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?

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.

Figure 1: Diagram of the common Czerny-Turner Monochromator design

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

Entrance slit controlled by a micrometer coupled to a fiber optic.

Exit where CCD detector is located

Grating turret holding 3 gratings of different groove density

An artists rendering

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 = d/dx = (d cos / (f × m)

• At small angles of diffraction ( < 20˚) then cos – 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 m?

BP = W × Rdd = 1 mm/ 1200 gr × 106 (nm/mm) = 833.33 nm/grW = 50 m × 10-3 (m/mm) = 0.05 mmf = 500 mmRd = d / (f × m) = 833.33 nm / (500 mm × 1)Rd = 1.667 nm/mmBP = 0.05 mm × 1.667 nm/mm

BP = 0.083 nm

Two Questions need to be AddressedQuestion 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?

Spectral Resolution Vs. Slit Width using a 600 grating

0

1

2

3

4

5

6

7

8

0 20 40 60 80 100 120 140

Slit Width ( m)

FWHM measured from the 785 laser line

Bandwidth predicted from BP calculation

Near level slope.

Spectral Resolution Vs. Slit Width using a 1200 grating

0

0.5

1

1.5

2

2.5

3

3.5

0 20 40 60 80 100 120 140

Slit Width ( m)

FWHM measured with the 785 laser line

P redicted FWHM from BP calculation

Near level slope again,

is this a pattern?

FWHM of 600 and 1200 gratings Vs. Slit Width

0

1

2

3

4

5

6

7

5 15 25 35 45 55 65 75 85 95 105 115 125

Slit Width ( m)

FWHM 600 gr

FWHM 1200 gr

BP predicted FWHM 600

BP predicted FWHM 1200 gr

Both gratings yield a relatively constant FWHM until approximately a 40 m slit width meaning the exit slit is defined by 2 pixels of 20 m each.

☺ Setting the entrance slit smaller that 40 m will not improve resolution!

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) + ddλλ22

(resolution)(resolution) + dλ2(line))½

• Does this trend extend over a wide range?

Actual FWHM compared to predicted BP calculations.

1200 gr/mm

Slit Width (m) BP calc. (cm-1) Actual FWHM (cm-1) at 785 nm

10 0.210961905 1.224547357

20 0.438151649 1.237559259

30 0.649113555 1.256955603

35 0.762708427 1.333200348

40 0.86007546 1.378575927

45 0.973670333 1.573224458

50 1.087265205 1.513154548

60 1.298227112 1.758089774

70 1.509189019 2.140940032

80 1.720150927 2.189489011

90 1.947340674 2.53326762

100 2.158302584 2.734451493

120 2.596454244 3.284369483

600 gr/mm

Slit Width (m) BP calc. (cm-1)

Actual FWHM (cm-1) at 785 nm

10 0.503063005 2.331401982

20 1.006126011 2.393937952

30 1.49296118 2.435301932

35 1.752606605 2.530827112

40 1.996024192 2.673016324

45 2.255669619 2.904527885

50 2.499087208 3.155810158

60 3.00215023 3.496531409

70 3.50521326 4.015252055

80 3.992048457 4.688346393

90 4.495111503 5.170371898

100 4.99817456 5.779925324

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 m.

• 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 !