An achromatic lens or achromat is a lens

Lens (optics)

A lens is an optical device with perfect or approximate axial symmetry which transmits and refracts light, converging or diverging the beam. A simple lens consists of a single optical element...

 that is designed to limit the effects of chromatic

Chromatic aberration

In optics, chromatic aberration is a type of distortion in which there is a failure of a lens to focus all colors to the same convergence point. It occurs because lenses have a different refractive index for different wavelengths of light...

 and spherical aberration

Spherical aberration

thumb|right|Spherical aberration. A perfect lens focuses all incoming rays to a point on the [[Optical axis|optic axis]]. A real lens with spherical surfaces suffers from spherical aberration: it focuses rays more tightly if they enter it far from the optic axis than if they enter closer to the...

. Achromatic lenses are corrected to bring two wavelengths (typically red and blue) into focus in the same plane.

The most common type of achromat is the achromatic doublet

Doublet (lens)

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...

, which is composed of two individual lenses made from glass

Glass

Glass is an amorphous solid material. Glasses are typically brittle and optically transparent.The most familiar type of glass, used for centuries in windows and drinking vessels, is soda-lime glass, composed of about 75% silica plus Na2O, CaO, and several minor additives...

es with different amounts of dispersion

Dispersion (optics)

In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency, or alternatively when the group velocity depends on the frequency.Media having such a property are termed dispersive media...

. Usually one element is a concave lens made out of flint glass

Flint glass

Flint glass is optical glass that has relatively high refractive index and low Abbe number. Flint glasses are arbitrarily defined as having an Abbe number of 50 to 55 or less. The currently known flint glasses have refractive indices ranging between 1.45 and 2.00...

 such as F2, which has relatively high dispersion, while the other, convex, element is made of crown glass

Crown glass (optics)

Crown glass is type of optical glass used in lenses and other optical components. It has relatively low refractive index and low dispersion...

 such as BK7, which has lower dispersion; other low dispersion glass

Low dispersion glass

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

es may be used instead. 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 (illustrated at right), the positive power

Optical power

Optical power is the degree to which a lens, mirror, or other optical system converges or diverges light. It is equal to the reciprocal of the focal length of the device. The dioptre is the most common unit of measurement of optical 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

Wavelength

In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...

s of light to a common focus

Focus (optics)

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...

. 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

Isaac Newton

Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

's statement that such a correction was impossible (see History of the telescope). Credit for the invention of the first achromatic doublet is often given to an English barrister

Barrister

A barrister is a member of one of the two classes of lawyer found in many common law jurisdictions with split legal professions. Barristers specialise in courtroom advocacy, drafting legal pleadings and giving expert legal opinions...

 and amateur optician named Chester Moore Hall

Chester Moore Hall

Chester Moore Hall was a British lawyer and inventor who produced the first achromatic lenses in 1729 or 1733 ....

. Hall wished to keep his work on the achromatic lenses a secret and contracted the manufacture of the crown

Crown glass (optics)

Crown glass is type of optical glass used in lenses and other optical components. It has relatively low refractive index and low dispersion...

 and flint

Flint glass

Flint glass is optical glass that has relatively high refractive index and low Abbe number. Flint glasses are arbitrarily defined as having an Abbe number of 50 to 55 or less. The currently known flint glasses have refractive indices ranging between 1.45 and 2.00...

 lenses to two different opticians, Edward Scarlett and James Mann. They in turn sub-contracted the work to the same person, George Bass

George Bass (optician)

George Bass was an optician known to have made an achromatic doublet around 1733.The instructions for the constructions were given by Chester Moore Hall. According to Hoyle, Hall wished to keep his work on the achromatic lenses a secret and contracted the manufacture of the crown and flint lenses...

. He realized the two components were for the same client and, after fitting the two parts together, noted the achromatic properties. Hall failed to appreciate the importance of his invention, and it remained known to only a few opticians.

In the late 1750s, Bass mentioned Hall's lenses to John Dollond

John Dollond

John Dollond was an English optician, known for his successful optics business and his patenting and commercialization of achromatic doublets.-Biography:...

, 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

Peter Dollond

Peter Dollond was an English maker of optical instruments, the son of John Dollond. He is known for his successful optics business, and for the invention of the apochromat.-Biography:...

 invented the apochromat

Apochromat

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

, an improvement on the achromat, in 1763.

Types

Several different types of achromat have been devised. They differ in the shape of the included lenses as well as in the optical properties of their glass (most notably in their optical dispersion or Abbe number

Abbe number

In physics and optics, the Abbe number, also known as the V-number or constringence of a transparent material, is a measure of the material's dispersion in relation to the refractive index...

