Chromatic aberration

An alternative to achromatic doublets is the use of diffractive optical elements. Diffractive optical elements are able to generate arbitrary complex wave fronts from a sample of optical material which is essentially flat.[9] Diffractive optical elements have negative dispersion characteristics, complementary to the positive Abbe numbers of optical glasses and plastics. Specifically, in the visible part of the spectrum diffractives have a negative Abbe number of −3.5. Diffractive optical elements can be fabricated using diamond turning techniques.^[10]

Telephoto lenses using diffractive elements to minimize chromatic aberration are commercially available from Canon and Nikon for interchangeable-lens cameras; these include 800mm f/6.3, 500mm f/5.6, and 300mm f/4 models by Nikon (branded as "phase fresnel" or PF), and 800mm f/11, 600mm f/11, and 400mm f/4 models by Canon (branded as "diffractive optics" or DO). They produce sharp images with reduced chromatic aberration at a lower weight and size than traditional optics of similar specifications and are generally well-regarded by wildlife photographers.^[11]

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.^[12] 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:

${\displaystyle f_{1}\cdot V_{1}+f_{2}\cdot V_{2}=0}$

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:

${\displaystyle {\frac {1}{f}}={\frac {1}{f_{1}}}+{\frac {1}{f_{2}}}}$

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.

Chromatic aberration is used during a duochrome eye test to ensure that a correct lens power has been selected. The patient is confronted with red and green images and asked which is sharper. If the prescription is right, then the cornea, lens and prescribed lens will focus the red and green wavelengths just in front, and behind the retina, appearing of equal sharpness. If the lens is too powerful or weak, then one will focus on the retina, and the other will be much more blurred in comparison.^[13]

Image processing to reduce the appearance of lateral chromatic aberration

In some circumstances, it is possible to correct some of the effects of chromatic aberration in digital post-processing. However, in real-world circumstances, chromatic aberration results in permanent loss of some image detail. Detailed knowledge of the optical system used to produce the image can allow for some useful correction.^[14] In an ideal situation, post-processing to remove or correct lateral chromatic aberration would involve scaling the fringed color channels, or subtracting some of a scaled versions of the fringed channels, so that all channels spatially overlap each other correctly in the final image.^[15]

As chromatic aberration is complex (due to its relationship to focal length, etc.) some camera manufacturers employ lens-specific chromatic aberration appearance minimization techniques. Almost every major camera manufacturer enables some form of chromatic aberration correction, both in-camera and via their proprietary software. Third party software tools such as PTLens are also capable of performing complex chromatic aberration appearance minimization with their large database of cameras and lens.

In reality, even theoretically perfect post-processing based chromatic aberration reduction-removal-correction systems do not increase image detail as well as a lens that is optically well-corrected for chromatic aberration would for the following reasons:

• Rescaling is only applicable to lateral chromatic aberration but there is also longitudinal chromatic aberration
• Rescaling individual color channels result in a loss of resolution from the original image
• Most camera sensors only capture a few and discrete (e.g., RGB) color channels but chromatic aberration is not discrete and occurs across the light spectrum
• The dyes used in the digital camera sensors for capturing color are not very efficient so cross-channel color contamination is unavoidable and causes, for example, the chromatic aberration in the red channel to also be blended into the green channel along with any green chromatic aberration.

The above are closely related to the specific scene that is captured so no amount of programming and knowledge of the capturing equipment (e.g., camera and lens data) can overcome these limitations.

Photography

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

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 de-mosaicing algorithm may affect the apparent degree of the problem.

• 
  Color shifting through corner of eyeglasses
• 
  Severe purple fringing can be seen at the edges of the horse's forelock, mane, and ear.
• 
  This photo taken with the lens aperture wide open resulting in a narrow depth-of-field and strong axial CA. The pendant has purple fringing in the near out-of-focus area and green fringing in the distance. Taken with a Nikon D7000 camera and an AF-S Nikkor 50mm f/1.8G lens.

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 (and change the resulting image). (This is only true with

Electron microscopy

Chromatic aberration also affects electron microscopy, although instead of different colors having different focal points, different electron energies may have different focal points.^[16]

See also

• Achromatic telescope
• Cooke triplet
• Superachromat
• Chromostereopsis – Stereo visual effects due to chromatic aberration
• Theory of Colours

References

External links

Wikimedia Commons has media related to Chromatic aberration.

• Methods to correct chromatic aberrations in lens design
• Explanation of chromatic aberration by Paul van Walree
• PanoTools Wiki article about chromatic aberration
• Use in video games