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diffraction

diffraction

diffraction Sentence Examples

  • From the measured distances of the diffraction bands the width of the slit may be easily deduced.

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  • DIFFRACTION OF LIGHT.

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  • In 1799 he was induced by his fellow-student, Henry Brougham, to study the diffraction of light.

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  • Diffraction when the Source of Light is not seen in Focus.

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  • By this procedure the width of the central band in the diffraction pattern is halved, and so far an advantage is attained.

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  • By this procedure the width of the central band in the diffraction pattern is halved, and so far an advantage is attained.

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  • If the image of the line be =o, the intensity at any point E, n of the diffraction pattern may be represented by ?2a2t2 S A2f2 the same law as obtains for a luminous point when horizontal directions are alone considered.

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  • - Spectroscopes may be divided into two classes: prism spectroscopes, with angular or direct vision, and grating spectroscopes; the former acting by refraction (q.v.), the latter by diffraction or interference.

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  • The diffraction pattern is therefore that due to a single aperture, merely brightened n times.

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  • The first dark ring in the diffraction pattern of the complete circular aperture occurs when r/f = 1.2197 XO /2R (15).

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  • If the aperture and wave-length increase in the same proportion, the size and shape of the diffraction pattern undergo no change.

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  • On the electromagnetic theory, the problem of diffraction becomes definite when the properties of the obstacle are laid down.

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  • When the functions C and S have once been calculated, the discussion of various diffraction problems is much facilitated by the idea, due to M.

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  • intensity is zero, and this band is accompanied by a number of fainter images corresponding to the diffraction of a star image in a telescope.

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  • If the angular interval between the components of a double star were equal to twice that expressed in equation (15) above, the central disks of the diffraction patterns would be just in contact.

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  • when the grating is so situated that the angles of incidence and diffraction are equal.

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  • Let us reconsider, following Cornu, the diffraction of a screen unlimited on one side, and on the other terminated by a straight edge.

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  • - The explanation of diffraction phenomena given by Fresnel and his followers is 1 H.

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  • This question was treated by Stokes in his " Dynamical Theory of Diffraction " (Camb.

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  • Experiments may be made with plane and curved mirrors to verify these laws, but it is necessary to use short waves, in order to diminish diffraction effects.

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  • When light proceeding from a small source falls upon an opaque object, a shadow is cast upon a screen situated behind the obstacle, and this shadow is found to be bordered by alternations of brightness and darkness, known as " diffraction bands."

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  • If the aperture be increased, not only is the total brightness over the focal plane increased with it, but there is also a concentration of the diffraction pattern.

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  • In these expressions we are to replace p by ks/f, or rather, since the diffraction pattern is symmetrical, by kr/f, where r is the distance of any point in the focal plane from the centre of the system.

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  • Diffraction Gratings.

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  • Diffraction of Soitnd Waves.

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  • Many of the well-known phenomena of optical diffraction may be imitated with sound waves, especially if the waves be short.

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  • Lord Rayleigh, to whom we owe the first general discussion of the theory of the spectroscope, found by observation that if two spectroscopic lines of frequencies n1 and n, are observed in an instrument, they are just seen as two separate lines when the centre of the central diffraction band of one coincides with the first minimum intensity of the other.

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  • Trans., 1834) in his original investigation of the diffraction of a circular object-glass, and readily obtained from (6), is z z 3 25 27 J1(z) = 2 2 2.4 + 2 2.4 2.6 2 2.4 2.6 2.8 + When z is great, we may employ the semi-convergent series Ji(s) = A/ (7, .- z)sin (z-17r) 1+3 8 1 ' 6 (z) 2 3.5.7.9.1.3.5 5 () 3 1 3.5.7.1 1 3 cos(z - ?r) 8 ' z (z) 3.5.7.9.11.1.3.5.7 1 5 + 8.16.24.32.40 (z

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  • The halo diminishes in brightness from the centre outwards, and is probably due to the diffraction of light.

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  • The halo diminishes in brightness from the centre outwards, and is probably due to the diffraction of light.

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  • He was also the inventor of the diffraction grating.

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  • Later investigations by Fraunhofer, Airy and others have greatly widened the field, and under the head of " diffraction " are now usually treated all the effects dependent upon the limitation of a beam of light, as well as those which arise from irregularities of any kind at surfaces through which it is transmitted, or at which it is reflected.

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  • In observing the bands he received them at first upon a screen of finely ground glass, upon which a magnifying lens was focused; but it soon appeared that the ground glass could be dispensed with, the diffraction pattern being viewed in the same way as the image formed by the object-glass of a telescope is viewed through the eye-piece.

