Chromatic aberration

“ It occurred to Sir Isaac Newton that although a single lens could never be free from chromatic aberration, yet it might be possible to arrange a so-called achromatic combination of lenses in such a manner as to overcome the defect and bring all the rays issuing from a point, whatever their refrangibility, to one focus. Experiments which he undertook for the purpose of testing the matter led him to form the conclusion that such a result could never be attained, the amount of colour dispersion in all substances being, as he stated, always exactly proportional to that of refraction. ”

“ 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. ”

“ A lens may be considered to be a prism of revolution and it thus becomes evident that the blue rays will be brought [Pg 20] to a focus at a lesser distance than the red rays; that is, the former are bent more from their original path than the latter. This defect of lenses is known as chromatic aberration and is quite obvious in the eye. It may be demonstrated by any simple lens, for the image of the sun, for example, will appear to have a colored fringe. A purple filter which transmits only the violet and red rays is useful for this demonstration. ”

“ Chromatic aberration is easily cured by using an achromatic or compound lens made by cementing together two lenses of crown and flint glass respectively, as in Fig. 40.
It will be seen that the flint glass component by itself is a concave lens and therefore neutralises in part, or in whole, the convex crown lens. Flint glass has both greater dispersive power and also greater refractive power than crown glass, but fortunately not to the same degree ”

“ And even after Chester More Hall in 1729, and John Dollond in 1757, had shown that chromatic aberration could be nearly eliminated by the combination of a flint-glass lens with one of crown glass, William Herschel, who began his observations in 1774, devoted his skill entirely to the making of reflectors, seeing no prospect of much advance in the power of refractors. ”

“ This is known as [99] chromatic aberration, or the scattering of light in a telescope due simply to its color or wave length. When light passes through a prism, red is refracted the least and violet the most. Through a lens it is the same, because a lens may be regarded as an indefinite system of prisms. The image of a star or planet, then, formed by a single lens cannot be optically perfect ”

“ The perfect achromatism of a reflector is, of course, a great advantage, but the chromatic aberration of refractors is now so well corrected that their inferiority in that respect may be disregarded. It must be admitted that reflectors are cheaper and easier to make, but, on the other hand, they require more care, and their mirrors frequently need resilvering, while an object glass with reasonable care never gets seriously out of order, and will last for many a lifetime. ”

“ The Oil-immersion, represented by the last illustration consists of a front lens, hemispherical, behind which is a meniscus, which is in turn followed by a doublet and a triplet, these latter acting as the correcting lenses of the combination.
We manufacture both Achromatic and Apochromatic objectives. They differ in that the glasses made use of in the apochromatics and the manner in which they are combined permit a more perfect correction of chromatic aberration. This advantage is not gained without a certain sacrifice of simplicity in construction ”

“ M. Helmholtz has carried M. Cramer’s methods to perfection, and has been able to formulate a complete theory of all the phenomena of accommodation. The laws of optics show that the rays emitted by a luminous point may unite at another point by the action of the refracting surfaces of the eye. Nevertheless, a white light being composed of rays of diverse refrangibility, particular effects, known under the name of chromatic aberration, are produced through the decomposition of light, which we will proceed to study, under M. Helmholtz’s auspices11. ”

“ There is a very great difficulty introduced by the fact that a lens made out of a single piece of glass gives an image which is surrounded by fringes of color, so that some device has to be adopted in order to destroy, as far as possible, this enemy of good definition. In the early history of the telescope, this so-called chromatic aberration was considerably reduced by making small object-glasses of very great focal length. ”

“ The non-perception under ordinary circumstances of the chromatic aberration of the eye is largely due to the greater intensity of the colours which differ least in their refrangibilities. The clearness of our vision does not, therefore, practically suffer from this defect of the eye. Professor Helmholtz constructed lenses which rendered his eyes really achromatic, and looking through these when the pupil was half covered, no coloured fringes were seen at the edges of dark or light objects, or when the objects were looked at with an imperfect accommodation of the eye. ”

“ In the manufacture of our objectives only such glass is employed as has been subjected to the most rigid scientific tests. By these the exact index of refraction and the exact degree of dispersion of the glass are determined, and with these data available it is possible to very perfectly correct both spherical and chromatic aberrations while still making use of wide angular apertures in the objectives. ”

