Optical Dispersion physics and clever optical techniques to cancel it in microscope/telescope optics

[Emmy Noether]

Subject - Optical Dispersion physics and clever optical techniques to
cancel it in microscope/telescope optics

groups - sci.techniques.microscopy, sci.optics,
sci.physics,sci.materials,sci.math
multidisciplinary , optics, micrscopy, physics of dispersion,
materials science of glass, geometrical tricks of math


Material dispersion in optics
The variation of refractive index vs. vacuum wavelength for various
glasses. The wavelengths of visible light are shaded in red.
Influences of selected glass component additions on the mean
dispersion of a specific base glass (nF valid for λ = 486 nm (blue),
nC valid for λ = 656 nm (red))[2]

Material dispersion can be a desirable or undesirable effect in
optical applications. The dispersion of light by glass prisms is used
to construct spectrometers and spectroradiometers. Holographic
gratings are also used, as they allow more accurate discrimination of
wavelengths. However, in lenses, dispersion causes chromatic
aberration, an undesired effect that may degrade images in
microscopes, telescopes and photographic objectives.

The phase velocity, v, of a wave in a given uniform medium is given by

v = \frac{c}{n}

where c is the speed of light in a vacuum and n is the refractive
index of the medium.

In general, the refractive index is some function of the frequency f
of the light, thus n = n(f), or alternatively, with respect to the
wave's wavelength n = n(λ). The wavelength dependence of a material's
refractive index is usually quantified by its Abbe number or its
coefficients in an empirical formula such as the Cauchy or Sellmeier
equations.

Because of the Kramers–Kronig relations, the wavelength dependence of
the real part of the refractive index is related to the material
absorption, described by the imaginary part of the refractive index
(also called the extinction coefficient). In particular, for non-
magnetic materials (μ = μ0), the susceptibility χ that appears in the
Kramers–Kronig relations is the electric susceptibility χe = n2 − 1.

The most commonly seen consequence of dispersion in optics is the
separation of white light into a color spectrum by a prism. From
Snell's law it can be seen that the angle of refraction of light in a
prism depends on the refractive index of the prism material. Since
that refractive index varies with wavelength, it follows that the
angle that the light is refracted by will also vary with wavelength,
causing an angular separation of the colors known as angular
dispersion.

For visible light, refraction indices n of most transparent materials
(e.g., air, glasses) decrease with increasing wavelength λ:

1 < n(\lambda_{\rm red}) < n(\lambda_{\rm yellow}) <
n(\lambda_{\rm blue})\ ,

or alternatively:

\frac{{\rm d}n}{{\rm d}\lambda} < 0.

In this case, the medium is said to have normal dispersion. Whereas,
if the index increases with increasing wavelength (which is typically
the case for X-rays), the medium is said to have anomalous dispersion.

At the interface of such a material with air or vacuum (index of ~1),
Snell's law predicts that light incident at an angle θ to the normal
will be refracted at an angle arcsin(sin(θ)/n). Thus, blue light, with
a higher refractive index, will be bent more strongly than red light,
resulting in the well-known rainbow pattern.


more at http://en.wikipedia.org/wiki/Dispersion_%28optics%29


Cauchy's equation
From Wikipedia, the free encyclopedia
Not to be confused with Cauchy's functional equation.
Refractive index vs. wavelength for BK7 glass. Red crosses show
measured values. Over the visible region (red shading), Cauchy's
equation (blue line) agrees well with the measured refractive indices
and the Sellmeier plot (green dashed line). It deviates in the
ultraviolet and infrared regions.

Cauchy's equation is an empirical relationship between the refractive
index and wavelength of light for a particular transparent material.
It is named for the mathematician Augustin Louis Cauchy, who defined
it in 1836.
[edit] The equation

The most general form of Cauchy's equation is

n(\lambda) = A + \frac {B}{\lambda^2} + \frac{C}{\lambda^4} +
\cdots,

where n is the refractive index, λ is the wavelength, A, B, C, etc.,
are coefficients that can be determined for a material by fitting the
equation to measured refractive indices at known wavelengths. The
coefficients are usually quoted for λ as the vacuum wavelength in
micrometres.

