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aberration

She is normally calm and level headed, so this outburst is an aberration.

16882The discovery of the aberration of light in 1725, due to James Bradley, is one of the most important in the whole domain of astronomy.

13079We considered our defeat to be an aberration, since we'd easily beaten this team last season.

8145It has been in the past a source of much perplexity to observers of transits, but is now understood to be a result of irradiation, produced by the atmosphere or by the aberration of the telescope.

6171The chromatic aberration of the object-glass of one of these telescopes is corrected for photographic rays, and the image formed by it is received on a highly sensitive photographic plate.

6059The aberration is here unsymmetrical, the wave being in advance of its proper place in one half of the aperture, but behind in the other half.

5252The residents considered the recent surge in burglaries to be an aberration, since their neighborhood was known for its safety.

4034When parallel rays fall directly upon a spherical mirror the longitudinal aberration is only about one-eighth as great as for the most favourably shaped single lens of equal focal length and aperture.

3845The indirect method is based upon the observed constant of aberration or the displacement of the stars due to the earth's motion.

3637The indirect method is based upon the observed constant of aberration or the displacement of the stars due to the earth's motion.

3637The swing to the right in the voter survey were considered to be a short-term aberration and of no consequence to the election.

3335Hence for the rain to centrally traverse the tube, this must be inclined at an angle BAD to the vertical; this angle is conveniently termed the aberration due to these two motions.

2938Both the aberration of axis points, and the deviation from the sine condition, rapidly increase in most (uncorrected) systems with the aperture.

2938Bradley recognized the fact that the experimental determination of the aberration constant gave the ratio of the velocities of light and of the earth; hence, if the velocity of the earth be known, the velocity of light is determined.

2440Bradley recognized the fact that the experimental determination of the aberration constant gave the ratio of the velocities of light and of the earth; hence, if the velocity of the earth be known, the velocity of light is determined.

2440Assured that his explanation was true, Bradley corrected his observations for aberration, but he found that there still remained a residuum which was evidently not a parallax, for it did not exhibit an annual cycle.

2335the spherical aberration of an object-glass.

31If the surrounding aether is thereby disturbed, the waves of light arriving from the stars will partake of its movement; the ascertained phenomena of the astronomical aberration of light show that the rays travel to the observer, across this disturbed aether near the earth, in straight lines.

10Not very long after the disappearance of serfdom in the most advanced communities comes into sight the new system of colonial slavery, which, instead of being the spontaneous outgrowth of social necessities and subserving a temporary need of human development, was politically as well as morally a monstrous aberration.

11Since then, two elaborate series of observations made with the zenith telescope for the purpose of determining the variation of latitude and the constant of aberration have been carried on by Professor C. L.

11Thus in estimating the intensity at a focal point, where, in the absence of aberration, all the secondary waves would have exactly the same phase, we see that an aberration nowhere exceeding 4X can have but little effect.

12focus might have an aperture of 22 in., and the image would not suffer materially from aberration.

12If "=4), the term of the first order vanishes, and the reduction of the difference of path via P and via A to a term of the fourth order proves not only that Q and Q' are conjugate foci, but also that the foci are exempt from the most important term in the aberration.

12For a single lens of very small thickness and given power, the aberration depends upon the ratio of the radii r: r', and is a minimum (but never zero) for a certain value of this ratio; it varies inversely with the refractive index (the power of the lens remaining constant).

12In general, we may say that aberration is unimportant when it nowhere (or at any rate over a relatively small area only) exceeds a small fraction of the wavelength (X).

13Its original use was the determination of geographical latitudes in the field work of geodetic operations; more recently it has been extensively employed for the determination S of variation of latitude, at fixed stations, under the auspices of the International Geodetic Bureau, and for the astronomical determination of the constant of aberration.

001828), professor of practical astronomy at Edinburgh University, to characterize a superior achromatism, and, subsequently, by many writers to denote freedom from spherical aberration.

00It requires the middle of the aperture stop to be reproduced in the centres of the entrance and exit pupils without spherical aberration.

00The aberrations of the third order are: (1) aberration of the axis point; (2) aberration of points whose distance from the Aberra- axis is very small, less than of the third order - the tions of deviation from the sine condition and coma here fall together in one class; (3) astigmatism; (4) curvature of the field; (5) distortion.

00(1) Aberration of the third order of axis points is dealt with in all text-books on optics.

00The total aberration of two or more very thin lenses in contact, being the sum of the individual aberrations, can be zero.

00Of thin positive lenses with n= 1-5, four are necessary to correct spherical aberration of the third order.

