ABERRATION (Latin aberratio — a deviation) — a deviation in a structure or function from norm, a representative sample.
In morphology and physiology the term «aberration» is usually used for designation of individual aberrations; sometimes as a synonym of deviation (see. Biogenetic law). In a systematics of some groups of animals (hl. obr. butterflies, bugs and fishes) this term is applied in the taxonomical purposes (see. Taxonomic categories) on the basis of allocation of insignificant, accidental deviations in coloring, the drawing and structure of covers. In genetics apply the concept «aberation chromosomes», i.e. the changes of a line structure of chromosomes caused by their gap with redistribution, loss or partial doubling of genetic material (see the Mutation).
Special case And. aberrations of optical systems, i.e. errors of the images given by optical systems (a glass lens or a set of lenses, mirrors, the refracting environments of an eye) are.
And. optical systems are numerous. Among them distinguish chromatic and monochromatic, or geometrical.
Chromatic aberrations arise owing to dependence of index of refraction of lenses on the wavelength of light. For an eye indices of refraction of transparent environments of subjects it is more, than less length of waves. It leads to the fact that the refracting force of an eye in blue beams (length of waves about 450 nanometers) on 1,3 dioptries (dptr) is more, than in red beams (650 nanometers). Focal lengths of simple convex lenses for red beams appear more (for 1 — 3% depending on a grade of glass), than for blue (fig. 1). Red beams create sharp images further from a lens, than blue (so arises longitudinal chromatic And.), and in larger scale — a so-called chromatic difference of increases. The image of a bright white point represents the bright color speck surrounded with an aura of complementary colors.
Chromatic And. it is symmetric around an axis of an eye and is almost identical angering all an eye. Owing to chromatic And. a usual emmetropichesky eye is short-sighted at blue lighting. In usual light conditions when on perception only sensitivity of an eye to a middle part of a visible range, chromatic significantly affects And. only slightly reduces the clearness of contours.
Geometrical aberrations are shown at action of the beams of light far from the main optical axis of system, or the bunches which are strongly inclined to an axis. Protozoa And. spherical lenses and mirrors are: spherical And., coma, astigmatism of slanting bunches, curvature of the field and distortion.
Spherical aberration. The beams which left the point lying on the main optical axis of a convex lens, and passed through its edges will meet earlier, than paraxial (i.e. the lenses which passed through the middle) beams. The turning-out distributions of illumination in the image of a bright point for some provisions of the screen are given in fig. 2 (and and b). In fig. 2, and the path of rays is represented. Fig. 2, would represent the schedule of qualitative dependence of illumination in the image of one point from distance of z from the main optical axis B at different provisions of the screen (O 1 — About 1 ), for each of which illumination is postponed to the right. As a result of spherical And. the bright point lying on an optical axis is represented in the form of «a circle of dispersion». Radius of this circle call cross spherical And.
The coma is shown the stronger, than from the main optical axis the represented point and what the diaphragm is more open is spaced far apart. The image of a point has an appearance of an oblong asymmetrical speck (fig. 3). Lines in the drawing connected points to equal osveshchennost. The greatest illumination in a point of the Lake. Direct OO 1 crosses the main optical axis.
Astigmatism of slanting bunches. Beams in an astigmatic bunch (contrary to a homocentric stigmatic bunch of a pla which all beams are crossed in one point) in some cases can be crossed, as shown in fig. 4. The light wave has various curvature in different sections here: in sections of ABM and CDN curvature is maximum; and in ACP and BDQ — it is minimum. Therefore the beams lying in the section of AVM pass through a point of M, and beams of section of ASR pass through a point of River. Thus, all beams limited to a contour of ABDC cross the corresponding points of a piece of MN, and then a piece of PQ. The distance between MN and P Q characterizing degree of uncertainty of situation is more best go than the image, is called an astigmatic difference. At slanting falling of beams from the shining point on a convex lens (the lens has no axial symmetry to an axis of a bunch) the beams which passed at the top and a bottom of a lens, will meet in a point of M, and passed through different points of its horizontal diameter — in a point P (fig. 5). In this case the radial direct OS planes, a perpendicular optical axis of a lens (and the planes of the drawing), will be represented sharply on the surface of rotation r (RO formed by rotation' around OO'), and concentric circles of the same plane will be represented accurately on a surface of t. On a surface of l, average between p and m, length of the spot representing any point of the OS plane is minimum.