Usually, it is sufficient to use a two-term form of the equation:

n(\lambda) = A + \frac{B}{\lambda^2},

where the coefficients A and B are determined specifically for this
form of the equation.

A table of coefficients for common optical materials is shown below:
Material A B (μm2)
Fused silica 1.4580 0.00354
Borosilicate glass BK7 1.5046 0.00420
Hard crown glass K5 1.5220 0.00459
Barium crown glass BaK4 1.5690 0.00531
Barium flint glass BaF10 1.6700 0.00743
Dense flint glass SF10 1.7280 0.01342

The theory of light-matter interaction on which Cauchy based this
equation was later found to be incorrect. In particular, the equation
is only valid for regions of normal dispersion in the visible
wavelength region. In the infrared, the equation becomes inaccurate,
and it cannot represent regions of anomalous dispersion. Despite this,
its mathematical simplicity makes it useful in some applications.

The Sellmeier equation is a later development of Cauchy's work that
handles anomalously dispersive regions, and more accurately models a
material's refractive index across the ultraviolet, visible, and
infrared spectrum.
[edit] References

F.A. Jenkins and H.E. White, Fundamentals of Optics, 4th ed.,
McGraw-Hill, Inc. (1981).

[edit] See also

Sellmeier equation


http://en.wikipedia.org/wiki/Cauchy%27s_equation





Also

1. E. L. McCarthy, “Optical system with corrected secondary spectrum,”
U.S. Patent No.
2,698,555 (4 January 1955).
2. C. G. Wynne, “Secondary spectrum correction with normal glasses,”
Opt. Commun.
21, 419–424 (1977).
3. C. G. Wynne, “A comprehensive first-order theory of chromatic
aberration Secondary
spectrum correction without special glasses,” Opt. Acta 25, 627–636
(1978).
4. M. Rosete-Aguilar, “Correction of secondary spectrum using standard
glasses,” in Design
and Engineering of Optical Systems, J. J. Braat, ed., Proc. SPIE 2774,
378–386 (1996).
5. M. Rosete-Aguilar, “Application of the extended first-order
chromatic theory to the
correction of secondary spectrum,” Revista Mexicana de F´ısica 43, 895–
905 (1997).
6. M. J. Kidger, Intermediate Optical Design (SPIE Press, Bellingham,
2004), pp. 109–112.


In order to correct secondary longitudinal chromatic aberration in
conventional
refracting optical systems it is necessary to use at least one optical
material having anomalous partial dispersion. This paper presents a
novel lens
system with correction of secondary spectrum by using only normal
glasses.
The lens system comprises three widely separated lens components, both
second
and third components are subaperture. The presented example of an
apochromatic
telescope demonstrates secondary spectrum correction with the use
of only crown BK7 and flint F2, which are among the most inexpensive
optical
glasses available at the market. Two more similar designs are
presented, both
with the use of low-cost slightly anomalous dispersion glasses. These
telescopes
have a higher relative aperture and a smaller tertiary spectrum.

[Emmy Noether]

> more athttp://en.wikipedia.org/wiki/Dispersion_%28optics%29

Why does fluorite have low dispersion ? How is dispersion of a
compound depend on electron density of electrons in inner orbitals and
bonding orbitals as well as the ion hardnesses ?


Variants

Some glasses have a peculiar property called anomalous partial
dispersion. Their use in long focal length lens assemblies was
pioneered by Leitz. Before their availability, calcium fluoride in the
form of fluorite crystals were used as material for these lenses;
however the low refraction index of calcium fluoride required high
curvatures of the lenses, therefore increasing spherical aberration.
Fluorite also has poor shape retention and is very fragile. Abnormal
dispersion is required for design of apochromat lenses.[4]

Glass with addition of thorium dioxide has high refraction and low
dispersion and was in use since before World War II (WW2), but its
radioactivity led to its replacement with other compositions. Even
during WW2, Kodak managed to make high-performance thorium-free
optical glass for use in aerial photography, but it was yellow-tinted.
In combination with black and white film, the tint was actually
beneficial acting as a photographic filter improving contrast.

Leitz laboratories discovered that lanthanum(III) oxide can be a
suitable thorium dioxide replacement. Other elements however had to be
added to preserve the amorphous character of the glass and prevent
crystallization that would cause striae defects.

