Lenz's law: Difference between revisions
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[[Image:Chromatic abberation lens diagram.svg|thumb|right|Chromatic aberration of a single lens causes different wavelengths of light to have differing focal lengths.]] | |||
[[File:Lens6b-en.svg|thumb|right|An '''achromatic doublet''' brings red and blue light to the same focus, and is the earliest example of an achromatic lens.]] | |||
[[File:Achromatic focal curve.svg|thumb|right|In an achromatic lens, two wavelengths are brought into the same focus, here red and blue.]] | |||
An '''achromatic lens''' or '''achromat''' is a [[lens (optics)|lens]] that is designed to limit the effects of [[chromatic aberration|chromatic]] and [[spherical aberration]]. 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 (lens)|doublet]]''', which is composed of two individual lenses made from [[glass]]es with different amounts of [[Dispersion (optics)|dispersion]]. Typically, one element is a negative ([[Lens (optics)#Types of simple lenses|concave]]) element made out of [[flint glass]] such as F2, which has relatively high dispersion, and the other is a positive ([[Lens (optics)#Types of simple lenses|convex]]) element made of [[Crown glass (optics)|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 [[Optical power|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]]s of light to a common [[focus (optics)|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 [[Isaac Newton|Newton]]'s statement that such a correction was impossible (see [[History of the telescope#Achromatic refracting telescopes|History of the telescope]]). Credit for the invention of the first achromatic doublet is often given to an English [[barrister]] and amateur optician named [[Chester Moore Hall]].<ref name="daumas">Daumas, Maurice, ''Scientific Instruments of the Seventeenth and Eighteenth Centuries and Their Makers'', Portman Books, London 1989 ISBN 978-0-7134-0727-3</ref><ref name=Stargazer>{{cite book |url=http://books.google.com/books?id=2LZZginzib4C&pg=PA140 |title=Stargazer: the life and times of the telescope |first=Fred |last=Watson |publisher=Allen & Unwin |year=2007 |pages=140–55 |isbn=978-1-74175-383-7}}</ref> Hall wished to keep his work on the achromatic lenses a secret and contracted the manufacture of the [[Crown glass (optics)|crown]] and [[flint glass|flint]] lenses to two different opticians, Edward Scarlett and James Mann.<ref>Fred Hoyle, ''Astronomy; A history of man's investigation of the universe'', Rathbone Books, 1962, LC 62-14108</ref><ref>{{cite web |url=http://www.mhs.ox.ac.uk/sphaera/index.htm?issue8/articl5 |title=Sphaera—Peter Dollond answers Jesse Ramsden |accessdate=July 31, 2009}} A review of the events of the invention of the achromatic doublet with emphasis on the roles of Hall, Bass, John Dollond and others.</ref><ref>{{cite book |title=Techniques in microscopy for biomedical applications |first1=Terje |last1=Dokland |first2=Mary Mah-Lee |last2=Ng |page=23 |year=2006 |isbn=981-256-434-9 |url=http://books.google.com/books?id=Ix3G9_Rr0EAC&pg=PA23&lpg=PA23&dq=achromatic+lens+subcontract#v=onepage&q=&f=false |accessdate=July 31, 2009}}</ref> They in turn sub-contracted the work to the same person, [[George Bass (optician)|George Bass]]. 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]], who understood their potential and was able to reproduce their design.<ref name=Stargazer/> 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 Dollond|Peter]] invented the [[apochromat]], an improvement on the achromat, in 1763.<ref name=Stargazer/> | |||
==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]] or [[Abbe number]]). | |||
In the following, 'R' denotes the [[radius]] of the [[sphere]]s that define the optically relevant [[refraction|refracting]] lens surfaces. By convention, R<sub>1</sub> denotes the first lens surface counted from the object. A doublet lens has four surfaces with radii R<sub>1</sub> to R<sub>4</sub>. | |||
===Littrow doublet=== | |||
Uses an equiconvex crown glass lens with R<sub>1</sub>=R<sub>2</sub>, and a second flint glass lens with R<sub>3</sub>=-R<sub>2</sub>. The back of the flint glass lens is flat. A Littrow doublet can produce a ghost image between R<sub>2</sub> and R<sub>3</sub> because the lens surfaces of the two lenses have the same radii. It may also produce a ghost image between the flat R<sub>4</sub> surface and rear of the telescope tube. | |||
===Fraunhofer doublet (Fraunhofer objective)=== | |||
The first lens has positive refractive power, the second negative. R<sub>1</sub> is set greater than R<sub>2</sub>, and R<sub>2</sub> is set close to, but not equal to, R<sub>3</sub>. R<sub>4</sub> is usually greater than R<sub>3</sub>. In a Fraunhofer doublet, the dissimilar curvatures of R<sub>2</sub> and R<sub>3</sub> are mounted close, but not in contact.<ref>[http://books.google.com/books?id=0xxV3zbafeYC&pg=PA38&dq=Fraunhofer+dialyte&hl=en&ei=-JkHTYniEYH-8Aax9tjwDA&sa=X&oi=book_result&ct=result&resnum=8&ved=0CEQQ6AEwBw#v=onepage&q=Fraunhofer%20dialyte&f=false William L. Wolfe, Optics made clear: the nature of light and how we use it, page 38]</ref> This design yields more degrees of freedom (one more free radius, length of the air space) to correct for [[optical aberration]]s. | |||
===Clark doublet=== | |||
Uses an equiconvex crown with R<sub>1</sub>=R<sub>2</sub>, and a flint with R<sub>3</sub>≃R<sub>2</sub> and R<sub>4</sub>≫R<sub>3</sub>. R<sub>3</sub> is set slightly shorter than R<sub>2</sub> to create a focus mismatch between R<sub>2</sub> and R<sub>3</sub>, 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 R<sub>2</sub>=R<sub>3</sub>. It can also increase light transmission slightly and reduce the impact of errors in R<sub>2</sub> and R<sub>3</sub>. | |||
