In optics, chromatic aberration is a failure of a lens to focus all colors to the same point. 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. Since the focal length of a lens depends on the refractive index, this variation in refractive index affects focusing. Chromatic aberration manifests itself as "fringes" of color along boundaries that separate dark and bright parts of the image. There are two types of chromatic aberration: axial, transverse. Axial aberration occurs when different wavelengths of light are focused at different distances from the lens. 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 varies with wavelength. Lateral aberration is typical at short focal lengths.

The ambiguous acronym LCA is sometimes used for either lateral chromatic aberration. The two types of chromatic aberration have different characteristics, may occur together. Axial CA occurs throughout the image and is specified by optical engineers and vision scientists in diopters, 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 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, difficult to remedy in post-processing, while transverse CA results in the red and blue planes being at different magnifications, can be corrected by radially scaling the planes appropriately so they line up. 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 long telescopes such as the 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. 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 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, not the degree, an achromat made with sufficiently low dispersion glass can yield better correction than an achromat made with more conventional glass.

The benefit of apochromats is not that they focus three wavelengths but that their error on other wavelengths is quite small. Many types of glass have been developed to reduce chromatic aberration; these are low. These hybridized glasses have a low level of optical dispersion; 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, flat. Diffractive optical elements have negative dispersion characteristics, complementary to the positive Abbe numbers of optical glasses and plastics. 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. 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 are f1 and f2 best correction occurs for the condition: f 1 ⋅ V 1 + f 2 ⋅ 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: 1 f = 1 f 1 + 1 f 2 and the above condition ensures this will be the focal length of the doublet for light at the blue and red F

An annular solar eclipse occurred on September 7, 1820. A solar eclipse occurs when the Moon passes between Earth and the Sun, thereby or obscuring the image of the Sun for a viewer on Earth. An annular solar eclipse occurs when the Moon's apparent diameter is smaller than the Sun's, blocking most of the Sun's light and causing the Sun to look like an annulus. An annular eclipse appears as a partial eclipse over a region of the Earth thousands of kilometres wide; this map was drawn in the book Elementa eclipsium, published in Prague in 1816, by Franz Ignaz Cassian Hallaschka, contained maps of the paths of solar eclipses from 1816 and 1860. The geometric constructions used by Hallaschka anticipated the standard theory of eclipses developed by Friedrich Wilhelm Bessel, it is a part of solar Saros 122. NASA chart graphics Googlemap NASA Besselian elements Cassian Hallaschka. Elementa eclipsium, quas patitur tellus, luna eam inter et solem versante ab anno 1816 usque ad annum 1860: ex tabulis astronomicis recentissime conditis et calculo parallactico deducta, typo ecliptico et tabulis proiectionis geographicis collustrata.

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Linda Howell is a former professional tennis player from the United States. Howell played collegiate tennis at San Diego State University in the 1980s, during which time she competed on the professional tour, she joined San Diego State in 1982 and in 1984 was a NCAA doubles semi-finalist with Cynthia MacGregor. At the 1984 US Open she featured in the main draw of a grand slam tournament for the first time and was beaten in the opening round by Helena Suková. A month she was a quarter-finalist at a Virginia Slims event back in San Diego at the end of the year she went overseas to compete in Australia, she was unable to qualify for the Australian Open but played at the 1984 NSW Open, where she lost a three-set match to Steffi Graf. The following year at the 1985 Wimbledon Championships she featured in both the women's doubles and mixed doubles main draws, she had a small role in the 1990 film Total Recall starring Arnold Schwarzenegger, as the tennis instructor hologram being used by the character played by Sharon Stone.

Now living in New Mexico, she has a career in a different sport, working as the head PGA professional at Rockwind Community Links in Hobbs. Linda Howell at the Women's Tennis Association Linda Howell at the International Tennis Federation