7.3 Wavelength Separators

advertisement
7.3 Wavelength Separators
• colored glass filters are used to separate large
regions of wavelengths
• interference filters are used to isolate
intermediate-sized bands of wavelengths
• gratings separate wavelengths by angular
dispersion
P the grating equation
P grating resolution
P grating efficiency
• grating monochromators are used to isolate
narrow bands of wavelengths
•monochromator throughput is determined by its
f/#
7.3 : 1/15
Colored Filters (1)
The figure shows the transmission curve for three bandpass filters.
51715 passes everything except the deep UV. It would be used to
reject the mercury 253.7 nm line. 51670 passes a band from the
near UV to the green, while 51660 passes a band from ~280 to
400 nm. These would be used with fluorescence excitation.
http://www.oriel.com/netcat/VolumeIII/tablepage/s32col.htm
7.3 : 2/15
Colored Filters (2)
The figure shows the transmission curve for two high pass filters.
51294 rejects wavelengths below 500 nm and passes those
above. 5131 performs the same function with a cutoff
wavelength of ~580 nm. Note that it is nearly impossible to
make a low pass colored glass filter.
http://www.oriel.com/netcat/VolumeIII/tablepage/s32col.htm
7.3 : 3/15
Interference Filter (1)
Center wavelengths can be from the UV to the infrared. Pass
bands are narrower than colored filters, but broader than grating
monochromators. The filter above is centered at 415 nm with a
10 nm FWHM and a transmission ~33%. As the bandwidth
narrows the transmission drops.
7.3 : 4/15
http://www.oriel.com/netcat/VolumeIII/Descrippage/v3t2vnb.htm
Interference Filter (2)
An interference filter is created
when light is multiply reflected
between two parallel surfaces.
The beams exiting the filter must
be in phase. This means that
the sum of x and d must equal
an integral number of
wavelengths.
R
R
θ
air
t
2θ
air
x + d = mλ n
x + x cos ( 2θ ) = mλ n
x (1 + cos ( 2θ ) ) = mλ n
x 2 cos 2 θ = mλ n
2t cos θ = mλ n
mλ = 2nt cos θ
7.3 : 5/15
transparent
material with
refractive
index of n
Note that the equation in your text
on page 156 is incorrect.
The pass band varies with the
order, m. To restrict transmission
to only one order, the exit surface
is most often a colored glass filter.
Prisms
Because of a complicated mathematical
relationship between wavelength and bend
angle, prisms are seldom used in modern
instruments.
For maximum dispersion (angular
resolution), visible light is separated with a
glass prism and ultraviolet is separated with
a quartz prism.
One common design is the constant
deviation, or Pellen-Broca, prism shown in
the figure. Constructed from one piece of
material, it can be viewed as three separate
prisms. For a given orientation, only one
wavelength exits at a 90° deviation. To
select a different wavelength the prism is
rotated about the juncture of the dotted
lines, P.
7.3 : 6/15
30 45
60
30
45
P
60
Diffraction Grating
-2
A diffraction grating is created by a spatial
modulation in phase or amplitude of an
incoming plane wave.
-1
m=0
θ+1 +1
When exiting the grating, the input is
separated into several plane waves
traveling at angle to the original direction
of propagation - these are called
diffraction orders. The number and
intensity of the orders depends upon the
functional form of the modulation.
The figure at the top is a transmission
grating, while that at the bottom is a
reflection grating. The diffraction angle
depends upon order, m, wavelength, λ,
and spatial modulation period, a.
sin θ m = mλ a
7.3 : 7/15
+2
a8
9
-2
-1
θ+1
a8
9
+1
θr
+2
θi
Blazed Gratings
By forming the bottom of the grooves into
a saw tooth shape, the angle of reflection
can be made to correspond to one of the
diffraction orders. One order then blazes,
that is, it has most of the incoming optical
power.
Show below are three gratings blazed at
300, 400 and 500 nm. Note how the
efficiency drops on either side of the blaze
wavelength.
http://www.oceanoptics.com/technical/gratingcharts.asp
7.3 : 8/15
-2
-1
+1
θ+1
a8
9
+2
θr
θi
Grating Resolution
The angular distribution of a monochromatic beam of light reflecting
off a diffraction grating is a sinc2 function (sinx/x)2. The node
spacing of the sinc function is called the angular resolution, Δθ,
Δθ =
2λ
Na cos θ m
dθ
m
=
d λ a cos θ m
where N is the number of grating grooves and a is the groove
spacing. The goal is to minimize Δθ, which is accomplished by
maximizing the grating width, Na. You can also increase the order,
which increases θm.
Grating spectral resolution is defined as,
R=
λ
∝ mN
Δλ
where Δλ is the range of wavelengths occurring over Δθ, and λ is the
center wavelength. High resolution means small Δλ.