After 1930, George W. Morey introduced the lanthanum oxide and oxides
of other rare earth elements in borate glasses, greatly expanding the
available range of high-index low-dispersion glasses. Borate glasses
have lower wavelength-refraction dependence in the blue region of
spectrum than silicate glasses with the same Abbe number. These so
called "borate flint" glasses, or KZFS, are however highly susceptible
to corrosion by acids, alkalis, and weather factors. However borate
glass with more than 20 mol.% of lanthanum oxide is very durable under
ambient conditions.[5] The use of rare earths allowed development of
high-index low-dispersion glasses of both crown and flint types.[6]

Another high-performance glass contains high content of zirconium
dioxide; however its high melting point requires use of platinum lined
crucibles to prevent contamination with crucible material.

A good high-refraction replacement for calcium fluoride as a lens
material can be a fluorophosphate glass. Here, a proportion of
fluorides is stabilized with a metaphosphate, with addition of
titanium dioxide. [7]

Several of the mentioned high-performance glasses are expensive
because highly pure chemicals must be produced in substantial
quantities.


http://en.wikipedia.org/wiki/Low_dispersion_glass

This is very old technology and knowledge so be generous ...........

[Emmy Noether]

Biography

Working together with his father and subsequently with his younger
brother and nephew (George Dollond) he successfully designed and
manufactured a number of optical instruments. He is particularly
credited with the invention of the triple achromatic lens in 1763,
still in wide use today,[1][2] though known as the Cooke triplet after
a much later 1893 patent.

Peter Dollond worked at first silk weaving with his father, but his
father's passion for optics inspired him so much that in 1750 Peter
quit the silk business and opened an optical instruments shop in
Kennington, London. After two years, his father gave up silk, too, and
joined him.

Dollond telescopes, for sidereal or terrestrial use, were amongst the
most popular in both Great Britain and abroad for a period of over one
and half centuries. Admiral Lord Nelson himself owned one. Another had
sailed with Captain Cook in 1769 to observe the Transit of Venus.

The Peter Dollond compound chest microscope is based on improvements
to the Cuff-style microscope introduced by British scientific
instrument designers Edward Nairne and Thomas Blunt around 1780.
Another design was for the Peter Dollond compound monocular Eriometer
around 1790 used to accurately measure the thickness and size of wool
fibres.

After successfully defending a legal challenge to the patent he held
for the achromatic lens the business prospered and he successfully
sued his rivals for patent infringement.[2] Dollond's reputation,
especially with his father being a Fellow of the Royal Society as a
result of his invention of the achromat, provided the company with the
de facto right of refusal on the best optical flint glass.[3] This
privilege permitted Dollond to maintain an edge in quality over
competitor's telescopes and optical instruments for many years.

Notable customers also included:[2]

* Leopold Mozart
* Frederick the Great
* Thomas Jefferson

Dollond & Co merged with Aitchison & Co in 1927 to form Dollond &
Aitchison, the well-known British high street chain of opticians.

http://en.wikipedia.org/wiki/Peter_Dollond

The Apochromatic lens is usually of three elements and brings light of
three different frequencies to a common focus

http://en.wikipedia.org/wiki/Apochromat

Cooke triplet

From Wikipedia, the free encyclopedia

Jump to: navigation, search
Cooke triplet
Cooke.png
Introduced in: 1893
Author: Dennis Taylor
Construction: 3 elements in 3 groups
Aperture: f/3.5 (early)
f/2.8 (rare-earth optical glass)

The Cooke triplet is a photographic lens designed and patented (patent
number GB 22,607) in 1893 by Dennis Taylor who was employed as chief
engineer by T. Cooke & Sons of York. It was the first lens system that
allowed elimination of most of the optical distortion or aberration at
the outer edge of lenses.

A Cooke triplet comprises a negative flint glass element in the centre
with a crown glass element on each side. In this design, the sum of
all the curvatures times indices of refraction can be zero, so that
the field of focus is flat (zero Petzval field curvature). In other
words, the negative lens can be as strong as the outer two combined,
when one measures in dioptres, yet the lens will converge light,
because the rays strike the middle element close to the optic axis.
The curvature of field is determined by the sum of the dioptres, but
the focal length is not.