00In most cases, two thin lenses are combined, one of which has just so strong a positive aberration (" under-correction," vide supra) as the other a negative; the first must be a positive lens and the second a negative lens; the powers, however, may differ, so that the desired effect of the lens is maintained.

00By one, and likewise by several, and even by an infinite number of thin lenses in contact, no more than two axis points can be reproduced without aberration of the third order.

00Freedom from aberration for two axis points, one of which is infinitely distant, is known as " Herschel's condition."

00In order to render spherical aberration and the deviation from the sine condition small throughout the whole aperture, there is given to a ray with a finite angle of aperture u* (with infinitely distant objects: with a finite height of incidence the same distance of intersection, and the same sine ratio as to one neighbouring the axis (u* or h* may not be much smaller than the largest aperture U or H to be used in the system).

00Spherical aberration and changes of the sine ratios are often represented graphically as functions of the aperture, in the same way as the deviations of two astigmatic image surfaces of the image plane of the axis point are represented as functions of the angles of the field of view.

00(b) Chromatic or Colour Aberration.

00white light) all these images are formed; and since they are all ultimately intercepted by a plane (the retina of the eye, a focussing screen of a camera, &c.), they cause a confusion, named chromatic aberration; for instance, instead of a white margin on a dark background, there is perceived a coloured margin, or narrow spectrum.

00In a plane containing the image point of one colour, another colour produces a disk of confusion; this is similar to the confusion caused by two " zones " in spherical aberration.

00For infinitely distant objects the radius of the chromatic disk of confusion is proportional to the linear aperture, and independent of the focal length (vide supra," Monochromatic Aberration of the Axis Point "); and since this disk becomes the less harmful with an increasing image of a given object, or with increasing focal length, it follows that the deterioration of the image is proportional to the ratio of the aperture to the focal length, i.e.

00Two other conditions may also be postulated: one is always the elimination of the aberration on the axis; the second either the " Herschel " or " Fraunhofer condition," the latter being the best (vide supra, " Monochromatic Aberration ").

00The most important is the chromatic difference of aberration of the axis point, which is still present to disturb the image, after par-axial rays of different colours are united by an appropriate combination of glasses.

00It increases rapidly with the aperture, and is more important with medium apertures than the secondary spectrum of par-axial rays; consequently, spherical aberration must be eliminated for two colours, and if this be impossible, then it must be eliminated for those particular wave-lengths which are most effectual for the instrument in question (a graphical representation of this error is given in M.

00His researches in optics, continued until his death, appear to have been begun about the year 1814, when he prepared a paper on the aberration of light, which, however, was not published.

00the equation of light, the constant of aberration, and the parallactic inequality of the moon; the value of the velocity of propagation of light enters in the reduction of the two first, but as this is better known than the sun's parallax, no disadvantage results.

00The constant of aberration introduces the sun's distance by a comparison between the velocity of the earth in its orbit and the velocity of light.

00His memorable discovery of the aberration of light (see Aberration) was communicated to the Royal Society in January 1729 (Phil.

00Orthodox evangelicalism is tempted to view it as an apostasy or an aberration.

00This implies that the whole of Western theology has been an aberration or an exoteric veiling of the truth.'

00James Bradley discovered in 1728 the annual shifting of the stars due to the aberration of light, and in 1748, the complicating effects upon precession of the "nutation" of the earth's axis.

00Again, since the constant of aberration defines the ratio between the velocity of light and the earth's orbital speed, the span of the terrestrial circuit, in other words, the distance of the sun, is immediately deducible from known values of the first two quantities.

00The spherical aberration of a diamond lens can be brought down to one-ninth of a glass lens of equal focus.

00With this mineral also spherical and chromatic aberration are a fraction of that of a glass lens, but double refraction, which involves a doubling of the image, is fatal to its use.

00When well made such constructions are almost free from spherical aberration, and the chromatic errors are very small.

00Axial aberration is reduced by distributing the refraction between two lenses; and by placing the two lenses farther apart the errors of the pencils of rays proceeding from points lying outside the axis are reduced.

00As shown in Lens and Aberration, for reproduction through a single lens with spherical surfaces, a combination of the rays is only possible for an extremely small angular aperture.

00The aberration of rays in which the outer rays intersect the axis at a shorter distance than the central rays is known as " undercorrection."

00Correction of the spherical aberration in strong systems with very large aperture can not be brought about by means of a single combination of two lenses, but several partial systems are necessary.

00If, by these methods, a point in the optic axis has been freed from aberration, it does not follow that a point situated only a very small distance from the optic axis can also be represented without spherical aberration.

00The representation, free from aberration, of a small surface-element, is only possible, as Abbe has shown, if the objective simultaneously fulfils the " sine-condition," i.e.

