Aberration

“ Spherical aberration is the inability to bring to a focus the rays of light that pass through the lens near the margins at the same time as those that pass through near the center. For these reasons—and, in lesser degree, some others—the eye cannot see sharp lines, and a lens that gives sharp definition to the edges of objects produces results that are esthetically unpleasing, because foreign to our experience. ”

“ If we make crudely the theory of aberration, we reach a very curious result The apparent positions of the stars differ from their real positions because of the earth's motion, and as this motion is variable, these apparent positions vary. The real position we can not ascertain, but we can observe the variations of the apparent position. The observations of the aberration show us, therefore, not the earth's motion, but the variations of this motion; they can not, therefore, give us information about the absolute motion of the earth. ”

“ A lens having a spherical surface bends the rays so that they do not all come to a focus at the same point. What is the effect of this on our theoretically perfect image? Again it is slight blurring of the sharpness of outline. It is said the spherical aberration in a perfectly corrected optician’s lens is less than that in the lens of the human eye. This must be remembered in connection with our later remarks. In the lower animals, spherical aberration is nearly absent. Their vision therefore is more periscopic, and therefore more like that of an optician’s lens. ”

“ The indistinctness of the image is partly due to the obliquity of the pencils which form parts of the image, and partly to what is termed spherical aberration. The first cause cannot be modified by the optician's skill, and is not important when the field of view is small. Spherical aberration causes those parts of a pencil which fall near the boundary of a convex lens to converge to a nearer (i.e. shorter) focus than those which fall near the centre. ”

“ When an object-glass has its aberrations balanced for viewing an opaque object, and it is required to examine that object by transmitted light, the correction will remain; but if it is necessary to immerse the object in a fluid, or to cover it with glass or talc, an aberration will arise from these circumstances, which will disturb the previous correction, and consequently deteriorate the definition; and this effect will be more obvious with the increase of the distance between the object and the object-glass. ”

“ The ordinary aberration can be readily detected with modern astronomical instruments, because it goes through a yearly change in direction or amount; but systematic aberration is constant so long as the planetary system moves uniformly in a sensibly straight line. Only then in the course of ages, when the curvature of the sun’s path becomes apparent, can we hope to verify the existence of this kind of aberration. ”

“ Aplan ́atism (a, not, πλανἁω, to wander) .—The effect of spherical aberration in rendering the image of an object seen through a lens indistinct and misty may now be intelligible. In order that such image may be distinct, the rays emanating from each point of the object must converge at one spot upon the retina. But since, when spherical aberration exists, the marginal rays are more refracted than the central ones, they will meet at foci before those formed by the latter ”

“ This aberration is quite distinct from that of the sharpness of reproduction; in unsharp, reproduction, the question of distortion arises if only parts of the object can be recognized in the figure. If, in an unsharp image, a patch of light corresponds to an object point, the “centre of gravity” of the patch may be regarded as the image point, this being the point where the plane receiving the image, e.g. ”

“ But inasmuch as the telescope or line of vision is inclined at the angle of dispersion to the direction of the incident ray, ordinary aberration must come in, as it always does when an observer moves athwart his line of vision; and so there will be a spurious or apparent Doppler effect due to common aberration. That is to say a spectrum line will not be seen in its true place, but will appear to be shifted by an amount almost exactly imitative of a real Doppler effect—the imitation being correct up to the second order of aberration magnitude. ”

“ Hence actual configurations on the sphere are only changed conformally by the effect of aberration, or in other words any small area is altered only in size and not in shape. We know that aberration merely changes the scale of a photograph of a small part of the sky, and the truth of this fact now becomes independent of the velocity (however large) of the observer. Also stars which appear to lie on a circle at any one time will continue to do so permanently. ”

“ If, 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. when the wave-surface deviates at each end by a quarter wave-length from the true plane. ”

“ What has been proved here for a lens is equally applicable to the cases of reflexion, and refraction at a single surface, as in both of these, the aberration of a ray inclined to the axis varies as the square of the distance of the point of reflexion or refraction from the axis. ”

“ This is called chromatic aberration, because the colored rays do not all converge to the same focus; thus the image seen through them is surrounded by a fringe or border of color.
Single lenses lack the power of producing a straight image of a straight object; the image will have the curve of the lens through which the light passes to form it; a double convex lens will give a greater curve than a plano-convex. This is called spherical aberration. ”

“ Optical Power of Instruments.—Our 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 wave-surface from its intended position. ”

“ Defn: The convergence to different foci, by a lens or mirror, of rays of light emanating from one and the same point, or the deviation of such rays from a single focus; called spherical aberration, when due to the spherical form of the lens or mirror, such form giving different foci for central and marginal rays; and chromatic aberration, when due to different refrangibilities of the colored rays of the spectrum, those of each color having a distinct focus.
5. (Physiol.)
Defn: The passage of blood or other fluid into parts not appropriate for it. ”

“ All these results would follow immediately from the theory of aberration which I proposed in the July number of this Magazine; nor have I been able to obtain any result, admitting of being compared with experiment, which would be different according to which theory we adopted. This affords a curious instance of two totally different theories running parallel to each other in the explanation of phænomena. ”

