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An achromatic lens or achromat is a
lens A lens is a transmissive optical device which 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 ...
that is designed to limit the effects of
chromatic Diatonic and chromatic are terms in music theory that are most often used to characterize scales, and are also applied to musical instruments, intervals, chords, notes, musical styles, and kinds of harmony. They are very often used as a p ...
and
spherical aberration In optics, spherical aberration (SA) is a type of aberration found in optical systems that have elements with spherical surfaces. Lenses and curved mirrors are prime examples, because this shape is easier to manufacture. Light rays that strik ...
. Achromatic lenses are corrected to bring two wavelengths (typically red and blue) into focus on the same plane. The most common type of achromat is the achromatic doublet, which is composed of two individual lenses made from
glass Glass is a non- crystalline, often transparent, amorphous solid that has widespread practical, technological, and decorative use in, for example, window panes, tableware, and optics. Glass is most often formed by rapid cooling (quenchin ...
es with different amounts of
dispersion Dispersion may refer to: Economics and finance *Dispersion (finance), a measure for the statistical distribution of portfolio returns *Price dispersion, a variation in prices across sellers of the same item *Wage dispersion, the amount of variatio ...
. Typically, one element is a negative (
concave Concave or concavity may refer to: Science and technology * Concave lens * Concave mirror Mathematics * Concave function, the negative of a convex function * Concave polygon, a polygon which is not convex * Concave set In geometry, a subset o ...
) element made out of
flint glass Flint glass is optical glass that has relatively high refractive index and low Abbe number (high dispersion). Flint glasses are arbitrarily defined as having an Abbe number of 50 to 55 or less. The currently known flint glasses have refractiv ...
such as F2, which has relatively high dispersion, and the other is a positive (
convex Convex or convexity may refer to: Science and technology * Convex lens, in optics Mathematics * Convex set, containing the whole line segment that joins points ** Convex polygon, a polygon which encloses a convex set of points ** Convex polytop ...
) element made of crown glass such as BK7, which has lower dispersion. The lens elements are mounted next to each other, often cemented together, and shaped so that the chromatic aberration of one is counterbalanced by that of the other. In the most common type (shown), the positive power of the crown lens element is not quite equalled by the negative power of the flint lens element. Together they form a weak positive lens that will bring two different
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tr ...
s of light to a common focus. Negative doublets, in which the negative-power element predominates, are also made.


History

Theoretical considerations of the feasibility of correcting chromatic aberration were debated in the 18th century following Newton's statement that such a correction was impossible (see
History of the telescope The history of the telescope can be traced to before the invention of the earliest known telescope, which appeared in 1608 in the Netherlands, when a patent was submitted by Hans Lippershey, an eyeglass maker. Although Lippershey did not rec ...
). Credit for the invention of the first achromatic doublet is often given to an English
barrister A barrister is a type of lawyer in common law jurisdictions. Barristers mostly specialise in courtroom advocacy and litigation. Their tasks include taking cases in superior courts and tribunals, drafting legal pleadings, researching law and givin ...
and amateur optician named Chester Moore Hall.Daumas, Maurice, ''Scientific Instruments of the Seventeenth and Eighteenth Centuries and Their Makers'', Portman Books, London 1989 Hall wished to keep his work on the achromatic lenses a secret and contracted the manufacture of the crown and
flint Flint, occasionally flintstone, is a sedimentary cryptocrystalline form of the mineral quartz, categorized as the variety of chert that occurs in chalk or marly limestone. Flint was widely used historically to make stone tools and start ...
lenses to two different opticians, Edward Scarlett and James Mann. – A review of the events of the invention of the achromatic doublet with emphasis on the roles of Hall, Bass, John Dollond and others. They in turn sub-contracted the work to the same person,
George Bass George Bass (; 30 January 1771 – after 5 February 1803) was a British naval surgeon and explorer of Australia. Early years Bass was born on 30 January 1771 at Aswarby, a hamlet near Sleaford, Lincolnshire, the son of a tenant farmer, George ...
. He realized the two components were for the same client and, after fitting the two parts together, noted the achromatic properties. Hall used the achromatic lens to build the first achromatic telescope, but his invention did not become widely known at the time. In the late 1750s, Bass mentioned Hall's lenses to John Dollond, who understood their potential and was able to reproduce their design. Dollond applied for and was granted a patent on the technology in 1758, which led to bitter fights with other opticians over the right to make and sell achromatic doublets. Dollond's son Peter invented the apochromat, an improvement on the achromat, in 1763.


Types

Several different types of achromat have been devised. They differ in the shape of the included lens elements as well as in the optical properties of their glass (most notably in their
optical dispersion In optics, and by analogy other branches of physics dealing with wave propagation, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency; sometimes the term chromatic dispersion is used for specificity to o ...
or Abbe number). In the following, ''R'' denotes the
radius In classical geometry, a radius (plural, : radii) of a circle or sphere is any of the line segments from its Centre (geometry), center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin ''radius'', ...
of the
sphere A sphere () is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance from a given point in three-dimensional space.. That given point is the c ...
s that define the optically relevant
refracting In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomeno ...
lens surfaces. By convention, ''R''1 denotes the first lens surface counted from the object. A doublet lens has four surfaces with radii ''R''1 to ''R''4.


