Chromatic aberration

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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.

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 colour aberration.

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

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:

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.