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Spherical aberration

2007 Schools Wikipedia Selection. Related subjects: General Physics

   Spherical aberration. A perfect lens (top) focuses all incoming rays to
   a point on the optic axis. A real lens with spherical surfaces (bottom)
   suffers from spherical aberration: it focuses rays more tightly if they
   enter it far from the optic axis than if they enter closer to the axis.
   It therefore does not produce a perfect focal point. (Drawing is
   exaggerated.)
   Enlarge
   Spherical aberration. A perfect lens (top) focuses all incoming rays to
   a point on the optic axis. A real lens with spherical surfaces (bottom)
   suffers from spherical aberration: it focuses rays more tightly if they
   enter it far from the optic axis than if they enter closer to the axis.
   It therefore does not produce a perfect focal point. (Drawing is
   exaggerated.)
   A point source as imaged by a system with (top) negative, (center)
   zero, and (bottom) positive spherical aberration. Images to the left
   are defocused toward the inside, images on the right toward the
   outside.
   Enlarge
   A point source as imaged by a system with (top) negative, (centre)
   zero, and (bottom) positive spherical aberration. Images to the left
   are defocused toward the inside, images on the right toward the
   outside.
   Longitudinal sections through a focused beam with (top) negative,
   (center) zero, and (bottom) positive spherical aberration. The lens is
   to the left.
   Enlarge
   Longitudinal sections through a focused beam with (top) negative,
   (centre) zero, and (bottom) positive spherical aberration. The lens is
   to the left.

   In optics, spherical aberration is an image imperfection that occurs
   due to the increased refraction of light rays that occurs when rays
   strike a lens or a reflection of light rays that occurs when rays
   strike a mirror near its edge, in comparison with those that strike
   nearer the centre. 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, as spherical shapes are much easier to produce than
   aspherical and so most lenses have spherical shapes.

   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.

   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.

   In lens systems, the effect can be minimized using special combinations
   of convex and concave lenses, as well as using aspheric 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[1] and R[2] 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) .

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