The angle at which light leaves a grating leads to an ambiguous
wavelength, e.g. 600 nm, m = 1; 300 nm, m = 2; 200 nm, m = 3.
7.3 : 9/15
Commercially Available Gratings
The vast majority of commercially available gratings are plastic
replicas. The master grating is coated with an epoxy resin to form
a negative image. A thin layer of plastic coats the negative and
cured. When removed from the negative, the replica is mounted
on glass for rigidity and coated with aluminum.
Ruled gratings are made with a spacing from 25 mm-1 to 1,800
mm-1. The upper size is 15×15 cm, with 5×5 cm being typical.
Concave ruled gratings can be manufactured with great difficulty.
Ruled gratings have a scattered light figure of 10-3.
Holographic gratings are made by coating the surface of glass with
a photoresist. Two laser beams irradiate the surface at an angle to
each other creating interference fringes. Bright fringes polymerize
the photoresist. The surface is washed with an organic solvent to
dissolve remaining monomer, then coated with aluminum.
Spacings up to 2,400 mm-1 are possible, as well as concave
gratings. Holographic gratings have a scattered light figure of 10-4.
7.3 : 10/15
Czerny-Turner Monochromator
• the source is imaged onto the entrance slit using an f/# that
matches the monochromator
• the first spherical mirror collects light from the slit (now the
object), collimates it, and irradiates the grating
• the grating diffracts each wavelength at a different angle
• the second mirror focuses the diffracted parallel beam onto the
exit slit - a narrow band, Δλ , passes through the slit
• light from the exit slit is focused by the lens into the sample cell
sample
(exit image)
lens
exit slit
(entrance image)
mirror
variable λ
monchromatic light
white light
source
7.3 : 11/15
lens
grating
entrance slit
(source image)
mirror
Monochromator Resolution (1)
The angular resolving power of a monochromator is given by the
derivative of the grating equation.
sin θ m =
mλ
a
cos θ m dθ =
m
dλ
a
dθ
m
=
d λ a cos θ m
Angular dispersion can be converted to linear dispersion at the exit
slit by using the diagram below,
dl
dθ
f
where f is the monochromator focal
length.
dθ ≈ tan ( dθ ) =
dl
f
dl
dθ
= f
dλ
dλ
Resolution is given as the reciprocal linear dispersion, dλ/dl, in
units of nm mm-1. For a grating with 1,200 grooves mm-1, a =
833 nm. For 500 nm light and m = 1, θ = 36.9°. The angular
dispersion is 0.00150 deg nm-1. For f = 250 mm, the linear
dispersion is 0.375 mm nm-1. The reciprocal is 2.66 nm mm-1.
7.3 : 12/15
Monochromator Resolution (2)
High resolution can be achieved by either using small slits or large
focal lengths. For the example on the last slide, a 0.1 mm slit will
combine with the reciprocal linear dispersion of 2.66 nm mm-1, to
produce a spectral resolution of Δλ = 0.27 nm.
If a 1,200 groove mm-1 grating is put into a 1-meter
monochromator, the reciprocal linear dispersion is 0.67 nm mm-1.
With a 1 mm slit the resolution is 0.67 nm, while with a 0.1 mm
slit the resolution is 0.067 nm.
For slits of 0.1 mm or larger width, the output of the
monochromator will have a triangular shape when inputting a
single wavelength.
For slits 0.01 mm or less, diffraction from the
slit will dominate grating dispersion. For this
case the monochromator output has the
shape of a sinc function squared.
7.3 : 13/15
⎛ sin (πλ λ0 ) ⎞
⎜
⎟
πλ
λ
0
⎝
⎠
2
Monochromator Throughput (1)
To obtain the calculated resolution it is necessary that the grating
be completely filled with light. This in turn requires that the
entrance optics have the same f/# as the monochromator.
With a "relay lens" arrangement, a lens with the same f/# as the
monochromator is used to focus the image on the slit. The lens
that gathers light from the source can have any desired f/#.
The image of the source on the slit will be magnified by the ratio
of the two lens focal lengths.
7.3 : 14/15
Monochromator Throughput (2)
The two-lens scheme suffers from four reflections off lens surfaces,
and the "real estate" required for implementation. A single lens
can be used by doing appropriate calculations. Seldom will the
lens diameter be exactly what is needed. To circumvent this
problem, buy a larger lens and "stop it down" by using an aperture
with the correct diameter.
If a lens with too small an f/# is used, the grating will be
overfilled. Much of the light is lost and shows up as scatter.
If a lens with too large an f/# is used, the grating will be under
filled. This reduces resolution, since fewer grooves are irradiated.
7.3 : 15/15
Download