At the time, the Cooke triplet was a major advancement in lens design.
It was superseded by later designs in high-end cameras, but is still
widely used in inexpensive cameras, including variations using
aspheric elements, particularly in cell-phone cameras.
Contents
[hide]

* 1 Early designs
* 2 Application
* 3 See also
* 4 External links

[edit] Early designs

Despite the fact that the Cooke design was patented in 1893 it seems
that the use of achromatic triplet designs in astronomy appeared as
early as 1765. The 1911 Encyclopædia Britannica wrote:

The triple object-glass, consisting of a combination of two convex
lenses of crown glass with a concave flint lens between them, was
introduced in 1765 by Peter, son of, John Dollond, and many excellent
telescopes of this kind were made by him.

This parallels the fact that John Dollond had in turn patented the
achromatic doublet in the 1750s, though it had been used decades
earlier.
[edit] Application

*

Triotar-Triplet on a Rollei range finder camera
*

Projection objektive Patrinast for a 35 mm slide projector by
Ed. Liesegang; 1:2.8/85
*

Projection objective Maginon by Wilhelm Will, Wetzlar, 1:2.8/100

The triplet soon became a standard in lens design still used with low-
end cameras today. The main optical manufacturers often further
developed the original Cooke triplet (e.g., the Zeiss Triotar) that
were produced for many decades.

Binoculars as well as refracting telescopes often use triplets. The
same holds for many projection lenses, e.g., for 35 mm slide
projectors.

A similar design is used in the strong focusing synchrotron, invented
first by Nicholas Christofilos in 1949, but his work was not known in
the U.S., where parallel development took place.
[edit] See also

* Achromatic lens
* Chromatic aberration

[edit] External links

* Strong focussing synchrotron

http://en.wikipedia.org/wiki/Cooke_triplet

[Emmy Noether]

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]

http://en.wikipedia.org/wiki/Achromatic_lens



What a bunch of greedy and hungry wolves !!!!!!!

[Emmy Noether]

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).

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.
[edit] 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.
[edit] 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.
[edit] 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.
[edit] 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.
[edit] 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]
[edit] 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]
[edit] Design

The first-order design of an achromat involves choosing the overall
power ϕsys of the doublet and the two glasses to use. The choice of
glass gives the mean refractive index, often written as nd (for the
refractive index at the Fraunhofer "d" spectral line wavelength), and
the Abbe number V (for the reciprocal of the glass dispersion). To
make the linear dispersion of the system zero, the system must satisfy
the equations

\begin{align} \phi_1 + \phi_2 &= \phi_{\text{sys}} \\ \frac{\phi_1}
{V_1} + \frac{\phi_2}{V_2} &= 0 \ ,\end{align}

where the lens power is ϕ = 1 / f for a lens with focal length f.
Solving these two equations for ϕ1 and ϕ2 gives

\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} \ .

Since ϕ2 = − ϕ1V2 / V1, and the Abbe numbers are positive-valued, the
power of the second element in the doublet is negative when the first
element is positive.
[edit] See also

* Achromatic telescope
* Superachromat

[edit] References

1. ^ Daumas, Maurice, Scientific Instruments of the Seventeenth and
Eighteenth Centuries and Their Makers, Portman Books, London 1989 ISBN
978-0713407273
2. ^ a b c Watson, Fred (2007). Stargazer: the life and times of
the telescope. Allen & Unwin. pp. 140–55. ISBN 9781741753837.
http://books.google.com/books?id=2LZZginzib4C&pg=PA140.
3. ^ Fred Hoyle, Astronomy; A history of man's investigation of the
universe, Rathbone Books, 1962, LC 62-14108
4. ^ "Sphaera—Peter Dollond answers Jesse Ramsden".
http://www.mhs.ox.ac.uk/sphaera/index.htm?issue8/articl5. Retrieved
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.
5. ^ Dokland, Terje; Ng, Mary Mah-Lee (2006). Techniques in
microscopy for biomedical applications. p. 23. ISBN 9812564349.
http://books.google.com/books?id=Ix3G9_Rr0EAC&pg=PA23&lpg=PA23&dq=achromatic+lens+subcontract#v=onepage&q=&f=false.
Retrieved July 31, 2009.
6. ^ William L. Wolfe, Optics made clear: the nature of light and
how we use it, page 38
7. ^ Kidger, M.J. (2002) Fundamental Optical Design. SPIE Press,
Bellingham, WA, pp. 174ff
8. ^ Peter L. Manly, Unusual Telescopes, page 55
9. ^ Fred A. Carson, Basic optics and optical instruments, page
AJ-4

[Kevin Cunningham]

> more athttp://en.wikipedia.org/wiki/Dispersion_%28optics%29

No one has ever thought of this! Why optical companies with all their
super computers can't even do math!!!!

