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	The Acousto-Optic Modulator and Optical Heterodyning
		Bragg diffraction of x-rays occurs for atomic planes that are at rest in the laboratory, while acousto-optic diffraction occurs from acoustic wave planes that travel at the relatively high speed v
		The fact that the diffracting acoustic planes move with respect to the laboratory leads to a Doppler shift of the frequency of the diffracted beams.
		Adjust the angle of AOM1 for a diffracted beam that is frequency upshifted, as in Fig.
	cat.middlebury.edu /~PHManual/acousto.html (4169 words)

	Department of Physics, Cavendish Laboratory
		Bragg's father, then Professor of Physics at Leeds, heard of the German work in the summer of 1912 and discussed it with his son, who set about re-interpreting the X-ray pictures of zinc blende published by the Munich group.
		Bragg himself modestly attributes it to a "concatenation of fortunate circumstances" but his paper soon convinces you that its success owed more to Bragg's astute powers of penetrating through the apparent complexities of physical mechanisms to their underlying simplicity.
		Bragg's superb powers of combining simplicity with rigour, his enthusiasm, liveliness and charm of manner, and his beautiful demonstrations all conspired to make him one of the best lecturers on science that ever lived.
	www.phy.cam.ac.uk /cavendish/history/years/bragg.php (1535 words)

	Diffraction - Biocrawler (Site not responding. Last check: 2007-09-24)
		Diffraction also occurs when any group of waves of a finite size is propagating; for example, a narrow beam of light waves from a laser must, because of diffraction of the beam, eventually diverge into a wider beam at a sufficient distance from the laser.
		Bragg diffraction is used in X-ray crystallography to deduce the structure of a crystal from the angles at which X-rays are diffracted from it.
		The most common demonstration of Bragg diffraction is the spectrum of colors seen reflected from a compact disc: the closely-spaced tracks on the surface of the disc form a diffraction grating, and the individual wavelengths of white light are diffracted at different angles from it, in accordance with Bragg's law.
	www.biocrawler.com /encyclopedia/Diffraction (1539 words)

	NationMaster - Encyclopedia: Diffraction grating
		In optics, a diffraction grating is a reflecting or transparent element, whose optical properties are periodically modulated.
		Diffraction gratings are often used in monochromators, spectrometers, wavelength division multiplexing devices, optical pulse compressing devices, and many other optical instruments.
		Diffraction Federal Standard 1037C entitled Telecommunications: Glossary of Telecommunication Terms is a U.S. Federal Standard, issued by the General Services Administration pursuant to the Federal Property and Administrative Services Act of 1949, as amended.
	www.nationmaster.com /encyclopedia/Diffraction-grating (2364 words)

	Science Fair Projects - Diffraction
		Diffraction is one particular type of wave interference.
		Diffraction is the specific type of interference caused by the partial obstruction or lateral restriction of a wave.
		Because diffraction is an interference effect, diffraction will not occur if the wave is not coherent, and diffraction effects become weaker (and ultimately undetectable) as the size of obstruction is made larger and larger compared to the wavelength.
	www.all-science-fair-projects.com /science_fair_projects_encyclopedia/Diffraction (1677 words)

	Encyclopedia :: encyclopedia : Bragg diffraction (Site not responding. Last check: 2007-09-24)
		Bragg diffraction was first proposed by William Lawrence Bragg in 1912 as a means of analyzing the structure of crystals.
		Bragg and his father William Henry Bragg collimated x-rays to diffract off of different crystal planes.
		In 1915, William Henry Bragg and William Lawrence Bragg were awarded the Nobel Prize for their contributions to crystal structure analysis.
	www.hallencyclopedia.com /topic/Bragg_diffraction.html (392 words)

	Bragg diffraction (Site not responding. Last check: 2007-09-24)
		The Bragg formulation of X-ray diffraction (also referred to as Bragg diffraction) was first proposed by William Lawrence Bragg and William Henry Bragg in 1913 in response to their discovery that crystalline solids produced surprising patterns of reflected X-rays (in contrast to that of, say, a liquid).
		Bragg explained this result by modeling the crystal as a set of discrete parallel planes separated by a constant parameter d.
		Thus the condition for diffraction can be equivalently stated as the requirement that the incoming wavevector (when placed at the origin of k-space) lie on a Bragg plane or on a Brillouin zone.
	encyclopedia.vestigatio.com /Bragg_diffraction (751 words)

	Spartanburg SC \| GoUpstate.com \| Spartanburg Herald-Journal (Site not responding. Last check: 2007-09-24)
		Diffraction refers to various phenomena associated with wave propagation, such as the bending, spreading and interference of waves passing by an object or aperture that disrupts the wave.
		Diffraction from a three dimensional periodic structure such as atoms in a crystal is called Bragg diffraction.
		Bragg diffraction may be carried out using either light of very short wavelength like x-rays or matter waves like neutrons whose wavelength is on the order of the atomic spacing.
	www.goupstate.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=Diffraction (3029 words)

