page_title: Spherical aberration
section_title: Correction
hierarchical_section_title: Spherical aberration / Correction
caption_attribution_description: English: A simulation of spherical aberration in an optical system with a circular, unobstructed aperture admitting a monochromatic point source. The top row is over-corrected (half a wavelength), the middle row is perfectly corrected, and the bottom row is under-corrected (half a wavelength). Going left to right, one moves from being inside focus to outside focus. The middle column is perfectly focused. Also note the equivalence of inside-focus over-correction to outside-focus under-correction. See the corresponding longitudinal sections. See also en:Image:Spherical-aberration-slice.jpg
context_page_description: Spherical aberration is a type of aberration found in optical systems that use elements with spherical surfaces. Lenses and curved mirrors are most often made with surfaces that are spherical, because this shape is easier to form than non-spherical curved surfaces. Light rays that strike a spherical surface off-centre are refracted or reflected more or less than those that strike close to the centre. This deviation reduces the quality of images produced by optical systems.
context_section_description: In lens systems, aberrations can be minimized using combinations of convex and concave lenses, or by using aspheric lenses or aplanatic lenses. 
  Lens systems with aberration correction are usually designed by numerical ray tracing. For simple designs one can sometimes analytically 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  and  of the front and back surfaces of the lens such that
   The signs of the radii follow the Cartesian sign convention.
  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 with focal ratio less than f/10 are usually made with non-spherical mirrors or with correcting lenses.
  Spherical aberration can be eliminated by making lenses with an aspheric surface. Descartes showed that lenses whose surfaces are well-chosen Cartesian ovals (revolved around the central symmetry axis) can perfectly image light from a point on the axis or from infinity in the direction of the axis. Such a design yields completely aberration-free focusing of light from a distant source.
  In 2018, Rafael G. González-Acuña and Héctor A. Chaparro-Romo, graduate students at the National Autonomous University of Mexico and the Monterrey Institute of Technology and Higher Education in Mexico, found a closed formula for a lens surface that eliminates spherical aberration. Their equation can be applied to specify a shape for one surface of a lens, where the other surface has any given shape.
caption: 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.
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