00The removal of the spherical aberration and the sine-condition can be accomplished only for two conjugate points.

00A second method of correcting the spherical aberration depends FIG.

00- Showing a system with chromatic difference of spherical aberration.

00By using these glasses and employing minerals with special optical properties, it is possible to correct objectives so that three colours can be combined, leaving only a quite slight tertiary spectrum, and removing the spherical aberration for two colours.

00A further aberration which can only be overcome with difficulty, and even then only partially, is the " curvature of the field, " i.e.

00A second method for diminishing the spherical aberration was to alter the distances of the single systems, a method still used.

00The lower surface of the slip causes undercorrection on being traversed by the pencil, with over-correction when it leaves it; and since the aberration of the surface lying farthest from the object, i.e.

00In order to counteract this aberration the whole objective must be correspondingly under-corrected.

00In the apochromats the chromatic difference of the spherical aberrations is eliminated, for the spherical aberration is completely avoided for three colours.

00The definition is better according as the chromatic and spherical aberrations are removed; there always remains in even the best constructions some slight aberration.

00In consequence of these residual aberrations, every object-point is not reproduced in an ideal image-point, but as a small circle of aberration.

00Object details will only be well seen if the aberration circles are small in comparison.

00In the case of a suitable ocular magnification, the details will be well seen, while the aberration circles remain invisible.

00Two ED glass elements minimize chromatic aberration in the entire zoom range while ensuring high resolution and contrast.

00A lens system comprising two elements, used to reduce chromatic aberration.

00I also looked into the immense size of chromatic aberration in the human eye.

00The image, despite the spherical aberration, was by far superior to any existing microscope made by his contemporaries.

00A further 10% arising as a result of a parental translocation and the remainder arise as a result of an unusual cytogenetic aberration.

00The transformation from apparent to topocentric consists of allowing for diurnal aberration.

00I knew the cause to be lateral chromatic aberration.

00aberration assays were likely to represent a cytotoxic response.

00The annual aberration is the aberration correction for an imaginary observer at the Earth's center.

00Three SLD glass elements are employed for effective compensation of color aberration, which is a common problem with super-wide angle lenses.

00The problem with many low priced cameras, is color aberration in the final image.

00Overall, the COM concluded that the results from the in vitro chromosomal aberration assays were likely to represent a cytotoxic response.

00chromatic aberration in the human eye.

00chromatic aberration of magnification, which is a critical problem for digital imaging.

00chromatic aberration of the fish lens.

00Two ED glass elements minimize chromatic aberration in the entire zoom range while ensuring high resolution and contrast.

00A lens system comprising two elements, used to reduce chromatic aberration.

00The use of mirrors instead of lenses was another way to avoid chromatic aberration.

00Newton was led by this reasoning to the erroneous conclusion that telescopes using refracting lenses would always suffer chromatic aberration.

00chromatic aberration at 60x magnification on the base model ES 80 GA SD is a real breakthrough.

00I knew the cause to be lateral chromatic aberration.

00The reduction of almost all visible chromatic aberration at 60x magnification on the base model ES 80 GA SD is a real breakthrough.

00The spherical aberration correction is in this region too.

00diffraction spikes, many people are used to seeing them and don't consider them an aberration.

00diurnal aberration.

00eld glass elements reduce chromatic aberration to a minimum and also ensure sharp, quality images of high contrast.

00Rudolf guides Santa's sleigh with the biological aberration of a red, glowing nose capable of penetrating thick fog?

00madmantraditional response of the state to racist murders such as this is to describe them as an aberration, perpetrated by evil madmen.

00minimize chromatic aberration in the entire zoom range while ensuring high resolution and contrast.

00refracting lenses would always suffer chromatic aberration.

00If you are using an achromatic refractor, the focus errors will be larger due to chromatic aberration of the telescope.

00spherical aberration, was by far superior to any existing microscope made by his contemporaries.

00I realize that this extends the tube length and will cause some spherical aberration.

00It incorporates aspherical lens elements in the front, as well as rear lens groups, to correct spherical aberration.

00Its design employs three (3) aspherical lens elements to minimize spherical aberration, astigmatism and sagittal comma flare.

00Because almost all reflecting telescopes produce diffraction spikes, many people are used to seeing them and don't consider them an aberration.

00peculiarities of the skeleton or portions of the skeleton of certain birds - one of the most remarkable of which is that on the component parts of the foot (pp. tot - toy) pointing out the aberration from the ordinary structure exhibited by the Goatsucker (Caprimulgus) and the Swift (Cypselus) - an aberration which, if rightly understood, would have conveyed a warning to those ornithological systematists who put their trust in birds' toes for characters on which to.