	Diffraction Summary
		Diffraction from multiple slits, as described above, is similar to what occurs when waves are scattered from a periodic structure, such as atoms in a crystal or rulings on a diffraction grating.
		Bragg diffraction is used in X-ray crystallography to deduce the structure of a crystal from the angles at which X-rays are diffracted from it.
		The most common demonstration of Bragg diffraction is the spectrum of colors seen reflected from a compact disc: the closely-spaced tracks on the surface of the disc form a diffraction grating, and the individual wavelengths of white light are diffracted at different angles from it, in accordance with Bragg's law.
	www.bookrags.com /Diffraction (3160 words)

	3) Diffraction
		The intensity distribution of the recorded diffraction pattern of an object is proportional to the square of the Fourier transform of the object.
		The diffraction pattern of narrow slits and the shape function are shown in (a0 and (b) respectively, and the operation of their convolution gives rise to (c), the diffraction pattern of N narrow slits.
		For a particular diffraction pattern, the scale factor K depends upon the wavelength of the radiation used and upon the geometry of the experimental arrangement.
	ncmir.ucsd.edu /~gina/Sec-III.C.6-D.1/Sec-III.C.6.html (5181 words)

	An Intuitive Explanation of Phase Conjugation
		Bragg diffraction is distinct from regular diffraction by the fact that the diffracting element is not a two-dimensional grating of lines etched on a flat sheet, as in standard diffraction, but a solid volume containing parallel planes of alternating refractive index.
		Bragg diffraction was first observed in x-ray crystallography as a sharp peak of reflection at a particular angle of incidence to the crystal lattice planes.
		Bragg refraction could be restored, however, by re-aligning either or both beams to make their wave vectors meet the shorter lattice vector.
	cns-alumni.bu.edu /~slehar/PhaseConjugate/PhaseConjugate.html (2738 words)

	Bragg's Law and Diffraction
		The Braggs were awarded the Nobel Prize in physics in 1915 for their work in determining crystal structures beginning with NaCl, ZnS and diamond.
		Although Bragg's law was used to explain the interference pattern of X-rays scattered by crystals, diffraction has been developed to study the structure of all states of matter with any beam, e.g., ions, electrons, neutrons, and protons, with a wavelength similar to the distance between the atomic or molecular structures of interest.
		Bragg's Law can easily be derived by considering the conditions necessary to make the phases of the beams coincide when the incident angle equals and reflecting angle.
	www.eserc.stonybrook.edu /ProjectJava/Bragg (847 words)

	Acousto-Optics
		Bragg scattering can be accomplished by having a very wide slab of material, the diffraction is said to be in the Bragg regime.
		The main characteristic of Bragg diffraction is two output beams: the undiffracted beam or carrier beam, and the principal diffracted beam or the sideband beam.
		This case is similar to Bragg diffraction of X-rays in a crystal lattice.
	www.me.gatech.edu /declercq/Acousto-optics.htm (942 words)

	Physics: Bragg Law
		Bragg diffraction has to do with wave interactions on crystal structure, specifically in plane spacing.
		If Bragg were to consider RI, the implication would be that the diffraction pattern would change based on the change in phase velocity.
		But Bragg looks at reflection of waves, and the interaction of the resulting differences in path length, while refractive index, in this context, would look at the change in angle with respect to the incident beam and the surface.
	en.allexperts.com /q/Physics-1358/Bragg-Law.htm (487 words)

	DoITPoMS TLP - X-ray Diffraction - Bragg's law
		Bragg's law is the cornerstone of X-ray diffraction analysis, it allows us to make accurate quantification of the results of experiments carried out to determine crystal structure.
		A Bragg condition is such that the scattered rays from two parallel planes interact with each other in such a way as to create constructive interference.
		The angle between the transmitted and Bragg diffracted beams is always equal to 2q as a consequence of the geometry of the Bragg condition.
	www.doitpoms.ac.uk /tlplib/xray-diffraction/bragg.php (397 words)

	Bragg Reflection of X-Rays
		Diffraction pattern of microwaves is observed much like the x-ray diffraction by a crystal.
		Plot the intensity of microwaves as a function of diffraction angle for both orientations.
		Using the technique of Bragg diffraction of x-rays, crystallographers can determine the interatomic space inside the crystal if the wavelength of the x-rays is known.
	www2.potsdam.edu /islamma/Phys306_XRay.htm (698 words)

	template x-ray David Keenahan Teachnet
		The Braggs were the first to successfully interpret x-ray diffraction patterns.
		Bragg devised conditions for constructive interference to arise in radiation scattered by crystals.
		Then by directing x-rays of known wavelength at more complex crystals, diffraction patterns were obtained and examined enabling the spacing of the Bragg planes to be determined and so the crystal structure established.
	www.teachnet.ie /dkeenahan/page21.html (338 words)

	Laser Diffraction \| Mie Scattering Theory
		The equation also established the concept of interference patterns that was used by Bragg to experimentally verify the concept of diffraction (bending) of light from layers of atoms in a crystal.
		The issue for particle size measurement is the ability to interpret the pattern from a mixture of particle sizes covering a wide range of particle sizes (Figure 2).
		Diffraction of light occurs at the edge of particles, but many substances have particles that are transparent and allow light to pass though.
	www.microtrac.com /laserdiffraction.cfm (1345 words)