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  • Talbot ascribes the appearance to diffraction; and he recommends the use of a telescope.

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  • Moseley, shortly after the discovery of the diffraction of X-rays by crystals, set to work to examine the X-ray spectrum of a number of elements each of which he made in turn the target of an X-ray tube.

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  • In September 1839 a 3-foot speculum was finished and mounted on an altazimuth stand similar to Herschel's; but, though the definition of the images was good (except that the diffraction at the joints of the speculum caused minute rays in the case of a very bright star), and its peculiar skeleton form allowed the speculum to follow atmospheric changes of temperature very quickly, Lord Rosse decided to cast a solid 3-foot speculum.

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  • Formerly classified by the ancient Greeks with halos, rainbows, &c., under the general group of "meteors," they came to receive considerable attention at the hands of Descartes, Christiaan Huygens, and Sir Isaac Newton; but the correct explanation of coronae was reserved until the beginning of the 19th century, when Thomas Young applied the theories of the diffraction and interference of light to this phenomenon.

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  • It has now been firmly established, both experimentally and mathematically, that coronae are due to diffraction by the minute particles of moisture and dust suspended in the atmosphere, and the radii of the rings depend on the size of the diffracting particles.

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  • Talbot ascribes the appearance to diffraction; and he recommends the use of a telescope.

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  • Moseley, shortly after the discovery of the diffraction of X-rays by crystals, set to work to examine the X-ray spectrum of a number of elements each of which he made in turn the target of an X-ray tube.

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  • Their absolute freedom from diffraction, the perfect control of the illumination and thickness of the lines, and the accuracy with which it will be possible to construct scales for zone observations will be important features of the new method.

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  • The former are for the most part concerned with questions relating to the theory of light, arising out of his professorial lectures, among which may be specially mentioned his paper "On the Diffraction of an Object-Glass with Circular Aperture."

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  • Fraunhofer's Diffraction Phenomena.

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  • - A very general problem in diffraction is the investigation of the distribution of light over a screen upon which impinge divergent or convergent spherical waves after passage through various diffracting apertures.

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  • A diminution of X thus leads to a simple proportional shrinkage of the diffraction pattern, attended by an augmentation of brilliancy in proportion to A-2.

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  • The contraction of the diffraction pattern with increase of aperture is of fundamental importance in connexion with the resolving power of optical instruments.

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  • According to common optics, where images are absolute, the diffraction pattern is supposed to be infinitely small, and two radiant points, however near together, form separated images.

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  • This indefiniteness of images is sometimes said to be due to diffraction by the edge of the aperture, and proposals have even been made for curing it by causing the transition between the interrupted and transmitted parts of the primary wave to be less abrupt.

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  • The results of the theory of the diffraction patterns due to circular apertures admit of an interesting application to coronas, such as are often seen encircling the sun and moon.

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  • By supposing the retardation to vary uniformly and continuously we, fall upon the case of an ordinary prism: but there;, is then no diffraction spectrum in the usual sense.

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  • We shall only consider one interesting case of sound diffraction which may be easily observed.

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  • The railings in fact do for sound what a diffraction grating does for light.

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  • When the slit is narrow light is lost through diffraction unless the angular aperture of this condensing lens, as viewed from the slit, is considerably greater than that of the collimator lens.

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  • With fairly homogeneous light the diffraction pattern may be observed at a distance, varying with the width of the slit from about the length of the collimator to one quarter of that length.

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  • Fraunhofer's Diffraction Phenomena.

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  • This indefiniteness of images is sometimes said to be due to diffraction by the edge of the aperture, and proposals have even been made for curing it by causing the transition between the interrupted and transmitted parts of the primary wave to be less abrupt.

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  • The railings in fact do for sound what a diffraction grating does for light.

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  • With fairly homogeneous light the diffraction pattern may be observed at a distance, varying with the width of the slit from about the length of the collimator to one quarter of that length.

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  • Gouy has studied the more simple case of diffraction at a straight' edge.

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  • It has in fact been found, with the very great precision of which optical experiment is capable, that all terrestrial optical phenomenareflexion, refraction, polarization linear and circular, diffraction - are entirely unaffected by the direction of the earth's motion, while the same result has recently been extended to electrostatic forces; and this is our main experimental clue.

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  • If we compare the spectrum produced by refraction in a glass prism with that of a diffraction grating, we find not only that the order of colours is reversed, but also that the same colours do not occupy corresponding lengths on the two spectra, the blue and violet being much more extended in the refraction spectrum.

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  • Grimaldi (1618-1663), the phenomenon of diffraction.