Geez, troll, try and come up with some stuff we optical people haven't
been doing since the 1870's.

Every once in a while we get a drooler who thinks that they can do
what 140 years, a bunch of Nobel prizes and hundreds and hundreds of
scientists haven't done. And the answer is.....some more crap that
goes away under it's own power. Remember, "Emmy" can't even find the
Nikon, Olympus or Carl Zeiss (!) web sites. Oh, well.......

Thanks,

Kevin Cunningham
SMS

[Emmy Noether]

Oh MY GOD SO MANY ACCOUTNS by the spoooks ...

chinese and korean have published better papers on optics and lens
design ........


nikon and olympus soon out of business .........

do another 9 11 and steal oil from russia !!!

Troll is your M O THER !!

Go and drink u rine of cheney's lesbian daughter and wave BIB BLE to
bait the voters .........

New Evidence Reveals Half of Pilots Were Only Assigned to 9/11 Flights
at the Last Minute

American Airlines Flight 11
Thomas McGuinness

Thomas McGuinness, the Co-Pilot of Flight 11
Thomas McGuinness, the co-pilot of American Airlines Flight 11 before
it became the first plane to be hijacked in the 9/11 attacks, only
assigned himself to be on the flight the afternoon before September
11, 2001, and pushed from it the original co-pilot, who had put his
name down for the flight less than half an hour earlier. This new
information means that, curiously, half of the pilots and co-pilots
originally at the controls of the four aircraft involved in the
attacks are now known to have been assigned to the doomed flights at
the last minute, very shortly before September 11. Additionally, more
than half of the flight attendants and many of the passengers are
known to have, similarly, not originally been booked onto those
flights.

The details of McGuinness's late assignment to Flight 11 were revealed
recently by Steve Scheibner, who was originally going to be the
plane's co-pilot. In a short film released on the Internet just before
the 10th anniversary of 9/11, Scheibner described how McGuinness came
to replace him on Flight 11 and thereby saved his life.

FLIGHT 11 HAD 'NO PILOT ASSIGNED TO IT YET'
At the time of the 9/11 attacks, Scheibner was a fundamentalist
Baptist pastor and a commander in the Naval Reserves, but he also
worked part-time as an on-call pilot for American Airlines. [1] He had
been available to fly on September 11. "So at about three o'clock in
the afternoon of September 10," Scheibner recalled, "I sat down at the
computer and I logged in like I normally do, to check to see if

[Emmy Noether]

On Feb 11, 6:21 am, Kevin Cunningham <sms...@mindspring.com> wrote:

Oh MY GOD SO MANY ACCOUTNS by the spoooks ...

chinese and korean have published better papers on optics and lens
design ........


nikon and olympus soon out of business .........

do another 9 11 and steal oil from russia !!!

TROLL is your MOTHER !!!

go and drin k urine of cheney 's lesbian daughter and wave BIBBLE to
bait the voters !!!

[Emmy Noether]

History

Historically, the calculation of glass properties is directly related
to the founding of glass science. At the end of the 19th century the
physicist Ernst Abbe developed equations that allow calculating the
design of optimized optical microscopes in Jena, Germany, stimulated
by co-operation with the optical workshop of Carl Zeiss. Before Ernst
Abbe's time the building of microscopes was mainly a work of art and
experienced craftsmanship, resulting in very expensive optical
microscopes with variable quality. Now Ernst Abbe knew exactly how to
construct an excellent microscope, but unfortunately, the required
lenses and prisms with specific ratios of refractive index and
dispersion did not exist. Ernst Abbe was not able to find answers to
his needs from glass artists and engineers; glass making was not based
on science at this time.[2]

[Emmy Noether]

[Emmy Noether]