This look And. often meets in life as one of shortcomings of the sight connected with defects of forms of a surface of an eye (see the Astigmatism of an eye).
Difference of a surface of n from the plane determines by itself one more look And. — curvature of the field, or curvature of a surface of the image. There are optical systems in which m and r are specularly symmetric concerning the O'S' plane. In them there is no curvature of the field, but there is an astigmatism. Also the return case — big curvature of the field without essential astigmatism is possible. Surfaces of m and p always kasatelna to the O'S' plane therefore both the astigmatism, and curvature of the field are insignificant for paraxial bunches.
Distortion — distortion of the image as a result of dependence of scalingup of parts of the image on their distance to the main optical axis. In this case the image is not similar to an object. If during removal from an axis increase grows, then the image of the object given in fig. 6 and, gets a subauriculate form (fig. 6, b); if with removal from an axis increase falls, then the barrel-shaped image of an object turns out (fig. 6, c). From the drawing it is also visible that radial circles direct and symmetric to rather main axis are not distorted by a distortion.
Rays of light can only conditionally be considered equivalent to geometrical straight lines.
Actually distribution of light is wave process, and rays of light are perpendiculars to wave surfaces. The spherical wave which left a point source of monochromatic light, having passed through optical system, stops being spherical. Derogation of a real surface of a wave from ideal spherical defines wave A.
Znaya wave And., it is possible to calculate precisely distribution of illumination in the field of the image. At the same time are considered at once and the above described protozoa geometrical And., and more difficult And., and diffraction phenomena. The last and in nonaberrational systems lead to degradation of images and essentially limit resolving power of optical devices (see Optics, the Optical method and researches).
Considered above And. are inherent also to faultlessly made and mounted systems. In practice owing to inhomogeneity of material of glasses, discrepancy of a form and the provision of surfaces to settlement there is still a number of the defects of the image reducing sharpness of contours, worsening transfer of the contrasts (especially fine details and in shadows) distorting a form of the image. Full elimination And., as a rule, it is impossible. Try to obtain their considerable reduction, selecting indices of refraction and dispersions of glasses of lenses, combining forms, a relative positioning of lenses (and mirrors). However need of observance of one technical specifications reduces quite often possibilities of performance of others. Therefore it is necessary to define according to purpose of the device what of And. main and in what measure it is necessary to eliminate this or that kind of A. Chasto but to the name of optical system it is possible to define what of And. in it are well compensated. In achromats are reduced chromatic and spherical A. V apochromats same And. are compensated much more precisely. In aplanats are corrected chromatic and spherical And., and also coma. If, except these And., the astigmatism and curvature of the field are eliminated, call a lens an anastigmat. Ortoskopicheskimi is called by systems with the corrected distortion.
For physicians And. it is important already the fact that an eye of the person owing to And. often creates the imperfect image, considerably the worst, than the nonaberrational system of the same svetosila and with the same focal length would give. And. eyes are various. The simplest of them are caused by the wrong focusing of an eye owing to anomalies of a refraction of an eye (see) and accommodations of an eye (see). These defects (see Short-sightedness, Far-sightedness, the Presbyopy) are compensated by usual spherical eyeglass lenses. Combinations of these abnormalities of aiming of an eye on sharpness with a simple astigmatism form the so-called correct astigmatism of an eye (see) corrected by a combination spherical and tsilind a hairstyle of lenses. The wrong astigmatism, small degrees is more difficult to-rogo occur at most of people and lead to bigger or smaller distortion of the image, do it to less contrast; visual acuity at the same time significantly does not change. Big degrees are already pathology. They arise, e.g., at a cone-shaped cornea. In such cases visual acuity is not compensated by usual points and apply contact lenses (see).
See also Aberration of an eye .
Bibliography: Landsberg G. S. General course of physics, t. 3, M., 1957; Paul R. V. Introduction to optics, the lane with it., M. — L. 1947; Slyusarsv G. G. Geometrical optics, M. — L., 1946, bibliogr.; Tudorovsky A. I. Theory of optical devices, t. 1, page 427, M. — L., 1948, bibliogr.
M. S. Smirnov, P. P. Nikolaev.