, while widely spaced fringes provide a low number of high precision data points.

Since fringe center data is all that one uses in the classical analysis, all of the other information that might theoretically be obtained by detailed analysis of the intensity variations in an interferogram is thrown away. Traditionally, this information would be obtained using non-automated means, such as by observing the direction that the fringes move when the reference surface is pushed.

Phase shifting interferometry overcomes these limitations by not relying on finding fringe centers, but rather by collecting intensity data from every point of the CCD image sensor. Alternatively, precise phase shifts can be introduced by modulating the laser frequency. The precision and reproducibility of PSI is far greater than possible in static interferogram analysis, with measurement repeatabilities of a hundredth of a wavelength being routine.

In coherence scanning interferometry , [76] interference is only achieved when the path length delays of the interferometer are matched within the coherence time of the light source. CSI monitors the fringe contrast rather than the phase of the fringes. The axial resolution of the system is determined in part by the coherence length of the light source. Holographic interferometry is a technique which uses holography to monitor small deformations in single wavelength implementations. In multi-wavelength implementations, it is used to perform dimensional metrology of large parts and assemblies and to detect larger surface defects.

Holographic interferometry was discovered by accident as a result of mistakes committed during the making of holograms. Early lasers were relatively weak and photographic plates were insensitive, necessitating long exposures during which vibrations or minute shifts might occur in the optical system. The resultant holograms, which showed the holographic subject covered with fringes, were considered ruined.

Eventually, several independent groups of experimenters in the mids realized that the fringes encoded important information about dimensional changes occurring in the subject, and began intentionally producing holographic double exposures. The main Holographic interferometry article covers the disputes over priority of discovery that occurred during the issuance of the patent for this method. Double- and multi- exposure holography is one of three methods used to create holographic interferograms.

A first exposure records the object in an unstressed state. Subsequent exposures on the same photographic plate are made while the object is subjected to some stress.

The composite image depicts the difference between the stressed and unstressed states. Real-time holography is a second method of creating holographic interferograms. A holograph of the unstressed object is created. This holograph is illuminated with a reference beam to generate a hologram image of the object directly superimposed over the original object itself while the object is being subjected to some stress. The object waves from this hologram image will interfere with new waves coming from the object.

This technique allows real time monitoring of shape changes. The third method, time-average holography, involves creating a holograph while the object is subjected to a periodic stress or vibration. This yields a visual image of the vibration pattern. Figure Interferometric synthetic aperture radar InSAR is a radar technique used in geodesy and remote sensing.

Satellite synthetic aperture radar images of a geographic feature are taken on separate days, and changes that have taken place between radar images taken on the separate days are recorded as fringes similar to those obtained in holographic interferometry. The technique can monitor centimeter- to millimeter-scale deformation resulting from earthquakes, volcanoes and landslides, and also has uses in structural engineering, in particular for the monitoring of subsidence and structural stability.

Electronic speckle pattern interferometry ESPI , also known as TV holography, uses video detection and recording to produce an image of the object upon which is superimposed a fringe pattern which represents the displacement of the object between recordings. When lasers were first invented, laser speckle was considered to be a severe drawback in using lasers to illuminate objects, particularly in holographic imaging because of the grainy image produced. It was later realized that speckle patterns could carry information about the object's surface deformations.

Butters and Leendertz developed the technique of speckle pattern interferometry in , [91] and since then, speckle has been exploited in a variety of other applications. A photograph is made of the speckle pattern before deformation, and a second photograph is made of the speckle pattern after deformation. Digital subtraction of the two images results in a correlation fringe pattern, where the fringes represent lines of equal deformation.

Short laser pulses in the nanosecond range can be used to capture very fast transient events. A phase problem exists: In the absence of other information, one cannot tell the difference between contour lines indicating a peak versus contour lines indicating a trough. To resolve the issue of phase ambiguity, ESPI may be combined with phase shifting methods. Initially, white light was split in two, with the reference beam "folded", bouncing back-and-forth six times between a mirror pair spaced precisely 1 m apart. Only if the test path was precisely 6 times the reference path would fringes be seen.