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  • Intermediate cases in which a few zones only are formed belong especially to the province of diffraction.

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  • Dynamical Theory of Diffraction.

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  • Lord Rayleigh's expression for the resolving power of different instruments is based on the assumption that the geometrical image of the slit is narrow compared with the width of the diffraction image.

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  • Halos are at definite distances (22° and 46 °) from the sun, and are coloured red on the inside, being due to refraction; coronae closely surround the sun at variable distances, and are coloured red on the outside, being due to diffraction.

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  • Krakatoa), are also explicable by the diffraction of light.

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  • But a deviation, termed diffraction, does occur, and consequently the complete theory of shadows involves considerations based on the nature of the rays themselves; this aspect is treated in Diffraction Of Light.

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  • The fourth essay is a systematic treatment of the nature of colour, with a description of many curious experiments and a discussion of the rainbow, halos, parhelia, diffraction, and the more purely physiological phenomena of colour.

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  • The chromatic halos which frequently encircle these images are due to diffraction.

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  • In 1818 he read a memoir on diffraction for which in the ensuing year he received the prize of the Academie des Sciences at Paris.

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  • By the use of two plane mirrors of metal, forming with each other an angle of nearly 180°, he avoided the diffraction caused in.

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  • In 1882, before the Physical Society of London, he gave a description of the diffraction gratings with which his name is specially associated, and which have been of enormous advantage to astronomical spectroscopy.

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  • In addition to the above facts of polarization mention may be made of the partial polarization, in a plane perpendicular to that of emission, of the light emitted in an oblique direction from a white-hot solid, and of the polarization produced by diffraction.

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  • Abbe applied the Fraunhofer diffraction phenomena to the explanation of the representation in the microscope of uniformly illuminated objects.

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  • If a grating is placed as object before the microscope objective, Abbe showed that in the image there is intermittent clear and dark banding only, if at least two consecutive diffraction spectra enter into the objective and contribute towards the image.

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  • If in this case the aperture of the objective be so small, or the diffraction spectra lie so far from each other, that only the pencil parallel to the axis, i.e.

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  • The resemblance is greater the more diffraction spectra enter the objective.

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  • From the Fraunhofer formula I =X/n sin a one can immediately deduce the limit to the diffraction constant I, so that the banding by an objective of fixed numerical aperture can be perceived.

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  • All details of the object so resolved are perceived, if two diffraction maxima can be passed through the objective, so that the character of the object is seen in the image, even if an exact resemblance has not yet been attained.

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  • The Fraunhofer diffraction phenomena, which take place in the 0 FIG.

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  • 20) and to the right and left the diffraction spectra, the images of different colours partially overlapping.

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  • If a resolvable grating is considered, the diffraction phenomenon has the appearance shown in fig.

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  • If the obliquity of illumination be so great that the principal maximum passes through the outermost edge of the objective, while a spectrum of 1st order passes the opposite edge, so that in the back focal plane the diffraction phenomenon shown in fig.

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  • 13, we suppose that a diffracting particle of such fineness is placed at 0 that the diffracted pencils of the 1st order make an angle w with the axis; the principal maximum of the Fraunhofer diffraction phenomena lies in F' 1; and the two diffraction maxima of the 1st order in P' and P' 1.

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  • Abbe showed that for the production of an image the diffraction maxima must lie within the exit pupil of the objective.

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  • If this object be viewed by the objective, so that at least the diffraction spectra of 1st order pass the finer divisions, then the corresponding diffraction phenomenon in the back focal plane of the objective has the appearance shown in fig.

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  • 21, while the diffraction figure corresponding to the coarser ruling appears as given in fig.

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  • If one cuts out by a diaphragm in the back focal plane of the objective all diffraction spectra except the principal maximum, one sees in the image a field divided into two halves, which show with different clearness, but no banding.

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  • If now the spectrum of Est order of the larger division be cut out from the diffraction figure, as is shown in fig.

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  • Still more strikingly is this phenomenon shown by Abbe's diffraction plate (fig.

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  • At least two successive diffraction maxima must be admitted through the objective for there to be any image of the objects.

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  • The image consists of a diffraction disk from whose form and size certain conclusions may be drawn as to the size and form of the object.

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  • Too much light is useless for observing delicately coloured or colourless preparations, whose parts only become visible as a result of slight differences of diffraction.

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  • The chief cone of rays then enters obliquely into the objective, the angle between the direct cone of rays and the diffraction spectrum of the first order can then become as large again as with direct lighting, and still be taken up in the objective.

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  • As was seen when discussing the physical theory, the minute details of the object cause diffractions, and can only be examined if the objective can take up at least two consecutive diffraction spectra.