00Not very long after the disappearance of serfdom in the most advanced communities comes into sight the new system of colonial slavery, which, instead of being the spontaneous outgrowth of social necessities and subserving a temporary need of human development, was politically as well as morally a monstrous aberration.

00But the difficulties interposed by spherical and chromatic aberration had arrested progress in that direction until, in 1655, Huygens, working with his brother Constantijn, hit upon a new method of grinding and polishing lenses.

00Since then, two elaborate series of observations made with the zenith telescope for the purpose of determining the variation of latitude and the constant of aberration have been carried on by Professor C. L.

00In addition to the doubt thrown on this result by the discrepancy between various determinations of the constant of aberration, it is sometimes doubted whether the latter constant necessarily expresses with entire precision the ratio of the velocity of the earth to the velocity of light.

00In Bode's Jahrbuch (1776-1780) he discusses nutation, aberration of light, Saturn's rings and comets; in the Nova acta Helvetica (1787) he has a long paper "Sur le son des corps elastiques," in Bernoulli and Hindenburg's Magazin (1787-1788) he treats of the roots of equation and of parallel lines; and in Hindenburg's Archiv (1798-1799) he writes on optics and perspective.

00This expression for the intensity becomes rigorously applicable when f is indefinitely great, so that ordinary optical aberration disappears.

00In telescopes of the best construction and of moderate aperture the performance is not sensibly prejudiced by outstanding aberration, and the limit imposed by the finiteness of the waves of light is practically reached.

00Our investigations and estimates of resolving power have thus far proceeded upon the supposition that there are no optical imperfections, whether of the nature of,, a regular aberration or dependent upon irregularities of material and workmanship. In practice there will always be a certain aberration or error of phase, which we may also regard as the deviation of the actual wavesurface from its intended position.

00In general, we may say that aberration is unimportant when it nowhere (or at any rate over a relatively small area only) exceeds a small fraction of the wavelength (X).

00Thus in estimating the intensity at a focal point, where, in the absence of aberration, all the secondary waves would have exactly the same phase, we see that an aberration nowhere exceeding 4X can have but little effect.

00The only case in which the influence of small aberration upon the entire image has been calculated (Phil.

00Mag., 1879) is that of a rectangular aperture, traversed by a cylindrical wave with aberration equal to cx 3 .

00The aberration is here unsymmetrical, the wave being in advance of its proper place in one half of the aperture, but behind in the other half.

00The effect of aberration may be considered in two ways.

00We may suppose the aperture (a) constant, and inquire into the operation of an increasing aberration; or we may take a given value of c (i.e.

00The results in the second case show that an increase of aperture up to that corresponding to an extreme aberration of half a period has no ill effect upon the central band (§ 3), but it increases unduly the intensity of one of the neighbouring lateral bands; and the practical conclusion is that the best results will be obtained from an aperture giving an extreme aberration of from a quarter to half a period, and that with an increased aperture aberration is not so much a direct cause of deterioration as an obstacle to the attainment of that improved definition which should accompany the increase of aperture.

00If, on the other hand, we suppose the aperture given, we find that aberration begins to be distinctly mischievous when it amounts to about a quarter period, i.e.

00Another obvious inference from the necessary imperfection of optical images is the uselessness of attempting anything like an absolute destruction of spherical aberration.

00If we inquire what is the greatest admissible longitudinal aberration (Sf) in an object-glass according to the above rule, we find Sf =Xa 2 (2), a being the angular semi-aperture.

00When parallel rays fall directly upon a spherical mirror the longitudinal aberration is only about one-eighth as great as for the most favourably shaped single lens of equal focal length and aperture.

00focus might have an aperture of 22 in., and the image would not suffer materially from aberration.

00If Q be on the circle described upon OA as diameter, so that u = a cos 4,, then Q' lies also upon the same circle; and in this case it follows from the symmetry that the unsymmetrical aberration (depending upon a) vanishes.

00If "=4), the term of the first order vanishes, and the reduction of the difference of path via P and via A to a term of the fourth order proves not only that Q and Q' are conjugate foci, but also that the foci are exempt from the most important term in the aberration.

00They are here focused (so far as the rays in the primary plane are concerned) upon the circle OQ' A, and the outstanding aberration is of the fourth order.

00If it were desired to use an angular aperture so large that the aberration according to (13) would be injurious, Rowland points out that on his machine there would be no difficulty in applying a remedy by making v slightly variable towards the edges.

00The absence of chromatic aberration gives a great advantage in the comparison of overlapping spectra, which Rowland has turned to excellent account in his determinations of the relative wavelengths of lines in the solar spectrum (Phil.

