Chromatic aberration

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Optical aberration
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Chromatic aberration lens diagram.svg Chromatic aberration

Contents

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 (abbreviated 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.

Optics The 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. Because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties.

Lens (optics) 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 and polished or molded to a desired 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.

Focus (optics) point where light rays originating from a point converge on an object

In geometrical optics, a focus, also called an image point, is the point where light rays originating from a point on the object converge. Although the focus is conceptually a point, physically the focus has a spatial extent, called the blur circle. This non-ideal focusing may be caused by aberrations of the imaging optics. In the absence of significant aberrations, the smallest possible blur circle is the Airy disc, which is caused by diffraction from the optical system's aperture. Aberrations tend to get worse as the aperture diameter increases, while the Airy circle is smallest for large apertures.

Types

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. Lateral aberration is typical at short focal lengths. The ambiguous acronym LCA is sometimes used for either longitudinal or lateral chromatic aberration. [2]

Magnification process of enlarging something only in appearance, not in physical size

Magnification is the process of enlarging the apparent size, not physical size, of something. This enlargement is quantified by a calculated number also called "magnification". When this number is less than one, it refers to a reduction in size, sometimes called minification or de-magnification.

Distortion (optics) deviation from rectilinear projection (optics)

In geometric optics, distortion is a deviation from rectilinear projection; a projection in which straight lines in a scene remain straight in an image. It is a form of optical aberration.

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 photography, stopping down refers to increasing the numerical f-stop number, which decreases the size (diameter) of the aperture of a lens, resulting in reducing the amount of light entering the iris of a lens.

Depth of field Distance between the nearest and the furthest objects that are in focus in an image

Depth of field is the distance between the nearest and the furthest objects that are in acceptably sharp focus in an image. The depth of field is determined by focal length, distance to subject, the acceptable circle of confusion size, and aperture. A particular depth of field may be chosen for technical or artistic purposes. Some post-processing methods, such as focus stacking allow extended depth of field that would be impossible with traditional techniques.

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] ).

Aerial telescope very long focal length refracting telescope without a tube, built in the 17th century; the objective was mounted on a pole, tree, etc. on a swivel ball-joint; the observer stood on the ground and maneuvered the eyepiece to aim at celestial objects

An aerial telescope is a type of very long focal length refracting telescope, built in the second half of the 17th century, that did not use a tube. Instead, the objective was mounted on a pole, tree, tower, building or other structure on a swivel ball-joint. The observer stood on the ground and held the eyepiece, which was connected to the objective by a string or connecting rod. By holding the string tight and maneuvering the eyepiece, the observer could aim the telescope at objects in the sky. The idea for this type of telescope may have originated in the late 17th century with the Dutch mathematician, astronomer and physicist Christiaan Huygens and his brother Constantijn Huygens, Jr., though it is not clear if they actually invented it.

Isaac Newton Influential British physicist and mathematician

Sir Isaac Newton was an English mathematician, physicist, astronomer, theologian, and author who is widely recognised as one of the most influential scientists of all time, and a key figure in the scientific revolution. His book Philosophiæ Naturalis Principia Mathematica, first published in 1687, laid the foundations of classical mechanics. Newton also made seminal contributions to optics, and shares credit with Gottfried Wilhelm Leibniz for developing the infinitesimal calculus.

Spectrum Continuous range of values, such as wavelengths in physics

A spectrum is a condition that is not limited to a specific set of values but can vary, without steps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors in visible light after passing through a prism. As scientific understanding of light advanced, it came to apply to the entire electromagnetic spectrum.

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. Note that "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]

Achromatic lens optical instrument corrected for dispersion at 2 wavelengths

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.

Doublet (lens) type of lens made up of two simple lenses paired together

In optics, a doublet is a type of lens made up of two simple lenses paired together. Such an arrangement allows more optical surfaces, thicknesses, and formulations, especially as the space between lenses may be considered an "element." With additional degrees of freedom, optical designers have more latitude to correct more optical aberrations more thoroughly.

Crown glass (optics)

Crown glass is a type of optical glass used in lenses and other optical components. It has relatively low refractive index (≈1.52) and low dispersion. Crown glass is produced from alkali-lime silicates containing approximately 10% potassium oxide and is one of the earliest low dispersion glasses.

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 the optical microscope and in 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]

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
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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. [11] 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. [12]

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. [13] 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. [14]

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 a theoretically perfect post-processing based chromatic aberration reduction-removal-correction systems do not increase image detail 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. [15]

See also

Related Research Articles

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.

Refracting telescope 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 spy glasses 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.

Optical telescope telescope which is used to focus light from the visible part of the electromagnetic spectrum

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 view, or to make a photograph, or to collect data through electronic image sensors.

Reflecting telescope telescopes that reflect light with a combination of mirrors

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. Reflecting telescopes come in many design variations and may 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.

Apochromat

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.

Eyepiece type of lens attached to a variety of optical devices such as telescopes and microscopes; usually the lens that is closest to the eye when someone looks through the device, placed near the focal point of the objective to magnify the image

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 so named because it is usually the lens that is closest to the eye when someone looks through the device. The objective lens or mirror collects light and brings it to focus creating an image. The eyepiece is placed near the focal point of the objective to magnify this image. The amount of magnification depends on the focal length of the eyepiece.

The science of photography refers to the use of science, such as chemistry and physics, in all aspects of photography. This applies to the camera, its lenses, physical operation of the camera, electronic camera internals, and the process of developing film in order to take and develop pictures properly.

Catadioptric system 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.

Purple fringing

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.

Superachromat

The superachromat or superachromatic lens was first conceived and developed by Maximilian Herzberger as the ultimately well-corrected lens. The color shift curve of a superachromat is a quartic, meaning that in theory four separate colors can be brought to focus in the same plane, while simultaneously correcting spherical aberration and field aberrations. This near-perfect correction of chromatic aberration is highly beneficial in film and digital multi-spectral photography, as a superachromat can focus near-infrared energy in the 0.7 to 1.0 micrometer wavelength band in the same focal plane as visible light, eliminating the need for refocusing. Unfortunately, due to the limited selection of optical glasses and partial dispersion properties, superachromats must be manufactured with costly fluorite glasses and to very tight tolerances.

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.

Achromatic telescope type of refracting telescope

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 low dispersion. 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.

References

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