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  • These diffracting details become especially distinct if the direct lighting cone of rays, the spectrum of zero:order or the chief maximum, is not allowed to enter the objective and instead only two or more diffraction maxima are taken up; the details then appear bright on a dark background.

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  • X-Ray Diffraction The group currently has two rotating anode and a sealed tube X-ray generator.

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  • anode X-ray source and an image plate detector system, both of which allow diffraction data to be recorded rapidly.

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  • Figure 5. The aging process of Casa Montero's cherts: X-Ray diffraction pattern of opal and opaline chert obtained from the same nodule.

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  • The Phenix is a unique closed cycle helium cryostat specifically designed for powder diffraction.

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  • The best way to find out the structure of a crystalline solid like a zeolite is to use single crystal X-ray diffraction.

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  • Working in Oxford she used x-ray crystallography, a technique based on the diffraction of x-rays by crystals.

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  • Also it is of considerable interest to produce bigger protein crystals for neutron diffraction studies of hydrogen deuterium exchange, in particular cases.

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  • The substage diaphragm was reduced to enhance diffraction colors.

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  • diffraction of X-rays by crystals.

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  • diffraction of light waves normally limits spatial resolution of nearby objects to no better than the wavelength of the light source.

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  • diffraction from subsequent crystals for a protein do not apparently merge well.

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  • This is a reason why D syntheses are performed in studies of electron densities by single-crystal X-ray diffraction.

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  • SEM electron backscattered diffraction (EBSD) analysis of cataclastic microstructures Click on a thumbnail image to see the full sized picture.

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  • In order to learn more about the mechanism of these reactions we have studies these reaction using time-resolved in-situ X-ray diffraction.

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  • Convergent beam electron diffraction In many materials, the crystal structure of minority phases is not known.

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  • We rely heavily on structural analysis by single crystal X-ray diffraction.

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  • diffraction grating in a cupboard.

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  • diffraction pattern from a protein crystal?

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  • diffraction maxima.

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  • diffraction spikes, many people are used to seeing them and don't consider them an aberration.

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  • diffraction peak in glasses?

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  • diffraction experiments using a glass block.

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  • For X-ray diffraction studies on organic thin films a portable vacuum chamber is used.

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  • Ted was ideally placed to make use of neutron diffraction to study the nature of the vortex state.

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  • Users may also submit their own powder diffraction data.

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  • For small molecules, it is possible to analyze X-ray diffraction data by means of the direct methods.

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  • We are currently broadening our repertoire into the developing of synchrotron X-ray diffraction.

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  • Here we report the measurement of electron diffraction patterns from these crystals.

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  • The new cavity configuration allowed tuning of the laser continuously over 25 nm of the erbium gain bandwidth by using a bulk diffraction grating.

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  • diffraction grating made from a high quality high efficiency blazed master.

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  • But the tunable diffraction grating could raise it by about 100 percent.

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  • We design distorted diffraction gratings that simulate the effects of long propagation distances in a short instrument.

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  • The Star Analyzer 100 is a high efficiency 100 lines/mm transmission diffraction grating, blazed in the first order.

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  • electron diffraction pattern by noting its symmetry.

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  • Measurements of such order are usually made by diffraction techniques, which detect the ionic cores and the spins of the conduction electrons.

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  • The neutron diffraction experiment is undertaken under relatively extreme conditions.

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  • In particular, diffraction of a wave from a thick sinusoidal grating or acoustic wave.

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  • Question 5 A student finds an old, unmarked diffraction grating in a cupboard.

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  • This window shows a simulated TEM diffraction pattern for the wurtzite structure, colour-coded to show the phase of diffracted intensity.

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  • In the 1930's, X-ray diffraction studies of solids showed that polymers contained large macromolecules.

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  • The filter wheel includes a 4x magnifier that results in 0.12 arcsec pixels for near diffraction limited imaging.

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  • neutron diffraction to study the nature of the vortex state.

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  • Neutron diffraction techniques are employed to investigate both atomic and magnetic structures, while longer range fluctuations are studied using small angle neutron diffraction techniques are employed to investigate both atomic and magnetic structures, while longer range fluctuations are studied using small angle neutron scattering.

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  • What else can we say about the diffraction pattern from a protein crystal?

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  • photoelectron diffraction is a method used to determine the geometry of molecules or atoms on single crystal surfaces.

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  • photoelectron diffraction experiment in two possible modes. • (a) Scanned energy scan mode.

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  • powder diffraction is also provided, along with a PDF file with slightly different content to the online notes.

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  • So far we have only considered the case of small- t diffraction with respect to the outgoing proton.