).

In the following, 'R' denotes the radius

Radius

In classical geometry, a radius of a circle or sphere is any line segment from its center to its perimeter. By extension, the radius of a circle or sphere is the length of any such segment, which is half the diameter. If the object does not have an obvious center, the term may refer to its...

 of the sphere

Sphere

A sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in two dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point...

s that define the optically relevant refracting

Refraction

Refraction is the change in direction of a wave due to a change in its speed. It is essentially a surface phenomenon . The phenomenon is mainly in governance to the law of conservation of energy. The proper explanation would be that due to change of medium, the phase velocity of the wave is changed...

 lens surfaces. By convention, R₁ denotes the first lens surface counted from the object. A doublet lens has four surfaces with radii R₁ to R₄.

Littrow doublet

Uses an equiconvex crown glass lens with R₁=R₂, and a second flint glass lens with R₃=-R₂. The back of the flint glass lens is flat. A Littrow doublet can produce a ghost image between R₂ and R₃ because the lens surfaces of the two lenses have the same radii. It may also produce a ghost image between the flat R₄ surface and rear of the telescope tube.

Fraunhofer doublet (Fraunhofer objective)

The first lens has positive refractive power, the second negative. R₁ is set greater than R₂, and R₂ is set close to, but not equal to, R₃. R₄ is usually greater than R₃. In a Fraunhofer doublet, the dissimilar curvatures of R₂ and R₃ are mounted in contact. This design yields more degrees of freedom (one more free radius, length of the air space) to correct for optical aberrations.

Clark doublet

Uses an equiconvex crown with R₁=R₂, and a flint with R₃≃R₂ and R₄≫R₃. R₃ is set slightly shorter than R₂ to create a focus mismatch between R₂ and R₃, thereby reducing ghosting between the crown and flint.

Oil-spaced doublet

The use of oil between the crown and flint eliminates the effect of ghosting, particularly where R₂=R₃. It can also increase light transmission slightly and reduce the impact of errors in R₂F and R₃.

Steinheil doublet

The Steinheil doublet, devised by Carl August von Steinheil

Carl August von Steinheil

Carl August von Steinheil was a German physicist, inventor, engineer and astronomer.-Biography:Steinheil was born in Ribeauvillé, Alsace. He studied law in Erlangen since 1821, then astronomy in Göttingen and Königsberg. He continued his studies in astronomy and physics when he started living on...

, 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 lens

Dialyte lens

A dialyte lens is a compound lens design that corrects optical aberrations where the lens elements are widely air-spaced. The design is used to save on the amount of glass used for specific elements or where elements can not be cemented because they have dissimilar curvatures...

es 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 R₂ and R₃ can not be cemented because they have dissimilar curvatures.

Design

The first-order design of an achromat involves choosing the overall power of the doublet and the two glasses to use. The choice of glass gives the mean refractive index, often written as (for the refractive index at the Fraunhofer

Fraunhofer

Fraunhofer, , may refer to:*Joseph von Fraunhofer , German physicist*Fraunhofer , a lunar crater*Fraunhofer Society , a large German research organization with 59 institutes throughout Germany...

 "d" spectral line wavelength

Abbe number

In physics and optics, the Abbe number, also known as the V-number or constringence of a transparent material, is a measure of the material's dispersion in relation to the refractive index...

), and the Abbe number

Abbe number

In physics and optics, the Abbe number, also known as the V-number or constringence of a transparent material, is a measure of the material's dispersion in relation to the refractive index...

  (for the reciprocal of the glass dispersion

Dispersion (optics)

In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency, or alternatively when the group velocity depends on the frequency.Media having such a property are termed dispersive media...

). To make the linear dispersion of the system zero, the system must satisfy the equations


where the lens power

Optical power

Optical power is the degree to which a lens, mirror, or other optical system converges or diverges light. It is equal to the reciprocal of the focal length of the device. The dioptre is the most common unit of measurement of optical power...

 is for a lens with focal length

Focal length

The focal length of an optical system is a measure of how strongly the system converges or diverges light. For an optical system in air, it is the distance over which initially collimated rays are brought to a focus...

 . Solving these two equations for and gives


Since , and the Abbe number

Abbe number

In physics and optics, the Abbe number, also known as the V-number or constringence of a transparent material, is a measure of the material's dispersion in relation to the refractive index...

s are positive-valued, the power of the second element in the doublet is negative when the first element is positive.