00During the 19th century, the hesitation about Colossians led to the rejection of Philemon by some critics as a pseudonymous little pamphlet on the slave question - an aberration of literary criticism (reproduced in Ency.

00Refraction and Dispersion.-The purely optical properties of refraction and dispersion, although of the greatest importance, cannot be dealt with in any detail here; for an account of the optical properties required in glasses for various forms of lenses see the articles Lens and Aberration: Ii.

00This Makuzu faience, produced by the now justly celebrated Miyagawa ShOzan of Ota (near Yokohama), survives in the form of vases and pots having birds, reptiles, flowers, crustacea and so forth plastered over the surfacespecimens that disgrace the period of their manufacture, and represent probably the worst aberration of Japanese ceramic conception.

00It has been in the past a source of much perplexity to observers of transits, but is now understood to be a result of irradiation, produced by the atmosphere or by the aberration of the telescope.

00If the surrounding aether is thereby disturbed, the waves of light arriving from the stars will partake of its movement; the ascertained phenomena of the astronomical aberration of light show that the rays travel to the observer, across this disturbed aether near the earth, in straight lines.

00If the path is to be unaltered by the motion of the aether, as the law of astronomical aberration suggests, this must differ from fds/V by terms not depending on the path - that is, by terms involving only the beginning and end of it.

00But the aether at a great distance must in any case be at rest; while the facts of astronomical aberration require that the motion of that medium must be irrotational.

00Lodge, " On Aberration Problems," Phil.

00He concluded that there could be no refraction without dispersion, and hence that achromatism was impossible of attainment (see Aberration).

00At Pulkowa he redetermined the " constant of aberration...

00ABERRATION (Lat.

00In optics, the word has two special applications: (1) Aberration of Light, and (2) Aberration in Optical Systems. These subjects receive treatment below.

00Aberration Of Light This astronomical phenomenon may be defined as an apparent motion of the heavenly bodies; the stars describing annually orbits more or less elliptical, according to the latitude of the star; consequently at any moment the star appears to be displaced from its true position.

00Hence for the rain to centrally traverse the tube, this must be inclined at an angle BAD to the vertical; this angle is conveniently termed the aberration due to these two motions.

00The discovery of the aberration of light in 1725, due to James Bradley, is one of the most important in the whole domain of astronomy.

00The application of this observation to the phenomenon which had so long perplexed him was not difficult, and, in 1727, he published his theory of the aberration of light - a corner-stone of the edifice of astronomical science.

00When the earth is at A, in consequence of aberration, the star is displaced to a point a, its displacement sa being parallel to the earth's motion at A; when the earth is at B, the star appears at b; and so on throughout an orbital revolution of the earth.

00This constant length subtends an angle of about 40" at the earth; the " constant of aberration " is half this angle.

00Assured that his explanation was true, Bradley corrected his observations for aberration, but he found that there still remained a residuum which was evidently not a parallax, for it did not exhibit an annual cycle.

00Aberration in Optical Systems >>

00James Gregory, in his Optica Promota (1663), discusses the forms of images and objects produced by lenses and mirrors, and shows that when the surfaces of the lenses or mirrors are portions of spheres the images are curves concave towards the objective, but if the curves of the surfaces are conic sections the spherical aberration is corrected.

00He did not attempt the formation of a parabolic figure on account of the probable mechanical difficulties, and he had besides satisfied himself that the chromatic and not the spherical aberration formed the chief faults of previous telescopes.

00in the refractive qualities of different kinds of glass with respect to their divergency of colours,"and was thus rapidly led to the construction of object-glasses in which first the chromatic and afterwards the spherical aberration were corrected (Phil.

00in diameter when viewing faint objects, we obtain the rule that the minimum magnifying power which can be efficiently employed is five times the diameter of the object-glass expressed in inches.`'- The defects of the Galilean and Kepler telescopes are due to the chromatic and spherical aberration of the simple lenses of which they are composed.

00When all is taken into consideration it is scarcely possible to reduce the secondary colour aberration at the focus of such a double object-glass to less than a fourth part of that prevailing at the focus of a double objective of the same aperture and focus, but made of the ordinary crown and flint glasses.

00For relatively short focal lengths a triple construction such as this is almost necessary in order to obtain an objective free from aberration of the 3rd order, and it might be thought at first that, given the closest attainable degree of rationality between the colour dispersions of the two glasses employed, which we will call crown and flint, it would be impossible to devise another form of triple objective, by retaining the same flint glass, but adopting two sorts of crown instead of only one, which would have its secondary spectrum very much further reduced.