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  • reflection high-energy electron diffraction (RHEED) that can be carried out during growth.

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  • Conventional high energy electron diffraction relies on elastic scattering.

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  • Synchrotron X-ray powder diffraction and computational investigation of purely siliceous zeolite Y under pressure.

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  • Polytype coalescence in Lely vapor grown silicon carbide (SiC) has been studied extensively using the technique of X-Ray Diffraction (XRD ).

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  • silicon carbide crystal shown by the extensive streaking evident along the diffraction rows.

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  • sophisticated mathematical techniques are then used to analyze the diffraction pattern.

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  • Software tools are available for calculating diffraction spectra for specified crystal structures.

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  • specular X-ray reflectivity, diffraction imaging and defect mapping.

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  • Because almost all reflecting telescopes produce diffraction spikes, many people are used to seeing them and don't consider them an aberration.

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  • substage diaphragm was reduced to enhance diffraction colors.

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  • synchrotron diffraction data.

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  • synchrotron X-ray diffraction patterns and to work out the diffractometer constants I refined a silicon pattern.

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  • Harford, J.J. & Squire, J.M. (1997) Time-resolved diffraction studies of muscle using synchrotron radiation.

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  • Diffraction spikes on a reflector's star images, caused by its secondary mirror spider vanes, are absent in an unobstructed refractor.

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  • X-ray diffraction data by means of the direct methods.

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  • I am analyzing synchrotron X-ray diffraction patterns and to work out the diffractometer constants I refined a silicon pattern.

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  • Working in Oxford she used X-ray crystallography, a technique based on the diffraction of x-rays by crystals.

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  • X-ray diffraction patterns.

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  • X-ray diffraction data by means of the direct methods.

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  • X-ray diffraction studies on material composition and crystal structure, or for contact radiography.

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  • X-ray diffraction techniques.

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  • I am analyzing synchrotron X-ray diffraction patterns and to work out the diffractometer constants I refined a silicon pattern.

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  • To fully understand the concepts and functions of the programs, the user should be familiar with surface X-ray diffraction, eg.

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  • The determination of the motion in the aether, due to the action of a periodic force at a given point, is discussed in the article Diffraction Of Light (§ Ii).

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  • Thus by equation (18) of § II of the article Diffraction Of Light, the secondary disturbance is expressed by D' - D n 2 Tsin sin (nt - kr) D 47rb2 r _ D' - D irTsin O sin (nt - kr) (3)1 The preceding investigation is based upon the assumption that in passing from one medium to another the rigidity of the aether does not change.

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  • The actual calculation follows a similar course to that by which Huygens's conception of the resolution of a wave into components corresponding to the various parts of the wave-front is usually verified (see Diffraction Of Light).

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  • Their absolute freedom from diffraction, the perfect control of the illumination and thickness of the lines, and the accuracy with which it will be possible to construct scales for zone observations will be important features of the new method.

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  • The former are for the most part concerned with questions relating to the theory of light, arising out of his professorial lectures, among which may be specially mentioned his paper "On the Diffraction of an Object-Glass with Circular Aperture."

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  • He was also the inventor of the diffraction grating.

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  • In 1799 he was induced by his fellow-student, Henry Brougham, to study the diffraction of light.

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  • Grimaldi (1618-1663), the phenomenon of diffraction.

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  • DIFFRACTION OF LIGHT.

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  • When light proceeding from a small source falls upon an opaque object, a shadow is cast upon a screen situated behind the obstacle, and this shadow is found to be bordered by alternations of brightness and darkness, known as " diffraction bands."

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  • Later investigations by Fraunhofer, Airy and others have greatly widened the field, and under the head of " diffraction " are now usually treated all the effects dependent upon the limitation of a beam of light, as well as those which arise from irregularities of any kind at surfaces through which it is transmitted, or at which it is reflected.

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  • Intermediate cases in which a few zones only are formed belong especially to the province of diffraction.

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  • - A very general problem in diffraction is the investigation of the distribution of light over a screen upon which impinge divergent or convergent spherical waves after passage through various diffracting apertures.

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  • A diminution of X thus leads to a simple proportional shrinkage of the diffraction pattern, attended by an augmentation of brilliancy in proportion to A-2.

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  • The linear dimension of the diffraction pattern is inversely as that of the aperture, and the brightness at corresponding points is as the square of the area of aperture.

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  • If the aperture and wave-length increase in the same proportion, the size and shape of the diffraction pattern undergo no change.

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  • If the aperture be increased, not only is the total brightness over the focal plane increased with it, but there is also a concentration of the diffraction pattern.