“ In 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”) . Since the index of refraction varies with the colour or wave length of the light (see Dispersion) , it follows that a system of lenses (uncorrected) projects images of different colours in somewhat different places and sizes and with different aberrations; i.e. there are “chromatic differences” of the distances of intersection, of magnifications, and of monochromatic aberrations. ”

“ The Gaussian theory is only an approximation; monochromatic or spherical aberrations still occur, which will be different for different colours; and should they be compensated for one colour, the image of another colour would prove disturbing. The 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. ”

“ The final correction for achromatism is made, if necessary, by departing slightly from a plane in the curvature of the last surface of the flint lens, and the final correction for spherical aberration in the figuring of the surfaces. In a lecture delivered at the Royal Institution on 2d April 1886 Sir Howard Grubb, optician, of Dublin, said:
"A truly spherical curve is the exception, not the rule. ”

“ But it failed to account for the fact proved by experiment that the aberration was unchanged when observations were made with a telescope filled with water. For if the tangent of the angle of aberration is the ratio of the velocity of the earth to the velocity of light, then, since the latter velocity in water is three-fourths its velocity in a vacuum, the aberration observed with a water telescope should be four-thirds of its true value. ”

“ We may simply say that experience with mirrors as nearly plane as those used by us has shown us that the method of observation supposed would suffice for angles of aberration at least twenty-five times that expected if the velocity-ratio is 10,000.
Since the experiment gives a null result, it is not worth the space to prove that what is true of this adjustment is true with sufficient approximation for an adjustment which differs from the assumed adjustment only by the rotation of mirror I by an angle of ten seconds around a perpendicular axis passing through its surface. ”

“ The specula ground and polished under Lord Rosse's method are almost entirely free from what is called spherical aberration,—that is to say, all rays proceeding from a single point of light, such as a star, are collected into a single point instead of being scattered in a round mass. ”

“ To measure or to detect this inclination is to measure or to detect the secondary aberration which interests us. If we could measure the perpendicular distance between these wave-fronts at a sufficient distance from B, we should know the angle between them. But h" is only a fictitious line. What we cannot measure between h and h" we can measure between a and a', provided we can determine the point of intersection between a and a', and provided this be found in a convenient position. ”

“ If we have reason to be dissatisfied with the results of the efforts hitherto made to determine the constant of aberration, we have little ground for taking into account the second-order effects. But on the other hand an optical experiment has been performed which cannot be reconciled with the ordinary theory, and we have been forced to admit that the theory, if not actually erroneous, can be no more than an approximation to the truth. ”

“ Hence, it is evident, that the first image Ff, is formed only by the union of those rays which pass very near the centre of the lens; but as the rays of light proceeding from every point of an object are very numerous, there is a succession of images formed, according to the parts of the lens where they penetrate, which necessarily produces indistinctness and confusion. This is the imperfection which is distinguished by the name of spherical aberration, or the error arising from the spherical form of lenses. ”

“ This was the celebrated discovery of the Aberration of Light, a triumph of exact observation and of clear insight. As to the exactness of Bradley's observations, it is sufficient to say that his determination of the value of the 'Constant of Aberration' gave it as 20·39 ́ ́ ”

“ In a single lens having spherical surfaces, aberration may be caused by differences in the focal lengths of the various parts of the lens: rays passing through the outer part of the lens come to a focus nearer the lens than do rays passing through its central part. ”

“ Practical Elimination of Aberrations.—The existence of an optical system, which reproduces absolutely a finite plane on another with pencils of finite aperture, is doubtful; but practical systems solve this problem with an accuracy which mostly suffices for the special purpose of each species of instrument. The problem of finding a system which reproduces a given object upon a given plane with given magnification (in so far as aberrations must be taken into account) could be dealt with by means of the approximation theory; in most cases, however, the analytical difficulties are too great. ”

“ The absence of this error is termed achromatism, and an optical system so corrected is termed achromatic. A system is said to be “chromatically under-corrected” when it shows the same kind of chromatic error as a thin positive lens, otherwise it is said to be “over-corrected.”
If, in the first place, monochromatic aberrations be neglected —in other words, the Gaussian theory be accepted—then every reproduction is determined by the positions of the focal planes, and the magnitude of the focal lengths, or if the focal lengths, as ordinarily happens, be equal, by three constants of reproduction. ”

“ There are various instrumental errors, and errors due to refraction; again, if a star's places at two different times are to be compared, precession must be taken into account; and Bradley himself unravelled in aberration and nutation two fresh sources of error. In order therefore to put into a form satisfactory for permanent reference a number of star observations, it is necessary to make corrections which have the effect of allowing for these various sources of error. ”

“ These glimpses of the depths to which one must dig if he is to unearth the complete explanations of visual perception—and consequently of illusions—indicate the futility of treating the theories in the available space without encroaching unduly upon the aims of this volume.
Certain defects of the optical system of the eye must contribute toward causing illusions. Any perfect lens of homogeneous material has at least two defects, known as spherical and chromatic aberration. ”