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Chromatic aberration

2007 Schools Wikipedia Selection. Related subjects: Space (Astronomy)

   Top - Corner detail from a photograph taken with a good quality lens.
   Bottom - Detail from a similar photograph taken with a wide angle lens
   showing visible chromatic aberration (especially at the dark edges on
   the right).
   Top - Corner detail from a photograph taken with a good quality lens.
   Bottom - Detail from a similar photograph taken with a wide angle lens
   showing visible chromatic aberration (especially at the dark edges on
   the right).

   In optics, chromatic aberration is caused by a lens having a different
   refractive index for different wavelengths of light (the dispersion of
   the lens). The term " purple fringing" is commonly used in photography,
   although not all purple fringing can be attributed to chromatic
   aberration.

   Longitudinal and lateral chromatic aberration of a lens is seen as
   "fringes" of color around the image, because each colour in the optical
   spectrum cannot be focused at a single common point on the optical
   axis.

   Since the focal length f of a lens is dependent on the refractive index
   n, different wavelengths of light will be focused on different
   positions. Chromatic aberration can be both longitudinal, in that
   different wavelengths are focused at a different distance from the
   lens; and transverse or lateral, in that different wavelengths are
   focused at different positions in the focal plane (because the
   magnification of the lens also varies with wavelength).

Minimizing chromatic aberration

   There exists a point called the circle of least confusion, where
   chromatic aberration can be minimized. It can be further minimized by
   using an achromatic lens or achromat, in which materials with differing
   dispersion are assembled together to form a compound lens. The most
   common type is an achromatic doublet, with elements made of crown and
   flint glass. This reduces the amount of chromatic aberration over a
   certain range of wavelengths, though it does not produce perfect
   correction. By combining more than two lenses of different composition,
   the degree of correction can be further increased, as seen in an
   apochromatic lens or apochromat.

   Many types of glass have been developed to reduce chromatic aberration,
   most notably, glasses containing fluorite. These hybridized glasses
   have a very low level of optical dispersion; only two compiled lenses
   made of these substances can yield a high level of correction.
   Chromatic aberration of a single lens causes different wavelengths of
   light to have differing focal lengths.
   Chromatic aberration of a single lens causes different wavelengths of
   light to have differing focal lengths.
   For an achromatic doublet, visible wavelengths have approximately the
   same focal length.
   For an achromatic doublet, visible wavelengths have approximately the
   same focal length.
   Diffractive optical element with complimentary dispersion properties to
   that of glass can be used to correct for color aberration.
   Diffractive optical element with complimentary dispersion properties to
   that of glass can be used to correct for colour aberration.
   An achromatic doublet brings two wavelengths to a common focus, leaving
   ultraviolet and infrared uncorrected and out of focus.
   An achromatic doublet brings two wavelengths to a common focus, leaving
   ultraviolet and infrared uncorrected and out of focus.

   The use of achromats was an important step in the development of the
   optical microscope.

   An alternative to achromatic doublets is the use of diffractive optical
   elements. Diffractive optical elements have complementary dispersion
   characteristics to that of optical glasses and plastics. In the visible
   part of the spectrum, diffractives have an Abbe number of -3.5.
   Diffractive optical elements can be fabricated using diamond turning
   techniques.

Mathematics of chromatic aberration minimization

   For a doublet consisting of two thin lenses in contact, the Abbe number
   of the lens materials is used to calculate the correct focal length of
   the lenses to ensure correction of chromatic aberration. If the focal
   lengths of the two lenses for light at the yellow Fraunhofer D-line
   (589.2 nm) are f[1] and f[2], then best correction occurs for the
   condition:

          f_1 \cdot V_1 + f_2 \cdot V_2 = 0

   where V[1] and V[2] are the Abbe numbers of the materials of the first
   and second lenses, respectively. Since Abbe numbers are positive, one
   of the focal lengths must be negative, i.e. a diverging lens, for the
   condition to be met.

   The overall focal length of the doublet f is given by the standard
   formula for thin lenses in contact:

          \frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2}

   and the above condition ensures this will be the focal length of the
   doublet for light at the blue and red Fraunhofer F and C lines (486.1
   nm and 656.3 nm respectively). The focal length for light at other
   visible wavelengths will be similar but not exactly equal to this.

Image processing to reduce chromatic aberration

   Post-processing to remove chromatic aberration usually involves scaling
   the fringed colour channel, or subtracting some of a scaled version of
   the fringed channel.

Black and white photography

   Chromatic aberration also affects black and white photography. Although
   there are no colors in the photograph, chromatic aberration will blur
   the image. It can be reduced by using a narrow band colour filter, or
   by converting a single colour channel to black and white. This will
   however require longer exposure.

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