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  • The contraction of the diffraction pattern with increase of aperture is of fundamental importance in connexion with the resolving power of optical instruments.

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  • According to common optics, where images are absolute, the diffraction pattern is supposed to be infinitely small, and two radiant points, however near together, form separated images.

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  • If the image of the line be =o, the intensity at any point E, n of the diffraction pattern may be represented by ?2a2t2 S A2f2 the same law as obtains for a luminous point when horizontal directions are alone considered.

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  • Since A' is in some sense the area of the diffraction pattern, it may be considered to be a rough criterion of the definition, and we infer that the definition of a point depends principally upon the area of the aperture, and only in a very secondary degree upon the shape when the area is maintained constant.

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  • Trans., 1834) in his original investigation of the diffraction of a circular object-glass, and readily obtained from (6), is z z 3 25 27 J1(z) = 2 2 2.4 + 2 2.4 2.6 2 2.4 2.6 2.8 + When z is great, we may employ the semi-convergent series Ji(s) = A/ (7, .- z)sin (z-17r) 1+3 8 1 ' 6 (z) 2 3.5.7.9.1.3.5 5 () 3 1 3.5.7.1 1 3 cos(z - ?r) 8 ' z (z) 3.5.7.9.11.1.3.5.7 1 5 + 8.16.24.32.40 (z

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  • In these expressions we are to replace p by ks/f, or rather, since the diffraction pattern is symmetrical, by kr/f, where r is the distance of any point in the focal plane from the centre of the system.

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  • The first dark ring in the diffraction pattern of the complete circular aperture occurs when r/f = 1.2197 XO /2R (15).

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  • If the angular interval between the components of a double star were equal to twice that expressed in equation (15) above, the central disks of the diffraction patterns would be just in contact.

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  • B is in fact the centre of the diffraction disk which constitutes the image of A. ??

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  • The results of the theory of the diffraction patterns due to circular apertures admit of an interesting application to coronas, such as are often seen encircling the sun and moon.

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  • The diffraction pattern is therefore that due to a single aperture, merely brightened n times.

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  • Diffraction Gratings.

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  • By supposing the retardation to vary uniformly and continuously we, fall upon the case of an ordinary prism: but there;, is then no diffraction spectrum in the usual sense.

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  • when the grating is so situated that the angles of incidence and diffraction are equal.

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  • Diffraction when the Source of Light is not seen in Focus.

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  • In observing the bands he received them at first upon a screen of finely ground glass, upon which a magnifying lens was focused; but it soon appeared that the ground glass could be dispensed with, the diffraction pattern being viewed in the same way as the image formed by the object-glass of a telescope is viewed through the eye-piece.

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  • When the functions C and S have once been calculated, the discussion of various diffraction problems is much facilitated by the idea, due to M.

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  • In applying the curve in special cases of diffraction to exhibit the effect at any point P (fig.

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  • Let us reconsider, following Cornu, the diffraction of a screen unlimited on one side, and on the other terminated by a straight edge.

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  • Dynamical Theory of Diffraction.

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  • - The explanation of diffraction phenomena given by Fresnel and his followers is 1 H.

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  • This question was treated by Stokes in his " Dynamical Theory of Diffraction " (Camb.

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  • If the direction of primary vibration be perpendicular to the plane of diffraction (containing both primary and secondary rays), sin 4, = I; but, if the primary vibration be in the plane of diffraction, sin 4, =cos 0.

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  • On the electromagnetic theory, the problem of diffraction becomes definite when the properties of the obstacle are laid down.

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  • Experiments may be made with plane and curved mirrors to verify these laws, but it is necessary to use short waves, in order to diminish diffraction effects.

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  • Diffraction of Soitnd Waves.

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  • Many of the well-known phenomena of optical diffraction may be imitated with sound waves, especially if the waves be short.

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  • We shall only consider one interesting case of sound diffraction which may be easily observed.

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  • It has in fact been found, with the very great precision of which optical experiment is capable, that all terrestrial optical phenomenareflexion, refraction, polarization linear and circular, diffraction - are entirely unaffected by the direction of the earth's motion, while the same result has recently been extended to electrostatic forces; and this is our main experimental clue.

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  • In September 1839 a 3-foot speculum was finished and mounted on an altazimuth stand similar to Herschel's; but, though the definition of the images was good (except that the diffraction at the joints of the speculum caused minute rays in the case of a very bright star), and its peculiar skeleton form allowed the speculum to follow atmospheric changes of temperature very quickly, Lord Rosse decided to cast a solid 3-foot speculum.

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  • Heaviside); the diffraction of light (E.

