What is "spherical aberration"

Aberration \Ab`er*ra"tion\, n. [L. aberratio: cf. F. aberration. See Aberrate.]

1. The act of wandering; deviation, especially from truth or moral rectitude, from the natural state, or from a type. ``The aberration of youth.''
   --Hall. ``Aberrations from theory.''
   --Burke.

2. A partial alienation of reason. ``Occasional aberrations of intellect.''
   --Lingard.

   Whims, which at first are the aberrations of a single brain, pass with heat into epidemic form.
   --I. Taylor.

3. (Astron.) A small periodical change of position in the stars and other heavenly bodies, due to the combined effect of the motion of light and the motion of the observer; called annual aberration, when the observer's motion is that of the earth in its orbit, and daily or diurnal aberration, when of the earth on its axis; amounting when greatest, in the former case, to 20.4'', and in the latter, to 0.3''. Planetary aberration is that due to the motion of light and the motion of the planet relative to the earth.

4. (Opt.) 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.) The passage of blood or other fluid into parts not appropriate for it.

6. (Law) The producing of an unintended effect by the glancing of an instrument, as when a shot intended for A glances and strikes B.

   Syn: Insanity; lunacy; madness; derangement; alienation; mania; dementia; hallucination; illusion; delusion. See Insanity.

alt. (context optics English) A type of lens aberration which causes blurriness, particularly away from the centre of the lens. n. (context optics English) A type of lens aberration which causes blurriness, particularly away from the centre of the lens.

n. a optical aberration resulting in a distorted image

Spherical aberration is an optical effect observed in an optical device ( lens, mirror, etc.) that occurs due to the increased refraction of light rays when they strike a lens or a reflection of light rays when they strike a mirror near its edge, in comparison with those that strike nearer the centre. It signifies a deviation of the device from the norm, i.e., it results in an imperfection of the produced image.

thumb|center|300px|On top is a depiction of a perfect lens without spherical aberration: all incoming rays are focused in the focal point.

The bottom example depicts a real lens with spherical surfaces, which produces spherical aberration: The different rays do not meet after the lens in one focal point. The further the rays are from the optical axis, the closer to the lens they intersect the optical axis (positive spherical aberration).

(Drawing is exaggerated.) A spherical lens has an aplanatic point (i.e., no spherical aberration) only at a radius that equals the radius of the sphere divided by the index of refraction of the lens material. A typical value of refractive index for crown glass is 1.5 (see list), which indicates that only about 43% of the area (67% of diameter) of a spherical lens is useful. It is often considered to be an imperfection of telescopes and other instruments which makes their focusing less than ideal due to the spherical shape of lenses and mirrors. This is an important effect, because spherical shapes are much easier to produce than aspherical ones. In many cases, it is cheaper to use multiple spherical elements to compensate for spherical aberration than it is to use a single aspheric lens.

"Positive" spherical aberration means peripheral rays are bent too much. "Negative" spherical aberration means peripheral rays are not bent enough.

The effect is proportional to the fourth power of the diameter and inversely proportional to the third power of the focal length, so it is much more pronounced at short focal ratios, i.e., "fast" lenses.

thumb|center|Longitudinal sections through a focused beam with negative (top row), zero (middle row), and positive spherical aberration (bottom row). The lens is to the left. In lens systems, the effect can be minimized using special combinations of convex and concave lenses, as well as using aspheric lenses or aplanatic lenses.

For simple designs one can sometimes calculate parameters that minimize spherical aberration. For example, in a design consisting of a single lens with spherical surfaces and a given object distance o, image distance i, and refractive index n, one can minimize spherical aberration by adjusting the radii of curvature R and R of the front and back surfaces of the lens such that

$$\frac{R_1+R_2}{R_1-R_2}=\frac{2 \left( n^2-1 \right)}{n+2}\left( \frac{i+o}{i-o} \right).$$

thumb|300 px|center|A point source as imaged by a system with negative (top row), zero (middle row), and positive spherical aberration (bottom row). The middle column shows the focused image, columns to the left shows defocusing toward the inside, and columns to the right show defocusing toward the outside. For small telescopes using spherical mirrors with focal ratios shorter than f/10, light from a distant point source (such as a star) is not all focused at the same point. Particularly, light striking the inner part of the mirror focuses farther from the mirror than light striking the outer part. As a result the image cannot be focused as sharply as if the aberration were not present. Because of spherical aberration, telescopes shorter than f/10 are usually made with non-spherical mirrors or with correcting lenses.