===Steinheil doublet=== | |||
The Steinheil doublet, devised by [[Carl August von Steinheil]], 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.<ref>Kidger, M.J. (2002) Fundamental Optical Design. SPIE Press, Bellingham, WA, pp. 174ff</ref> | |||
===Dialyte=== | |||
[[Dialyte lens]]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.<ref>[http://books.google.com/books?id=p282ijnF3C0C&pg=PA55&lpg=PA55&dq=dialyte+lens+telescope&source=bl&ots=ukPf6xKIDW&sig=WWZdN_FqeR4OElFXFhDdUH6z7Iw&hl=en&ei=zWz8S5r9OYH7lwff05TfDw&sa=X&oi=book_result&ct=result&resnum=8&ved=0CC4Q6AEwBzgK#v=onepage&q=dialyte%20lens%20telescope&f=false Peter L. Manly, Unusual Telescopes, page 55]</ref> They are also lenses where R<sub>2</sub> and R<sub>3</sub> can not be cemented because they have dissimilar curvatures.<ref>Fred A. Carson, Basic optics and optical instruments, page AJ-4</ref> | |||
==Design== | |||
The first-order design of an achromat involves choosing the overall power <math>\phi_{\text{sys}}</math> of the doublet and the two glasses to use. The choice of glass gives the mean refractive index, often written as <math>n_d</math> (for the refractive index at the [[Fraunhofer]] [[Abbe number|"d" spectral line wavelength]]), and the [[Abbe number]] <math>V</math> (for the reciprocal of the glass [[dispersion (optics)|dispersion]]). To make the linear dispersion of the system zero, the system must satisfy the equations | |||
:<math>\begin{align} \phi_1 + \phi_2 &= \phi_{\text{sys}} \\ \frac{\phi_1}{V_1} + \frac{\phi_2}{V_2} &= 0 \ ,\end{align}</math> | |||
where the [[optical power|lens power]] is <math>\phi = 1/f</math> for a lens with [[focal length]] <math>f</math>. Solving these two equations for <math>\phi_1</math> and <math>\phi_2</math> gives | |||
:<math>\frac{\phi_1}{\phi_{\text{sys}}} = \frac{V_1}{V_1 - V_2} \qquad \text{and} \qquad \frac{\phi_2}{\phi_{\text{sys}}} = \frac{-V_2}{V_1 - V_2} \ .</math> | |||
Since <math>\phi_2 = -\phi_1 V_2 / V_1</math>, and the [[Abbe number]]s are positive-valued, the power of the second element in the doublet is negative when the first element is positive. | |||
==See also== | |||
{{Comparison_chromatic_focus_shift_plots.svg}} | |||
* [[Achromatic telescope]] | |||
* [[Superachromat]] | |||
==References== | |||
{{reflist|30em}} | |||
[[Category:Lenses]] |
Revision as of 18:07, 25 January 2014
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 (typically red and blue) into focus in the same plane.
The most common type of achromat is the achromatic doublet, which is composed of two individual lenses made from glasses with different amounts of dispersion. Typically, one element is a negative (concave) element made out of flint glass such as F2, which has relatively high dispersion, and the other is a positive (convex) 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 wavelengths 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). Credit for the invention of the first achromatic doublet is often given to an English barrister and amateur optician named Chester Moore Hall.[1][2] Hall wished to keep his work on the achromatic lenses a secret and contracted the manufacture of the crown and flint lenses to two different opticians, Edward Scarlett and James Mann.[3][4][5] They in turn sub-contracted the work to the same person, George Bass. 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, who understood their potential and was able to reproduce their design.[2] 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.[2]
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 or Abbe number).
In the following, 'R' denotes the radius of the spheres that define the optically relevant refracting 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 close, but not in contact.[6] 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 R2 and R3.
Steinheil doublet
The Steinheil doublet, devised by Carl August von Steinheil, 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.[7]
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.[8] They are also lenses where R2 and R3 can not be cemented because they have dissimilar curvatures.[9]
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 "d" spectral line wavelength), and the Abbe number (for the reciprocal of the glass dispersion). To make the linear dispersion of the system zero, the system must satisfy the equations
where the lens power is for a lens with focal length . Solving these two equations for and gives
Since , and the Abbe numbers are positive-valued, the power of the second element in the doublet is negative when the first element is positive.
See also
Template:Comparison chromatic focus shift plots.svg
References
43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.
- ↑ Daumas, Maurice, Scientific Instruments of the Seventeenth and Eighteenth Centuries and Their Makers, Portman Books, London 1989 ISBN 978-0-7134-0727-3
- ↑ 2.0 2.1 2.2 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ Fred Hoyle, Astronomy; A history of man's investigation of the universe, Rathbone Books, 1962, LC 62-14108
- ↑ Template:Cite web A review of the events of the invention of the achromatic doublet with emphasis on the roles of Hall, Bass, John Dollond and others.
- ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ William L. Wolfe, Optics made clear: the nature of light and how we use it, page 38
- ↑ Kidger, M.J. (2002) Fundamental Optical Design. SPIE Press, Bellingham, WA, pp. 174ff
- ↑ Peter L. Manly, Unusual Telescopes, page 55
- ↑ Fred A. Carson, Basic optics and optical instruments, page AJ-4