00The extension of the image away from the axis or size of field available for covering a photographic plate with fair definition is a function in the first place of the ratio between focal length and aperture, the longer focus having the greater relative or angular covering power, and in the second a function of the curvatures of the lenses, in the sense that the objective must be free from coma at the foci of oblique pencils or must fulfil the sine condition (see Aberration).

00The chromatic aberration of the object-glass of one of these telescopes is corrected for photographic rays, and the image formed by it is received on a highly sensitive photographic plate.

00Its original use was the determination of geographical latitudes in the field work of geodetic operations; more recently it has been extensively employed for the determination S of variation of latitude, at fixed stations, under the auspices of the International Geodetic Bureau, and for the astronomical determination of the constant of aberration.

00(See LENS, ABERRATION and PHOTOGRAPHY.)

00ABERRATION IN OPTICAL SYSTEMS Aberration in optical systems, i.e.

00in lenses or mirrors or a series of them, may be defined as the non-concurrence of rays from the points of an object after transmission through the system; it happens generally that an image formed by such a system is irregular, and consequently the correction of optical systems for aberration is of fundamental importance to the instrument-maker.

00(a) Monochromatic Aberration.

00A review of the simplest cases of aberration will now be given.

00(I) Aberration of axial points (Spherical aberration in the restricted sense).

00If the angle u l be very small, O', is the Gaussian image; and 0', 0' 2 is termed the " longitudinal aberration," and 0'1R the " lateral aberration " of the pencils with aperture u 2.

00If the pencil with the angle u 2 be that of the maximum aberration of all the pencils transmitted, then in a plane perpendicular to the axis at O' 1 there is a circular " disk of confusion" of radius 0' 1 R, and in a parallel plane at 0'2 another one of radius 0' 2 R 2; between these two is situated the " disk of least confusion."

00The component S 1 of the system, situated between the aperture stop and the object 0, projects an image of the diaphragm, termed by Abbe the " entrance pupil "; the " exit pupil " is the image formed by the component S2 j which is placed behind the aperture stop. All rays which issue from 0 and pass through the aperture stop also pass through the entrance and exit pupils, since these are images of the aperture stop. Since the maximum aperture of the pencils issuing from 0 is the angle u subtended by the entrance pupil at this point, the magnitude of the aberration will be determined by the position and diameter of the entrance pupil.

00(2) Aberration of elements, i.e.

00A system fulfilling this condition and free from spherical aberration is called " aplanatic " (Greek a-, privative, irXavrl, a wandering).

001828), professor of practical astronomy at Edinburgh University, to characterize a superior achromatism, and, subsequently, by many writers to denote freedom from spherical aberration.

00Both the aberration of axis points, and the deviation from the sine condition, rapidly increase in most (uncorrected) systems with the aperture.

00Systems free of this aberration are called " ortho scopic " (ipgos, right, r ' 0-K071-6 1/, to look) .

00This aberration is quite distinct from that of the sharpness of reproduction; in unsharp reproduction, FIG.

00It requires the middle of the aperture stop to be reproduced in the centres of the entrance and exit pupils without spherical aberration.

00The aberrations of the third order are: (1) aberration of the axis point; (2) aberration of points whose distance from the Aberra- axis is very small, less than of the third order - the tions of deviation from the sine condition and coma here fall together in one class; (3) astigmatism; (4) curvature of the field; (5) distortion.

00(1) Aberration of the third order of axis points is dealt with in all text-books on optics.

00For a single lens of very small thickness and given power, the aberration depends upon the ratio of the radii r: r', and is a minimum (but never zero) for a certain value of this ratio; it varies inversely with the refractive index (the power of the lens remaining constant).

00The total aberration of two or more very thin lenses in contact, being the sum of the individual aberrations, can be zero.

00Of thin positive lenses with n= 1-5, four are necessary to correct spherical aberration of the third order.

00In most cases, two thin lenses are combined, one of which has just so strong a positive aberration (" under-correction," vide supra) as the other a negative; the first must be a positive lens and the second a negative lens; the powers, however, may differ, so that the desired effect of the lens is maintained.

00By one, and likewise by several, and even by an infinite number of thin lenses in contact, no more than two axis points can be reproduced without aberration of the third order.

00Freedom from aberration for two axis points, one of which is infinitely distant, is known as " Herschel's condition."

00(4) After eliminating the aberration on the axis, coma and astigmatism, the relation for the flatness of the field in the third order is expressed by the " Petzval equation," I 1 = o, where is the radius of a refracting surface, n and n' the refractive indices of the neighbouring media, and / the sign of summation for all refracting surfaces.

