Chromatic aberration

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Focal length of lens varies with the color of light Chromatic aberration lens diagram.svg
Focal length of lens varies with the color of light
Photographic example showing high quality lens (top) compared to lower quality model exhibiting transverse chromatic aberration (seen as a blur and a rainbow edge in areas of contrast) Chromatic aberration (comparison).jpg
Photographic example showing high quality lens (top) compared to lower quality model exhibiting transverse chromatic aberration (seen as a blur and a rainbow edge in areas of contrast)

In optics, chromatic aberration (CA), also called chromatic distortion and spherochromatism, is a failure of a lens to focus all colors to the same point. [1] It is caused by dispersion: the refractive index of the lens elements varies with the wavelength of light. The refractive index of most transparent materials decreases with increasing wavelength. [2] Since the focal length of a lens depends on the refractive index, this variation in refractive index affects focusing. [3] Chromatic aberration manifests itself as "fringes" of color along boundaries that separate dark and bright parts of the image.

Contents

Types

Comparison of an ideal image of a ring (1) and ones with only axial (2) and only transverse (3) chromatic aberration Comparison axial lateral chromatic aberration.svg
Comparison of an ideal image of a ring (1) and ones with only axial (2) and only transverse (3) chromatic aberration

There are two types of chromatic aberration: axial (longitudinal), and transverse (lateral). Axial aberration occurs when different wavelengths of light are focused at different distances from the lens (focus shift). Longitudinal aberration is typical at long focal lengths. Transverse aberration occurs when different wavelengths are focused at different positions in the focal plane, because the magnification and/or distortion of the lens also varies with wavelength. Transverse aberration is typical at short focal lengths. The ambiguous acronym LCA is sometimes used for either longitudinal or lateral chromatic aberration. [2]

The two types of chromatic aberration have different characteristics, and may occur together. Axial CA occurs throughout the image and is specified by optical engineers, optometrists, and vision scientists in diopters. [4] It can be reduced by stopping down, which increases depth of field so that though the different wavelengths focus at different distances, they are still in acceptable focus. Transverse CA does not occur in the center of the image and increases towards the edge. It is not affected by stopping down.

In digital sensors, axial CA results in the red and blue planes being defocused (assuming that the green plane is in focus), which is relatively difficult to remedy in post-processing, while transverse CA results in the red, green, and blue planes being at different magnifications (magnification changing along radii, as in geometric distortion), and can be corrected by radially scaling the planes appropriately so they line up.

Minimization

Chromatic correction of visible and near infrared wavelengths. Horizontal axis shows degree of aberration, 0 is no aberration. Lenses: 1: simple, 2: achromatic doublet, 3: apochromatic and 4: superachromat. Comparison chromatic focus shift plots.svg
Chromatic correction of visible and near infrared wavelengths. Horizontal axis shows degree of aberration, 0 is no aberration. Lenses: 1: simple, 2: achromatic doublet, 3: apochromatic and 4: superachromat.

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 such as the very long aerial telescopes of the 17th century. Isaac Newton's theories 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 1668. [5] )

Modern telescopes, as well as other catoptric and catadioptric systems, continue to use mirrors, which have no chromatic aberration.

There exists a point called the circle of least confusion , where chromatic aberration can be minimized. [6] 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. "Achromat" and "apochromat" refer to the type of correction (2 or 3 wavelengths correctly focused), not the degree (how defocused the other wavelengths are), and an achromat made with sufficiently low dispersion glass can yield significantly better correction than an achromat made with more conventional glass. Similarly, the benefit of apochromats is not simply that they focus three wavelengths sharply, but that their error on other wavelengths is also quite small. [7]

Many types of glass have been developed to reduce chromatic aberration. These are low dispersion glass, 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. [8]

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

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]

Chromatic aberration lens diagram.svg
Chromatic aberration of a single lens causes different wavelengths of light to have differing focal lengths.
Diffractive.png
Diffractive optical element with complementary dispersion properties to that of glass can be used to correct for color aberration.
Lens6b-en.svg
For an achromatic doublet, visible wavelengths have approximately the same focal length.

