Chromatic aberration

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On top is corner detail in a photograph taken with a higher quality lens; bottom is a similar photograph taken with a wide angle lens showing severe visible chromatic aberration, the effect is pronounced on the right side of the building's roof, where a long blue streak is visible.

In optics, chromatic aberration (also called achromatism) is the failure of a lens to focus all colors to the same point. It occurs because lenses have a different refractive index for different wavelengths of light (the dispersion of the lens). The refractive index decreases with increasing wavelength.

Chromatic aberration manifests itself as "fringes" of color along boundaries that separate dark and bright parts of 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).

[edit] Minimizing chromatic aberration

In the earliest uses of lenses, chromatic aberration was reduced by increasing the focal length of the lens where possible. For example, this could result in extremely long telescopes used by such astronomers as Christiaan Huygens. Isaac Newton theories on about white light being composed of a spectrum of colors led him to the conclusion that uneven refraction of light caused chromatic aberration (leading him to build the first reflecting telescope, his newtonian telescope, in 1669^[1]).

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.

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

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.

Chromatic aberration of a single lens causes different wavelengths of light to have differing focal lengths

Diffractive optical element with complementary dispersion properties to that of glass can be used to correct for color aberration

For an achromatic doublet, visible wavelengths have approximately the same focal length

An achromatic doublet brings two wavelengths to a common focus, leaving UV and IR uncorrected and out of focus

[edit] 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.

[edit] Image processing to reduce chromatic aberration

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

Since for some lenses, degree of chromatic aberration can have quite a complex relationship to the rectangular geometry of the projected image received by the camera focal plane, geometrical operations to reverse the aberration may be quite complex, and software may not have sufficient complexity and data to be able to properly correct an image, even when the subjects affected are in approximately the same focal plane.

All Panasonic Lumix cameras, and some recent Nikon DSLR's, do such processing automatically in camera.

[edit] Photography

Severe purple fringing can be seen at the edges of the horse's forelock, mane, and ear.

Chromatic aberrations around highlights (the white background).

The term "purple fringing" is commonly used in photography, although not all purple fringing can be attributed to chromatic aberration. Similar colored fringing around highlights may also be caused by lens flare. Colored fringing around highlights or dark regions may be due to the receptors^{[clarification needed]} for different colors having differing dynamic range or sensitivity -- therefore preserving detail in one or two color channels, while "blowing out" or failing to register, in the other channel or channels. On digital cameras, the particular demosaicing algorithm is likely to affect the apparent degree of this problem. Another cause of this fringing is chromatic aberration in the very small microlenses used to collect more light for each CCD pixel; since these lenses are tuned to correctly focus green light, the incorrect focusing of red and blue results in purple fringing around highlights. This is a uniform problem across the frame, and is more of a problem in CCD's with a very small pixel pitch such as those used in non-DSLR digital cameras; as a result, high-end compact cameras (for example, the Panasonic Lumix series and high-end Nikon DSLR's) sometimes feature a processing step specifically designed to remove it.

On photographs taken using a digital camera, very small highlights may frequently appear to have chromatic aberration where in fact the effect is because the highlight image is too small to stimulate all three color pixels, and so is recorded with an incorrect color. This may not occur with all types of digital camera sensor. Again, the demosaicing algorithm may affect the apparent degree of the problem.

[edit] 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 color filter, or by converting a single color channel to black and white. This will, however, require longer exposure. (This of course is only true with panchromatic black and white film, since orthochromatic film is already only sensitive to a limited spectrum.)

[edit] See also

• Aberration in optical systems
• Achromatic telescope
• Apochromatic lens
• Cooke triplet
• Superachromat
• Theory of Colours

[edit] External links

Wikimedia Commons has media related to: Chromatic aberration

• Explanation of chromatic aberration by Paul van Walree
• PanoTools Wiki article about chromatic aberration

[edit] References