“ In other words, a sufficiently good and distinct image as the resolving power permits cannot be arrived at, until the elimination, or a sufficient diminution, of the spherical and chromatic aberrations has been brought about.
The objective and eyepiece have such different functions that as a rule it is not possible to correct the aberrations of one system by those of the other. Such a compensation is only possible for one single defect, as we shall see later. The demands made upon the eyepiece, which has to represent a relatively large field by narrow cones of rays, are not very considerable. ”

“ It was at one time hoped, as the precious stones are more refractive than glass, and as the increased refractive power is unaccompanied by a correspondent increase in chromatic dispersion, that they would furnish valuable materials for lenses, inasmuch as the refractions would be accomplished by shallower curves, and consequently with diminished spherical aberration. But these hopes were disappointed; everything that ingenuity and perseverance could accomplish was tried by Mr. Varley and Mr. ”

“ The matter of achromatism is further complicated by the fact that objectives are usually over-achromatized to compensate for the chromatic errors in the eyepiece, and especially in the eye. As a general rule an outstanding error in any part of an optical system can be more or less perfectly balanced by an opposite error anywhere else in the system—the particular point chosen being a matter of convenience with respect to other corrections. ”

“ 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. ”

“ In optics, a spherical aberration is that wandering of the rays of light from the normal path which takes place when they are made to pass through curved lenses, or are reflected from curved mirrors, constituting portions of a sphere, instead of parts of a parabola. ”

“ In the best object-glasses the aberrations are so well balanced that the mere covering an object with thin glass is sufficient to disturb the balance and render very delicate markings either misty and coloured or wholly invisible. The effect produced by a plate of glass may be understood by reference to fig. 26, the rays being supposed to emanate from the object at a; and it is evident that the refraction of the glass so alters the direction of the rays that they will fall upon the lower combination nearer the centre than if the cover were absent, and thus negative aberration is produced. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ This arises from an imperfection of the glass lens, called its spherical aberration, which is due to the fact that the circumferential and central rays have not the same focus. The human eye labours under a similar defect, and from this, and other causes, it arises that when the naked light from fifty cells is looked at the blur of light upon the retina is sufficient to destroy the definition of the retinal image of the carbons. A long list of indictments might indeed be brought against the eye—its opacity, its want of symmetry, its lack of achromatism, its partial blindness. ”

“ If the image of an object as seen in the microscope appears to be unusually distorted and indistinct toward the edge of the field, and satisfactory definition is limited to a small portion of the center, the cause is often attributed to the spherical aberration of the objective, while really this phenomenon has nothing to do with that optical defect of the objective, if any exists, but is caused by a lack of optical symmetry. ”

“ 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. ”

“ This is, at the present day, the ordinary type, e.g., of telescope objective (fig. 10) ; the values of the four radii must satisfy the equations (2) and (4) . Two 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 Aberation”) . In practice, however, it is often more useful to avoid the second condition by making, the lenses have contact, i.e. equal radii. ”

“ It is impossible to avoid a fringe of color when using only a single lens, but where we have a complete optical system, consisting of two condensers and an objective, it must be possible to adjust the combination so that practically no color is visible. Spherical aberration is best tested for by laying out very accurately, as in Figure 26, a set of small squares upon some material that will not be damaged by the heat of the lamp—mica for instance—and projecting this upon the screen. ”

“ It takes a rather sharp eye and considerable experience to detect small amounts of spherical aberration; perhaps the best way of judging is in quickly passing from just inside to just outside focus and back again, using a yellow screen and watching very closely for variations in brightness. Truth to tell a small amount of residual aberration, like that of Fig. ”

“ But if F still approaches the glass, the angle of incidence [Pg 26] continues to increase with the increasing divergence of the ray, till it will exceed that of emergence, which has in the meanwhile been diminishing, and at length the spherical error produced by them will recover its original proportion to the opposite error of the curve of correction. When F has reached this point F ́ ́ (at which the angle of incidence does not exceed that of emergence so much as it had at first come short of it) , the rays again pass the glass free from spherical aberration. ”

“ In general, the aberration is positive or negative, that is, Av is greater or less than the ultimate value, according as m/∆−1/∆‵ is positive or negative.
This is positive, if ∆ be less than (m+1) r, and negative when A is above that value; when ∆= (m+1) r, there is no aberration. See p. 54. Note.
When r is negative, or the surface convex, the aberration is always positive.
99. We will now pass on to the aberration in a lens, (Fig. 96.) ”