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  • If we compare the spectrum produced by refraction in a glass prism with that of a diffraction grating, we find not only that the order of colours is reversed, but also that the same colours do not occupy corresponding lengths on the two spectra, the blue and violet being much more extended in the refraction spectrum.

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  • In a diffraction spectrum the diffraction is proportional to the wavelength, and the spectrum is said to be "normal."

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  • By introducing the concave grating which (see Diffraction Of Light, § 8) allows US to dispense with all lenses, Rowland produced a revolution in spectroscopic measurement.

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  • The so-called " diffraction " image of a homogeneously illuminated slit shows a central band limited on either side by a line along which the ' Michelson, Astrophys.

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  • intensity is zero, and this band is accompanied by a number of fainter images corresponding to the diffraction of a star image in a telescope.

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  • Lord Rayleigh, to whom we owe the first general discussion of the theory of the spectroscope, found by observation that if two spectroscopic lines of frequencies n1 and n, are observed in an instrument, they are just seen as two separate lines when the centre of the central diffraction band of one coincides with the first minimum intensity of the other.

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  • Lord Rayleigh's expression for the resolving power of different instruments is based on the assumption that the geometrical image of the slit is narrow compared with the width of the diffraction image.

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  • When the slit is narrow light is lost through diffraction unless the angular aperture of this condensing lens, as viewed from the slit, is considerably greater than that of the collimator lens.

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  • From the measured distances of the diffraction bands the width of the slit may be easily deduced.

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  • - Spectroscopes may be divided into two classes: prism spectroscopes, with angular or direct vision, and grating spectroscopes; the former acting by refraction (q.v.), the latter by diffraction or interference.

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  • Halos are at definite distances (22° and 46 °) from the sun, and are coloured red on the inside, being due to refraction; coronae closely surround the sun at variable distances, and are coloured red on the outside, being due to diffraction.

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  • Formerly classified by the ancient Greeks with halos, rainbows, &c., under the general group of "meteors," they came to receive considerable attention at the hands of Descartes, Christiaan Huygens, and Sir Isaac Newton; but the correct explanation of coronae was reserved until the beginning of the 19th century, when Thomas Young applied the theories of the diffraction and interference of light to this phenomenon.

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  • It has now been firmly established, both experimentally and mathematically, that coronae are due to diffraction by the minute particles of moisture and dust suspended in the atmosphere, and the radii of the rings depend on the size of the diffracting particles.

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  • (See Diffraction Of Light.) Other meteorological phenomena caused by the diffraction of light include the anthelia, and the chromatic rings seen encircling shadows thrown on a bank of clouds, mist or fog.

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  • Krakatoa), are also explicable by the diffraction of light.

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  • But a deviation, termed diffraction, does occur, and consequently the complete theory of shadows involves considerations based on the nature of the rays themselves; this aspect is treated in Diffraction Of Light.

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  • The fourth essay is a systematic treatment of the nature of colour, with a description of many curious experiments and a discussion of the rainbow, halos, parhelia, diffraction, and the more purely physiological phenomena of colour.

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  • The chromatic halos which frequently encircle these images are due to diffraction.

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  • In 1818 he read a memoir on diffraction for which in the ensuing year he received the prize of the Academie des Sciences at Paris.

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  • By the use of two plane mirrors of metal, forming with each other an angle of nearly 180°, he avoided the diffraction caused in.

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  • In 1882, before the Physical Society of London, he gave a description of the diffraction gratings with which his name is specially associated, and which have been of enormous advantage to astronomical spectroscopy.

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  • In addition to the above facts of polarization mention may be made of the partial polarization, in a plane perpendicular to that of emission, of the light emitted in an oblique direction from a white-hot solid, and of the polarization produced by diffraction.

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  • Gouy has studied the more simple case of diffraction at a straight' edge.

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  • According to Huygens's principle (see Diffraction) each aether particle, set vibrating by an incident wave, can itself act as a new centre of excitement, emitting a spherical wave; and similarly each particle on this wave itself produces wave systems. All systems which are emitted from a single source can by a suitable optical device be directed that they simultaneously influence one and the same aether particle.

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  • Abbe applied the Fraunhofer diffraction phenomena to the explanation of the representation in the microscope of uniformly illuminated objects.

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  • If a grating is placed as object before the microscope objective, Abbe showed that in the image there is intermittent clear and dark banding only, if at least two consecutive diffraction spectra enter into the objective and contribute towards the image.

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  • If in this case the aperture of the objective be so small, or the diffraction spectra lie so far from each other, that only the pencil parallel to the axis, i.e.

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  • The resemblance is greater the more diffraction spectra enter the objective.