00In order to render spherical aberration and the deviation from the sine condition small throughout the whole aperture, there is given to a ray with a finite angle of aperture u* (with infinitely distant objects: with a finite height of incidence the same distance of intersection, and the same sine ratio as to one neighbouring the axis (u* or h* may not be much smaller than the largest aperture U or H to be used in the system).

00Spherical aberration and changes of the sine ratios are often represented graphically as functions of the aperture, in the same way as the deviations of two astigmatic image surfaces of the image plane of the axis point are represented as functions of the angles of the field of view.

00(b) Chromatic or Colour Aberration.

00In optical systems composed of lenses, the position, magnitude and errors of the image depend upon the refractive indices of the glass employed (see Lens, and above, " Monochromatic Aberration ").

00white light) all these images are formed; and since they are all ultimately intercepted by a plane (the retina of the eye, a focussing screen of a camera, &c.), they cause a confusion, named chromatic aberration; for instance, instead of a white margin on a dark background, there is perceived a coloured margin, or narrow spectrum.

00In practice it is more advantageous (after Abbe) to determine the chromatic aberration (for instance, that of the distance of intersection) for a fixed position of the object, and express it by a sum in which each component contains the amount due to each refracting surface (see Czapski-Eppenstein, op. cit.

00In a plane containing the image point of one colour, another colour produces a disk of confusion; this is similar to the confusion caused by two " zones " in spherical aberration.

00For infinitely distant objects the radius of the chromatic disk of confusion is proportional to the linear aperture, and independent of the focal length (vide supra," Monochromatic Aberration of the Axis Point "); and since this disk becomes the less harmful with an increasing image of a given object, or with increasing focal length, it follows that the deterioration of the image is proportional to the ratio of the aperture to the focal length, i.e.

00Two other conditions may also be postulated: one is always the elimination of the aberration on the axis; the second either the " Herschel " or " Fraunhofer condition," the latter being the best (vide supra, " Monochromatic Aberration ").

00Photog., 1891, 5, p. 225; 18 93, 7, p. 221), cemented objectives of thin lenses permit the elimination of spherical aberration on the axis, if, as above, the collective lens has a smaller refractive index; on the other hand, they permit the elimination of astigmatism and curvature of the field, if the collective lens has a greater refractive index (this follows from the Petzval equation; see L.

00The most important is the chromatic difference of aberration of the axis point, which is still present to disturb the image, after par-axial rays of different colours are united by an appropriate combination of glasses.

00It increases rapidly with the aperture, and is more important with medium apertures than the secondary spectrum of par-axial rays; consequently, spherical aberration must be eliminated for two colours, and if this be impossible, then it must be eliminated for those particular wave-lengths which are most effectual for the instrument in question (a graphical representation of this error is given in M.

00His researches in optics, continued until his death, appear to have been begun about the year 1814, when he prepared a paper on the aberration of light, which, however, was not published.

00the equation of light, the constant of aberration, and the parallactic inequality of the moon; the value of the velocity of propagation of light enters in the reduction of the two first, but as this is better known than the sun's parallax, no disadvantage results.

00The constant of aberration introduces the sun's distance by a comparison between the velocity of the earth in its orbit and the velocity of light.

00His memorable discovery of the aberration of light (see Aberration) was communicated to the Royal Society in January 1729 (Phil.

00Orthodox evangelicalism is tempted to view it as an apostasy or an aberration.

00This implies that the whole of Western theology has been an aberration or an exoteric veiling of the truth.'

00Further, James Bradley discovered in 1728 the annual shifting of the stars due to the aberration of light (see Aberration), and in 1748, the complicating effects upon precession of the " nutation " of the earth's axis.

00Again, since the constant of aberration defines the ratio between the velocity of light and the earth's orbital speed, the span of the terrestrial circuit, in other words, the distance of the sun, is immediately deducible from known values of the first two quantities.

00These are: (I) chromatic aberration, (2) spherical aberration and (3) astigmatism (see Aberration).

00The spherical aberration of a diamond lens can be brought down to one-ninth of a glass lens of equal focus.

00With this mineral also spherical and chromatic aberration are a fraction of that of a glass lens, but double refraction, which involves a doubling of the image, is fatal to its use.

00When well made such constructions are almost free from spherical aberration, and the chromatic errors are very small.

00Axial aberration is reduced by distributing the refraction between two lenses; and by placing the two lenses farther apart the errors of the pencils of rays proceeding from points lying outside the axis are reduced.

00As shown in Lens and Aberration, for reproduction through a single lens with spherical surfaces, a combination of the rays is only possible for an extremely small angular aperture.

00The aberration of rays in which the outer rays intersect the axis at a shorter distance than the central rays is known as " undercorrection."