	Acousto-optic effect
		Passing the medium, the light diffracts on inhomogeneities of the refraction index, forming in the far field a salient diffraction pattern.
		On examination of light diffraction by a monochromatic acoustic wave, two limiting regimes are distinguished first of all — the regimes of Raman-Nath and Bragg.
		However, the acousto-optic selectivity peculiar to the Bragg diffraction restricts the frequency range of acousto-optic interaction and, as a consequence, speed of operation of acousto-optic devices.
	www.mt-berlin.com /frames_ao/descriptions/ao_effect.htm (656 words)

	Research Projects
		The only existing diffraction theory to date that can be phase-sensitive is the so-called dynamical theory, which includes all possible interactions among multiply-excited Bragg reflection waves inside a crystal.
		The practical need for a simple, phase-sensitive, first-principle x-ray diffraction theory is greatly exemplified by the recent experimental innovation of reference-beam diffraction which in principle allows a phase-sensitive intensity data collection of a large number of Bragg reflections using a routine crystallography setup.
		The final result is a simple analytical expression of a phase-sensitive diffracted intensity that is valid for all measured Bragg reflections and for the entire excitation range of the reference reflection G in a reference-beam diffraction experiment.
	staff.chess.cornell.edu /~shen/Research.html (2308 words)

	Beamline Technique 05: Hard X-Ray Diffraction
		In "Bragg" diffraction, the incident x-rays are monochromatic (single wavelength) and the sample is an oriented single crystal.
		Using hard x-ray powder diffraction and single-crystal diffraction, scientists solved the structure of a zeolite (potassium gallosilicate) that exhibits irreversible pressure-induced hydration: when the pressure is released, the material stays superhydrated.
		X-ray diffraction was used to analyze the texture of a nickel silicide (NiSi) thin film on a silicon substrate.
	www.er.doe.gov /bes/synchrotron_techniques/scattering05.htm (1552 words)

	notes
		The first term is just the ratio of focal lengths as normal, the second term is an anamorphic magnification, caused by the fact that the beam coming off the grating has a different diameter to the beam incident upon it.
		Diffraction of X-rays was used as a tool to analyse the structure of crystals in the early 20th century, but a crystal with a regular lattice spacing can be used as a diffraction element at X-ray wavelengths.
		Near the Bragg condition there is a Bragg envelope, where light at different wavelengths is diffracted at different angles, but at less efficiency than the light diffracted at the Bragg angle.
	www.astro.livjm.ac.uk /courses/phys362/notes (2692 words)

	(IUCr) Book Review
		Newer concepts in the treatment of powder diffraction data by profile analysis are given in the presentation of the Rietveld method.
		Applied research areas that have been made available by the use of high-intensity synchrotron sources and improved detectors are also described, including the study of crystalline surfaces and the use of extended X-ray absorption fine-structure spectroscopy to study the local environment of a chemical element in a crystal.
		The Russian school of electron diffraction has often relied on the use of texture diffraction patterns for data collection from a large specimen area, sampling a relatively wide distribution of crystal orientations.
	www.iucr.org /iucr-top/journals/bookreviews/by0087.html (1107 words)

	Bragg imaging
		The acousto-optic Bragg imaging technique is based on laser light incident on a sound field which is transmitted through a plate, immersed in a coupling medium such as water.
		The incident laser light is diffracted at the ultrasonic field and normally resembles diffraction at an optical grating.
		However, at high ultrasound frequencies, the diffraction phenomenon can be manipulated to resemble Bragg diffraction of X-rays at a crystal lattice.
	www.me.gatech.edu /declercq/bragg-imaging.htm (164 words)

	Bragg's Law
		But of course we are only interested in Fraunhofer diffraction, which means the distances of the needle from the source and the detector are very large.
		The dark brown vectors are the k-vectors corresponding to the incident and scattered wave.
		But in the particular Bragg condition shown, the distribution of the atoms on the Bragg planes does not affect the scattered intensity: in a way, quite a surprising result.
	www.rodenburg.org /theory/Braggslaw19.html (1143 words)

	Asher Research Group - Colloid Group
		Bragg diffraction was first proposed by William Lawrence Bragg in 1912 as a means of analyzing the structure of crystals.
		Since the basic physical phenomenon is based on diffraction, the periodicity of the photonic crystal structure has to be in the same length scale as the wavelength of the electromagnetic waves (~300 nm for photonic crystals operating in the visible part of the spectrum).
		The degree of redshift in diffraction observed is proportional to the amount of bound organophosphate.
	www.pitt.edu /~asher/homepage/colgrp.html (1090 words)

	X-Ray Powder Diffraction
		X-ray diffraction has been in use in two main areas, for the fingerprint characterization of crystalline materials and the determination of their structure.
		The diffraction pattern of copper metal was measured with x-ray radiation of wavelength of 1.315Å.
		The diffracted beam may be detected by using a moveable detector such as a Geiger counter, which is connected to a chart recorder.
	materials.binghamton.edu /labs/xray/xray.html (774 words)

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