Littrow doublet

Uses an equiconvex crown glass lens with , and a second flint glass lens with . The back of the flint glass lens is flat. A Littrow doublet can produce a ghost image between ''R''2 and ''R''3 because the lens surfaces of the two lenses have the same radii.


Fraunhofer doublet (Fraunhofer objective)

The first lens has positive refractive power, the second negative. ''R''1 is set greater than ''R''2, and ''R''2 is set close to, but not equal to, ''R''3. ''R''4 is usually greater than ''R''3. In a Fraunhofer doublet, the dissimilar curvatures of ''R''2 and ''R''3 are mounted close, but not in contact. This design yields more degrees of freedom (one more free radius, length of the air space) to correct for
optical aberration 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 t ...
s.


Clark doublet

Early Clark lenses follow the Fraunhofer design. After the late 1860s, they changed to the Littrow design, approximately equiconvex crown, , and a flint with and . By about 1880, Clark lenses had ''R''3 set slightly shorter than ''R''2 to create a focus mismatch between ''R''2 and ''R''3, thereby avoiding ghosting caused by reflections within the airspace.


Oil-spaced doublet

The use of oil between the crown and flint eliminates the effect of ghosting, particularly where . It can also increase light transmission slightly and reduce the impact of errors in ''R''2 and ''R''3.


Steinheil doublet

The Steinheil doublet, devised by
Carl August von Steinheil Carl August von Steinheil (12 October 1801 – 14 September 1870) was a German physicist, inventor, engineer and astronomer. Biography Steinheil was born in Ribeauvillé, Alsace. He studied law in Erlangen since 1821. He then studied astronomy ...
, is a flint-first doublet. In contrast to the Fraunhofer doublet, it has a negative lens first followed by a positive lens. It needs stronger curvature than the Fraunhofer doublet.


Dialyte

Dialyte lenses have a wide air space between the two elements. They were originally devised in the 19th century to allow much smaller flint glass elements down stream since flint glass was hard to produce and expensive. They are also lenses where the elements can not be cemented because ''R''2 and ''R''3 have different absolute values.Fred A. Carson, Basic optics and optical instruments, page AJ-4


Design

The first-order design of an achromat involves choosing the overall power \phi_ of the doublet and the two glasses to use. The choice of glass gives the mean refractive index, often written as n_d (for the refractive index at the Fraunhofer "d" spectral line wavelength), and the Abbe number V (for the reciprocal of the glass
dispersion Dispersion may refer to: Economics and finance *Dispersion (finance), a measure for the statistical distribution of portfolio returns *Price dispersion, a variation in prices across sellers of the same item *Wage dispersion, the amount of variatio ...
). To make the linear dispersion of the system zero, the system must satisfy the equations :\begin \phi_1 + \phi_2 &= \phi_ \\ \frac + \frac &= 0 \ ,\end where the lens power is \phi = 1/f for a lens with
focal length The focal length of an optical system is a measure of how strongly the system converges or diverges light; it is the inverse of the system's optical power. A positive focal length indicates that a system converges light, while a negative foc ...
f. Solving these two equations for \phi_1 and \phi_2 gives :\frac = \frac \qquad \text \qquad \frac = \frac \ . Since \phi_2 = -\phi_1 V_2 / V_1, and the Abbe numbers are positive-valued, the power of the second element in the doublet is negative when the first element is positive.


Further color correction

Lens designs more complex than achromatic can improve the precision of color images by bringing more wavelengths into exact focus, but require more expensive types of glass, and more careful shaping and spacing of the combination of simple lenses: ; apochromatic lenses: bring ''three'' wavelengths into a common focus and requires costly materials ; superachromatic lenses: bring ''four'' wavelengths into focus and must be manufactured with even more expensive fluoride glass and to considerably tighter tolerances In theory, the process can continue indefinitely: Compound lenses used in
camera A camera is an optical instrument that can capture an image. Most cameras can capture 2D images, with some more advanced models being able to capture 3D images. At a basic level, most cameras consist of sealed boxes (the camera body), with ...
s typically have six or more simple lenses (e.g. double-Gauss lens); several of those lenses can be made with different types of glass, with slightly altered curvatures, in order to bring more colors into focus. The constraint is extra manufacturing cost, and
diminishing returns In economics, diminishing returns are the decrease in marginal (incremental) output of a production process as the amount of a single factor of production is incrementally increased, holding all other factors of production equal ( ceteris pari ...
of improved image for the effort.


See also

* Barlow lens


References


External links

*{{Commons category inline Lenses