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:

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.

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:

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 lens flare. Colored fringing around highlights or dark regions may be due to the receptors 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 CCDs with a very small pixel pitch such as those used in compact cameras. Some cameras, such as the Panasonic Lumix series and newer Nikon and Sony DSLRs, 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 de-mosaicing algorithm may affect the apparent degree of the problem.

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 panchromatic black-and-white film, since orthochromatic film is already sensitive to only a limited spectrum.)

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

Related Research Articles

<span class="mw-page-title-main">Optical aberration</span> Deviation from perfect paraxial optical behavior

In optics, aberration is a property of optical systems, such as lenses, that causes light to be spread out over some region of space rather than focused to a point. Aberrations cause the image formed by a lens to be blurred or distorted, with the nature of the distortion depending on the type of aberration. Aberration can be defined as a departure of the performance of an optical system from the predictions of paraxial optics. In an imaging system, it occurs when light from one point of an object does not converge into a single point after transmission through the system. Aberrations occur because the simple paraxial theory is not a completely accurate model of the effect of an optical system on light, rather than due to flaws in the optical elements.

<span class="mw-page-title-main">Lens</span> Optical device which transmits and refracts light

A lens is a transmissive optical device that focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (elements), usually arranged along a common axis. Lenses are made from materials such as glass or plastic and are ground, polished, or molded to the required shape. A lens can focus light to form an image, unlike a prism, which refracts light without focusing. Devices that similarly focus or disperse waves and radiation other than visible light are also called "lenses", such as microwave lenses, electron lenses, acoustic lenses, or explosive lenses.

<span class="mw-page-title-main">Optics</span> Branch of physics that studies light

Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviolet, and infrared light. Light is a type of electromagnetic radiation, and other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties.

<span class="mw-page-title-main">Achromatic lens</span> Lens that is designed to limit the effects of chromatic and spherical aberration

An achromatic lens or achromat is a lens that is designed to limit the effects of chromatic and spherical aberration. Achromatic lenses are corrected to bring two wavelengths into focus on the same plane. Wavelengths in between these two then have better focus error than could be obtained with a simple lens.

<span class="mw-page-title-main">Camera lens</span> Optical lens or assembly of lenses used with a camera to create images

A camera lens is an optical lens or assembly of lenses used in conjunction with a camera body and mechanism to make images of objects either on photographic film or on other media capable of storing an image chemically or electronically.

<span class="mw-page-title-main">Angular resolution</span> Ability of any image-forming device to distinguish small details of an object

Angular resolution describes the ability of any image-forming device such as an optical or radio telescope, a microscope, a camera, or an eye, to distinguish small details of an object, thereby making it a major determinant of image resolution. It is used in optics applied to light waves, in antenna theory applied to radio waves, and in acoustics applied to sound waves. The colloquial use of the term "resolution" sometimes causes confusion; when an optical system is said to have a high resolution or high angular resolution, it means that the perceived distance, or actual angular distance, between resolved neighboring objects is small. The value that quantifies this property, θ, which is given by the Rayleigh criterion, is low for a system with a high resolution. The closely related term spatial resolution refers to the precision of a measurement with respect to space, which is directly connected to angular resolution in imaging instruments. The Rayleigh criterion shows that the minimum angular spread that can be resolved by an image forming system is limited by diffraction to the ratio of the wavelength of the waves to the aperture width. For this reason, high resolution imaging systems such as astronomical telescopes, long distance telephoto camera lenses and radio telescopes have large apertures.

<span class="mw-page-title-main">Refracting telescope</span> Type of optical telescope

A refracting telescope is a type of optical telescope that uses a lens as its objective to form an image. The refracting telescope design was originally used in spyglasses and astronomical telescopes but is also used for long-focus camera lenses. Although large refracting telescopes were very popular in the second half of the 19th century, for most research purposes, the refracting telescope has been superseded by the reflecting telescope, which allows larger apertures. A refractor's magnification is calculated by dividing the focal length of the objective lens by that of the eyepiece.