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  • From the Fraunhofer formula I =X/n sin a one can immediately deduce the limit to the diffraction constant I, so that the banding by an objective of fixed numerical aperture can be perceived.

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  • All details of the object so resolved are perceived, if two diffraction maxima can be passed through the objective, so that the character of the object is seen in the image, even if an exact resemblance has not yet been attained.

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  • The Fraunhofer diffraction phenomena, which take place in the 0 FIG.

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  • 20) and to the right and left the diffraction spectra, the images of different colours partially overlapping.

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  • If a resolvable grating is considered, the diffraction phenomenon has the appearance shown in fig.

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  • If the obliquity of illumination be so great that the principal maximum passes through the outermost edge of the objective, while a spectrum of 1st order passes the opposite edge, so that in the back focal plane the diffraction phenomenon shown in fig.

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  • 13, we suppose that a diffracting particle of such fineness is placed at 0 that the diffracted pencils of the 1st order make an angle w with the axis; the principal maximum of the Fraunhofer diffraction phenomena lies in F' 1; and the two diffraction maxima of the 1st order in P' and P' 1.

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  • Abbe showed that for the production of an image the diffraction maxima must lie within the exit pupil of the objective.

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  • If this object be viewed by the objective, so that at least the diffraction spectra of 1st order pass the finer divisions, then the corresponding diffraction phenomenon in the back focal plane of the objective has the appearance shown in fig.

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  • 21, while the diffraction figure corresponding to the coarser ruling appears as given in fig.

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  • If one cuts out by a diaphragm in the back focal plane of the objective all diffraction spectra except the principal maximum, one sees in the image a field divided into two halves, which show with different clearness, but no banding.

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  • If now the spectrum of Est order of the larger division be cut out from the diffraction figure, as is shown in fig.

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  • Still more strikingly is this phenomenon shown by Abbe's diffraction plate (fig.

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  • At least two successive diffraction maxima must be admitted through the objective for there to be any image of the objects.

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  • The image consists of a diffraction disk from whose form and size certain conclusions may be drawn as to the size and form of the object.

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  • Too much light is useless for observing delicately coloured or colourless preparations, whose parts only become visible as a result of slight differences of diffraction.

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  • The chief cone of rays then enters obliquely into the objective, the angle between the direct cone of rays and the diffraction spectrum of the first order can then become as large again as with direct lighting, and still be taken up in the objective.

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  • As was seen when discussing the physical theory, the minute details of the object cause diffractions, and can only be examined if the objective can take up at least two consecutive diffraction spectra.

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  • These diffracting details become especially distinct if the direct lighting cone of rays, the spectrum of zero:order or the chief maximum, is not allowed to enter the objective and instead only two or more diffraction maxima are taken up; the details then appear bright on a dark background.

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  • The MBE system features reflection high-energy electron diffraction (RHEED) that can be carried out during growth.

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  • Synchrotron X-ray powder diffraction and computational investigation of purely siliceous zeolite Y under pressure.

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  • Polytype coalescence in Lely vapor grown silicon carbide (SiC) has been studied extensively using the technique of X-Ray Diffraction (XRD).

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  • Figure 8. A good example of a highly disordered silicon carbide crystal shown by the extensive streaking evident along the diffraction rows.

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  • Sophisticated mathematical techniques are then used to analyze the diffraction pattern.

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  • Software tools are available for calculating diffraction spectra for specified crystal structures.

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  • The second section delves into the techniques and theory behind the applications such as specular X-ray reflectivity, diffraction imaging and defect mapping.

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  • The predictions have been validated against detailed synchrotron diffraction data.

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  • I am analyzing synchrotron x-ray diffraction patterns and to work out the diffractometer constants I refined a silicon pattern.

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  • Harford, J.J. & Squire, J.M. (1997) Time-resolved diffraction studies of muscle using synchrotron radiation.

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  • X-ray diffraction studies show it has the expected trigonal bipyramidal structure in the solid state.

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  • Keywords: Crystallography, X-ray, Powder diffraction, Crystal structure, Unit cell, Bragg reflections, Lattice parameters.

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  • Diffraction spikes on a reflector 's star images, caused by its secondary mirror spider vanes, are absent in an unobstructed refractor.

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  • Determination of crystal structures by interpretation of x-ray diffraction patterns.

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  • For x-ray diffraction studies on material composition and crystal structure, or for contact radiography.

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  • The Crystallography Center at NUI, Galway is dedicated to the determination of molecular structure by x-ray diffraction techniques.

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  • To fully understand the concepts and functions of the programs, the user should be familiar with surface x-ray diffraction, eg.

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