Transcript Spectral Resolution and Spectrometers

Spectral Resolution and
Spectrometers
A Brief Guide to Understanding and
Obtaining the Proper Resolution of
the 785 Raman System.
Spectral Resolution and
Spectrometers
• How does a monochromator work?
• How to calculate spectral resolution.
– How does entrance and exit slit width effect the
resolution?
– What defines which slit is used to calculate
resolution?
– What should we report as our resolution and
how do we obtain it?
How does a Monochromator work?
Figure 1: Diagram of
the common CzernyTurner Monochromator
design
Light (A) is focused onto an entrance slit (B) and is collimated by a
curved mirror (C). The collimated beam is diffracted from a rotatable
grating (D) and the dispersed beam re-focused by a second mirror (E)
at the exit slit (F). Each wavelength of light is focused to a different
position at the slit, and the wavelength which is transmitted through
the slit (G) depends on the rotation angle of the grating.
Monochromator vs. Spectrometer
• A spectrometer is a
monochromator with
an array type detector
and no exit slit.
• By having no slit at the
exit (or the slit all the
way open), you can
detect all of the
wavelengths focused at
the exit focal plane.
Figure 2: Spectrometer with grating turret and CCD detector
785 Raman Spectrometer
Grating turret holding 3
gratings of different
groove density
Entrance slit controlled
by a micrometer coupled
to a fiber optic.
An artists rendering
Exit where CCD
detector is located
Calculating Spectral Resolution
• In the most fundamental sense, both bandpass and
resolution are used as a measure of an
instrument’s ability to separate adjacent spectral
lines.
– Spectral bandpass is the FWHM of the wavelength
distribution passed by the exit slit.
– Resolution is related to bandpass but determines
whether the separation of two peaks can be
distinguished.
• Resolution of an instrument is limited by the
FWHM of its Instrumental Profile.
FWHM of Instrumental Profile
FWHM = (dλ2(slits) + dλ2(resolution) + dλ2(line))½
dλ2(slits) → bandpass determined by finite spectrometer slit widths
and the linear dispersion of the grating.
dλ2(resolution) → the limiting resolution of the spectrometer which
incorporates system aberrations, diffraction effects, and the laser
line width of our system.
dλ2(line) → natural line width of the spectral line being probed.
This FWHM is our limit of resolution for the spectrometer.
How do you calculate the FWHM of
the Instrumental Profile?
• The instrumental profile FWHM is something you can
measure experimentally.
• dλ2(line): By only observing the 785 laser line with the
spectrometer we can eliminate the broadening of the
FWHM due to the natural line width of a spectral line.
• dλ2(slits): The bandpass due to the slit width and the grating
of the spectrometer can be calculated.
• dλ2(resolution): The limiting resolution of the spectrometer is
something that you solve for knowing the other variables
of the equation.
How to Calculate Bandpass
• BP = W × Rd
where: Rd is reciprocal linear dispersion
W is the slit width of the entrance or exit slit
(which ever is larger)
• The reciprocal linear dispersion represents the number of
wavelength intervals (e.g., nm) contained in each interval
of distance (e.g., mm) along the focal plane.
– Rd = dl/dx = (d cos b) / (f × m)
• At small angles of diffraction (b < 20˚) then cos b ~ 1;
– Rd = d / (f × m)
• BP = W × (d / (f × m))
The only thing left to do now is to determine what our slit
width should be to solve for our bandpass.
Sample Bandpass Calculation
• Given a 1200 gr/mm grating, an angle of reflection less than 20˚,
and f = 500 mm, what is the BP of a spectrometer with a slit
width of 50 mm?
BP = W × Rd
d = 1 mm/ 1200 gr × 106 (nm/mm) = 833.33 nm/gr
W = 50 mm × 10-3 (mm/mm) = 0.05 mm
f = 500 mm
Rd = d / (f × m) = 833.33 nm / (500 mm × 1)
Rd = 1.667 nm/mm
BP = 0.05 mm × 1.667 nm/mm
BP = 0.083 nm
Two Questions need to be Addressed
Question 1:
• Which slit width do you use to calculate the bandpass
with?
– Earlier it was stated that the slit width that defines the BP is the
larger of the entrance and exit slit.
• Our spectrometers do not really have an exit slit, instead a CCD
detector sits in the focal plane of the exit, so what defines the exit
slit?!?!
Question 2:
• Is the bandpass a close enough estimation of the FWHM of
the instrumental profile?
What defines our exit slit?
• A CCD is an array detector with each pixel
acting as a tiny individual detector.
– The short answer to the our question is the size
of one pixel may define the exit slit. But is this
true?
Near level
slope.
Near level
slope again,
is this a
pattern?
☺ Setting the entrance slit
smaller that 40 mm will not
improve resolution!
Both gratings yield a relatively constant FWHM until
approximately a 40 mm slit width meaning the exit slit is
defined by 2 pixels of 20 mm each.
Is the bandpass a close enough estimation
of the limiting FWHM instrumental profile?
• As you have already seen it isn’t, but to what
extent?
• What causes this difference?
FWHM = (dλ2(slits) + dλ2(resolution) + dλ2(line))½
• Does this trend extend over a wide range?
Actual FWHM compared to
predicted BP calculations.
1200 gr/mm
600 gr/mm
Slit Width
(mm)
BP calc. (cm-1)
Actual FWHM (cm-1) at 785 nm
Slit Width
(mm)
BP calc. (cm-1)
Actual FWHM (cm-1) at 785
nm
10
0.210961905
1.224547357
10
0.503063005
2.331401982
20
0.438151649
1.237559259
20
1.006126011
2.393937952
30
0.649113555
1.256955603
30
1.49296118
2.435301932
35
0.762708427
1.333200348
35
1.752606605
2.530827112
40
0.86007546
1.378575927
40
1.996024192
2.673016324
45
0.973670333
1.573224458
45
2.255669619
2.904527885
50
1.087265205
1.513154548
50
2.499087208
3.155810158
60
1.298227112
1.758089774
60
3.00215023
3.496531409
70
1.509189019
2.140940032
70
3.50521326
4.015252055
80
1.720150927
2.189489011
80
3.992048457
4.688346393
90
1.947340674
2.53326762
90
4.495111503
5.170371898
100
2.158302584
2.734451493
100
4.99817456
5.779925324
120
2.596454244
3.284369483
120
6.004300711
6.946104285
Take Home Messages
• The smallest exit slit width that is possible on the
785 Raman system is approximately 2 pixels, or
40 mm.
• Bandpass is not an accurate representation of the
resolution achievable by our spectrometers.
– FWHM = (dλ2(slits) + dλ2(resolution) + dλ2(line))½
– The FWHM of the instrumental profile can be
measured experimentally and should be done when
conducting experiments so as to report the correct
resolution achievable at that time.
Take Home Messages Cont…
• The two largest contributing factors to the
broadening of the instrumental profile are:
– Laser line width
– Bandpass (which grating you chose controls the
dispersion which dictates the bandpass)
• It is also very important to note that condensed
phase molecules have natural line widths much
larger than either of these cases and will dominate
your resolution of your spectrum
• Your limiting resolution is still important when you
are looking for shifts in a spectrum.
Thank You !