00Correction of the spherical aberration in strong systems with very large aperture can not be brought about by means of a single combination of two lenses, but several partial systems are necessary.

00If, by these methods, a point in the optic axis has been freed from aberration, it does not follow that a point situated only a very small distance from the optic axis can also be represented without spherical aberration.

00The representation, free from aberration, of a small surface-element, is only possible, as Abbe has shown, if the objective simultaneously fulfils the " sine-condition," i.e.

00The removal of the spherical aberration and the sine-condition can be accomplished only for two conjugate points.

00A second method of correcting the spherical aberration depends FIG.

00The second aberration which must be removed from microscope objectives are the chromatic. To diminish these a collective lens of crown-glass is combined with a dispersing lens of flint; in such a system the red and the blue rays intersect at a point (see Aberration).

00- Showing a system with chromatic difference of spherical aberration.

00By using these glasses and employing minerals with special optical properties, it is possible to correct objectives so that three colours can be combined, leaving only a quite slight tertiary spectrum, and removing the spherical aberration for two colours.

00This aberration can, however, be successfully controlled by a suitable eyepiece (see below).

00A further aberration which can only be overcome with difficulty, and even then only partially, is the " curvature of the field, " i.e.

00A second method for diminishing the spherical aberration was to alter the distances of the single systems, a method still used.

00He used chiefly a highly curved piano-convex front lens, which has since always been employed in strong systems. Even if the object-point on the axis cannot be reproduced quite free from aberration through such a lens, because aberrations of the type of an under-correction have been produced by the first plane outer limiting surface, yet the defects with the strong refraction are relatively small and can be well compensated by other systems. Amici chiefly employed cemented pairs of lenses consisting of a plano-convex flint lens and a biconvex crown lens(fig.

00The lower surface of the slip causes undercorrection on being traversed by the pencil, with over-correction when it leaves it; and since the aberration of the surface lying farthest from the object, i.e.

00In order to counteract this aberration the whole objective must be correspondingly under-corrected.

00In the apochromats the chromatic difference of the spherical aberrations is eliminated, for the spherical aberration is completely avoided for three colours.

00The difference of chromatic magnification cannot even be overcome in apochromats, and to cancel this aberration Abbe devised the compensating ocular (fig.

00The definition is better according as the chromatic and spherical aberrations are removed; there always remains in even the best constructions some slight aberration.

00In consequence of these residual aberrations, every object-point is not reproduced in an ideal image-point, but as a small circle of aberration.

00Object details will only be well seen if the aberration circles are small in comparison.

00In the case of a suitable ocular magnification, the details will be well seen, while the aberration circles remain invisible.

00Chromatic Aberration, where different frequencies of light refract at different angles causing blurred images.

00If you are using an achromatic refractor, the focus errors will be larger due to chromatic aberration of the telescope.

00I realize that this extends the tube length and will cause some spherical aberration.

00It incorporates aspherical lens elements in the front, as well as rear lens groups, to correct spherical aberration.

00Its design employs three (3) aspherical lens elements to minimize spherical aberration, astigmatism and sagittal comma flare.

00For still images, the Nikon D300S has enhanced chromatic aberration editing, which removes color fringing and artifacts before the photo is even downloaded.

00Compared to previous Rebel lenses, the T2i lens has increased sharpness and decreased chromatic aberration.

00I can only hope these recent comments are an aberration or better yet, taken completely out of context..."

00Some polyamorists argue that, since many other cultures embrace the idea of multiple partners, monogamy is an aberration.

00At Pulkowa he redetermined the " constant of aberration...

01Aberration Of Light This astronomical phenomenon may be defined as an apparent motion of the heavenly bodies; the stars describing annually orbits more or less elliptical, according to the latitude of the star; consequently at any moment the star appears to be displaced from its true position.

01The application of this observation to the phenomenon which had so long perplexed him was not difficult, and, in 1727, he published his theory of the aberration of light - a corner-stone of the edifice of astronomical science.

01James Gregory, in his Optica Promota (1663), discusses the forms of images and objects produced by lenses and mirrors, and shows that when the surfaces of the lenses or mirrors are portions of spheres the images are curves concave towards the objective, but if the curves of the surfaces are conic sections the spherical aberration is corrected.

01He did not attempt the formation of a parabolic figure on account of the probable mechanical difficulties, and he had besides satisfied himself that the chromatic and not the spherical aberration formed the chief faults of previous telescopes.

01When all is taken into consideration it is scarcely possible to reduce the secondary colour aberration at the focus of such a double object-glass to less than a fourth part of that prevailing at the focus of a double objective of the same aperture and focus, but made of the ordinary crown and flint glasses.

01(a) Monochromatic Aberration.

01

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