<span class="mw-page-title-main">Optical telescope</span> Telescope for observations with visible light

An optical telescope is a telescope that gathers and focuses light mainly from the visible part of the electromagnetic spectrum, to create a magnified image for direct visual inspection, to make a photograph, or to collect data through electronic image sensors.

<span class="mw-page-title-main">Reflecting telescope</span> Telescopes which utilize curved mirrors to form an image

A reflecting telescope is a telescope that uses a single or a combination of curved mirrors that reflect light and form an image. The reflecting telescope was invented in the 17th century by Isaac Newton as an alternative to the refracting telescope which, at that time, was a design that suffered from severe chromatic aberration. Although reflecting telescopes produce other types of optical aberrations, it is a design that allows for very large diameter objectives. Almost all of the major telescopes used in astronomy research are reflectors. Many variant forms are in use and some employ extra optical elements to improve image quality or place the image in a mechanically advantageous position. Since reflecting telescopes use mirrors, the design is sometimes referred to as a catoptric telescope.

Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light. Because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties.

<span class="mw-page-title-main">Apochromat</span>

An apochromat, or apochromatic lens (apo), is a photographic or other lens that has better correction of chromatic and spherical aberration than the much more common achromat lenses.

<span class="mw-page-title-main">Eyepiece</span> Type of lens attached to a variety of optical devices such as telescopes and microscopes

An eyepiece, or ocular lens, is a type of lens that is attached to a variety of optical devices such as telescopes and microscopes. It is named because it is usually the lens that is closest to the eye when someone looks through an optical device to observe an object or sample. The objective lens or mirror collects light from an object or sample and brings it to focus creating an image of the object. The eyepiece is placed near the focal point of the objective to magnify this image to the eyes. The amount of magnification depends on the focal length of the eyepiece.

<span class="mw-page-title-main">Catadioptric system</span> Optical system where refraction and reflection are combined

A catadioptric optical system is one where refraction and reflection are combined in an optical system, usually via lenses (dioptrics) and curved mirrors (catoptrics). Catadioptric combinations are used in focusing systems such as searchlights, headlamps, early lighthouse focusing systems, optical telescopes, microscopes, and telephoto lenses. Other optical systems that use lenses and mirrors are also referred to as "catadioptric", such as surveillance catadioptric sensors.

<span class="mw-page-title-main">Purple fringing</span> Type of chromatic aberration in photography

In photography, purple fringing is the term for an unfocused purple or magenta "ghost" image on a photograph. This optical aberration is generally most visible as a coloring and lightening of dark edges adjacent to bright areas of broad-spectrum illumination, such as daylight or various types of gas-discharge lamps.

A non-achromatic objective is an objective lens which is not corrected for chromatic aberration. In telescopes they can a be pre-18th century simple single element objective lenses which were used before the invention of doublet achromatic lenses. They can also be specialty monochromatic lenses used in modern research telescopes and other instruments.

<span class="mw-page-title-main">Achromatic telescope</span> A refracting telescope design that reduces cromatic aberration

The achromatic telescope is a refracting telescope that uses an achromatic lens to correct for chromatic aberration.

Low-dispersion glass is a type of glass with a reduction in chromatic aberration. Crown glass is an example of a relatively inexpensive low-dispersion glass.

A flat lens is a lens whose flat shape allows it to provide distortion-free imaging, potentially with arbitrarily-large apertures. The term is also used to refer to other lenses that provide a negative index of refraction. Flat lenses require a refractive index close to −1 over a broad angular range. In recent years, flat lenses based on metasurfaces were also demonstrated.

<span class="mw-page-title-main">History of photographic lens design</span>

The invention of the camera in the early 19th century led to an array of lens designs intended for photography. The problems of photographic lens design, creating a lens for a task that would cover a large, flat image plane, were well known even before the invention of photography due to the development of lenses to work with the focal plane of the camera obscura.

References

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