Download Chromatic Dispersion

OPTICS | LIGHT TOUCH
Chromatic Dispersion
Stephen R. Wilk
O
ne of the
more interesting optical
phenomena is the
Christiansen effect, discovered by
the euphoniously
named Christian Christiansen of Denmark in 1884. He
found that, if he placed small
fragments of glass into a liquid
that had the same refractive
index but a different dispersion
(that is, a different dn/dl), the
combination would transmit
light at the wavelength where
the indices coincide, but scatter
at other wavelengths.
The effect is rather dramatic, with the
colorless liquid and solid collaborating to
create a brilliantly colored composite that
has a single spectral hue. Christiansen
used glass in a mixture of benzene
and carbon disulfide, but many other
combinations have been discovered,
including solid-in-solid mixtures.
Christiansen filters generally take
advantage of the considerably larger
dispersion that is often found in liquids.
The larger the difference in dispersion,
the narrower the bandwidth. One can
make a very serviceable Christiansen filter
by using methyl salicylate, which has a
high dispersion and is still available as a
liniment at specialty drug stores, mixed
with ethanol to vary the refractive index,
and combining the mixture with most
common glasses (microscope slides are
very useful and readily available).
12 | OPN November 2006
Because liquids tend to
have dispersion values
that are one or two
orders of magnitude
greater than solids, you
can “tune” the filter by
heating or cooling it,
changing the color of
the passband.
Because liquids also tend to have
dispersion values that are one or two
orders of magnitude greater than solids,
you can “tune” the filter by heating
or cooling it, changing the color of
the passband. You can also tailor a
Chrisitiansen filter by obtaining samples
of specialty glass from a supplier such
as Corning or Ohara and using indexmatching fluid from a firm such as
Cargill Specialty Liquids.
The basic relationships have been
derived several times. Some researchers
claim that the scattering is due to
multiple passes through grains causing
phase shifts to accumulate. However, it
seems clear to me from studying grains
of glass surrounded by index-matching
fluid that the coloration occurs in
regions where you have close to grazing
incidence. This is particularly apparent
when you look at glass microspheres in
fluid—the central region is quite clear
and there is no
observable deviation
of the rays, or
coloring.
The index match
is extremely good at
most angles. It’s only
when you approach
grazing incidence
that all wavelengths
encounter an index mismatch that causes
scattering. Unless the indices match
perfectly, near-grazing incidence, all
wavelengths but that one will scatter,
and you have a ring of transmitted light
corresponding to the wavelength at which
the indices coincide.
Inevitably, there will be some surface
of a grain of any shape for which you will
have such near-grazing incidence. This
is why no great care is needed to make a
Christiansen filter. No matter what shape
you grind your particles into, there will
be enough grazing-incidence surfaces
to guarantee satisfactory discrimination
between index-matched and non-indexmatched rays.
The use of Christansen filters as
passband filters was common before the
second World War. It’s easy to see why,
if you look at a broad-area Christiansen
filter made in a parallel-sided container.
No matter how well-matched the indices
are, in almost all cases a cell filled with
a mixture of solid-phase and liquidphase materials will only be effectively
transparent for an object held right
against it. The farther removed an
object is, the more translucent the filter
becomes. Over any significant distance,
the filter does a poor job of transmitting
coherent images. However, it works very
well as a method of removing unwanted
wavelengths by scattering.
The recommended method of using
such filters is to place them in a system
where a broad collimated beam is passed
through the cell. Given that the filters
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Optics
Chromatic dispersions are made of two immiscible
liquids with the same index at one wavelength, but
different dispersions.
need a liquid-tight seal (especially with
changing volumes) and that the passband
is temperature sensitive, Christiansen
filters are far less desirable than thin film
stacks.
My experience with Christiansen
constructions has been that very small
differences can cause enormous scattering
changes. Packages of glass microspheres
immersed in index-matching fluid
invariably reveal index variations. I have
had the same experience with plastic
pellets (intended for injection-molding
input feeds) immersed in index-matching
fluid.
In small quantities, or in round
bottles, the pellets look like excellent
cases of index matching, with the
individual beads losing their identity
to the fluid. (Plastics closely resemble
liquids in their optical properties, and it’s
possible to find combinations with very
nearly identical dispersion, so there is no
obvious coloring.) However, when the
pellets are placed in bulk in a flat-sided
cell, it is immediately clear that there is
more than one phase present.
Variations in refractive index due to
conditions of production or to stressinduced birefringence play a part in this
imperfect index-matching—so does
scattering due to surface contamination,
fractures and the like. Rayleigh
minimized this problem by grinding
his glass with an iron mortar and pestle,
boiling the resulting fragments in
hydrochloric acid to dissolve any iron
contamination, and then drying and
annealing the glass.
Even with such treatment, however,
it’s hard to avoid the problems that can
plague Christiansen filters. There is one
method, however, that avoids the pitfalls
of surface contamination, fractures, stress
birefringence and index variation from
piece to piece. It’s the only method that
I’ve been able to use to produce filters
that are truly transparent.
Chromatic dispersions are made of
two immiscible liquids with the same
index at one wavelength, but different
dispersions. The individual particles of
the phase consist of spherical droplets
of one phase in the other. In fact, one
will have droplets of each phase within
the other. Because it’s unlikely that two
liquids suited to this purpose will have
the same density, one will typically sit
atop the other. There will be an effective
dispersion only near the interface unless
the phases are vigorously mixed, or if the
lighter phase is continually pumped to
the bottom of the heavier phase.
Despite these difficulties, the
dispersions thus created allow transparent
viewing. A simple chromatic dispersion
can be made from turpentine and
glycerine. At room temperature, the
passband is blue, but changing the
temperature with a water bath will shift
it to green. This should be done carefully,
since turpentine is flammable. t
[ Stephen R. Wilk ([email protected]) is an
optical scientist at Textron Systems and a visiting scientist at MIT. ]
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[ References and Resources ]
>> W.G. Driscoll and W. Vaughan (eds.). Handbook of Optics (1978), pp. 8-103—8-106.
>> L. Auerbach. Am. J. Phys. 25(7), 440-2
(1957).
>> L. Auerbach. Am. J. Phys. 28(8), 743 (1960).
>> C.V. Raman. Proc. Indian Acad. Sci. A29,
381 (1949).
>> C.V. Raman and K.S. Viswanathan. Proc.
Indian Acad. Sci. A41, 55 (1955).
>> R.H. Clarke. Appl. Opt. 7, 861 (1968).
>> John Strong. Procedures in Experimental
Physics 373 (1938).
>> E.D. McAlister. Smithsonian Misc. Coll. 33(7)
(1935).
>> U. Wojak et al. Appl. Opt. 26, 4788 (1987).
>> Lord Rayleigh. Phil. Mag. 35, 373 (1918).
>> L. Auerbach. Am. J. Phys. 25(7), 440-2
(1957).
>> R.W. Wood, Physical Optics, 3rd ed.,
115-7 (1934).
>> Kento Okoshi et al. J. Colloid and Interface
Sci. 263, 473-7 (2003).
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