Repeated applications of this procedure allowed precise measurement of distances up to meters. Baselines thus established were used to calibrate geodetic distance measurement equipment, leading to a metrologically traceable scale for geodetic networks measured by these instruments. Other uses of interferometers have been to study dispersion of materials, measurement of complex indices of refraction, and thermal properties. They are also used for three-dimensional motion mapping including mapping vibrational patterns of structures.

Optical interferometry, applied to biology and medicine, provides sensitive metrology capabilities for the measurement of biomolecules, subcellular components, cells and tissues. At a larger scale, cellular interferometry shares aspects with phase-contrast microscopy, but comprises a much larger class of phase-sensitive optical configurations that rely on optical interference among cellular constituents through refraction and diffraction.

At the tissue scale, partially-coherent forward-scattered light propagation through the micro aberrations and heterogeneity of tissue structure provides opportunities to use phase-sensitive gating optical coherence tomography as well as phase-sensitive fluctuation spectroscopy to image subtle structural and dynamical properties. Optical coherence tomography OCT is a medical imaging technique using low-coherence interferometry to provide tomographic visualization of internal tissue microstructures.

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One interferometer arm is focused onto the tissue sample and scans the sample in an X-Y longitudinal raster pattern. The other interferometer arm is bounced off a reference mirror. Reflected light from the tissue sample is combined with reflected light from the reference. Because of the low coherence of the light source, interferometric signal is observed only over a limited depth of sample. X-Y scanning therefore records one thin optical slice of the sample at a time. By performing multiple scans, moving the reference mirror between each scan, an entire three-dimensional image of the tissue can be reconstructed.

Phase contrast and differential interference contrast DIC microscopy are important tools in biology and medicine. Most animal cells and single-celled organisms have very little color, and their intracellular organelles are almost totally invisible under simple bright field illumination. These structures can be made visible by staining the specimens, but staining procedures are time-consuming and kill the cells. As seen in Figs. This allows interferometry depth measurements to be combined with density measurements.

Various correlations have been found between the state of tissue health and the measurements of subcellular objects. For example, it has been found that as tissue changes from normal to cancerous, the average cell nuclei size increases. Phase-contrast X-ray imaging Fig.

For an elementary discussion, see Phase-contrast x-ray imaging introduction. For a more in-depth review, see Phase-contrast X-ray imaging. It has become an important method for visualizing cellular and histological structures in a wide range of biological and medical studies. There are several technologies being used for x-ray phase-contrast imaging, all utilizing different principles to convert phase variations in the x-rays emerging from an object into intensity variations. A disadvantage is that these methods require more sophisticated equipment, such as synchrotron or microfocus x-ray sources, x-ray optics , or high resolution x-ray detectors.

From Wikipedia, the free encyclopedia. Further information: Interference wave propagation. See also: Common-path interferometer. ESPI fringes showing a vibration mode of a clamped square plate. Spyrogira cell detached from algal filament under phase contrast. Toxoplasma gondii unsporulated oocyst, differential interference contrast. The History of Science and Technology. Houghton Mifflin Harcourt. Basics of Interferometry. Elsevier Inc. Optics Express. Bibcode : OExpr.. Retrieved 1 April Retrieved 22 June Optical Shop Testing. Wave Optics.

Discovery Publishing House. Retrieved 2 January Bibcode : ZPhy.. American Journal of Physics. Bibcode : AmJPh.. In Buschhorn, G.


American Association of Physics Teachers. Retrieved 5 April Principles of physics: a calculus-based text, Volume 1. Brooks Cole. Optical Interferometry for Biology and Medicine. Bibcode : oibm. Retrieved 8 April Physics Department, Westminster School, London. Engineer's thesis. California Institute of Technology. American Journal of Science. Bibcode : AmJS Reviews of Modern Physics.

Bibcode : RvMP White light fringes were chosen for the observations because they consist of a small group of fringes having a central, sharply defined black fringe which forms a permanent zero reference mark for all readings.

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