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 color 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

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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 doublet or achromat in which two materials with differing dispersion (usually crown and flint glass) are bonded together to form a single lens. 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 chemical 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.

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

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 f₁ and f₂, then best correction occurs for the condition:

$f\_1\; \backslash cdot\; V\_1\; +\; f\_2\; \backslash cdot\; V\_2\; =\; 0$

where V₁ and V₂ 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:

$\backslash frac\{1\}\{f\}\; =\; \backslash frac\{1\}\{f\_1\}\; +\; \backslash frac\{1\}\{f\_2\}$

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

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

See also

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• Cooke triplet
• Aberration in optical systems

External links

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• Explanation of chromatic aberration by Paul van Walree

Geometrical optics | Physical quantity

Aberració cromàtica | Chromatická aberace | Chromatische Aberration | Aberración cromática | Aberration chromatique | Aberrazione cromatica | Chromatische aberratie | Aberracja chromatyczna | Хроматическая аберрация | Kromatisk aberration