11

Dispersion (Terminology)

How do we quantify the spatial separation of wavelengths on the exit focal plane?

Angular Dispersion: Da = dθ/dλ (property of dispersive element)

Linear Dispersion: D = dy/dλ (property of dispersive device)

FDispersiveElement λ1

λ2

θ1

θ2 y1

y2

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More Dispersive Terminology

If dθ is small, it can be shown that:

• More commonly, we will use:

• Reciprocal Linear Dispersion (D-1) = 1/D• -typically around 0.1 - 20 Å/mm in UV/Vis

• Effective Bandwidth:

D = F × Da

Δλeff = D-1 × w

Slit-width

D-1 = 16 Å/mmw = 100 μm Δλeff = 1.6 Å

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Sin d = d = dy/F

33

Prism As we saw in the previous chapter, refraction of light

is given by Snell's law: n1 sin θ1 = n2 sin θ2

A prism is a transparent optic that is shaped to bend light. Since the refractive index of a material varies with wavelength, prisms are useful for dispersing different wavelengths of light.

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44

Dispersion of white light by a prism

Dispersedlight

IncidentWhite light

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Dispersion by a prism

(a) quartz Cornu types and (b) Littrow type

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77

Rainbow Rainbow

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88

Diffraction Gratings

Typically, a series of closely spaced facets ruled

onto a reflecting surface• Spacing of facets must be comparable to λ of EMR

• Parallel EMR rays striking adjacent facets will travel

different distances

• Constructive interference occurs if the difference in the

distance travelled by the two rays is an integer multiple of λs

• Constructive interference will be a function of the angles (incident and reflection) and the wavelength

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99

Let’s see how it works!

) sin sin ri(dn

ACBDn rdidn sin sin

ir

DC

BA

1

2

3

1

2

3

Grating normal

MonochromaticBeam at incident

Angle i

Diffraction beam at

Reflected angle r

dChemistry Department, University of Isfahan

Wave front

1010

Dispersion by Echelle Grating

Echelle grating: i = angle of incidence; r = angle of reflection; d = groove spacing. In usual practice, i r = = 6326.

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1111

Echelle Grating

Provides high dispersion and high resolution Difference with echellette grating

• Its blaze angle is significantly greater

• The short side of the blaze is used rather than the long side which is used in echellette grating

• The grating is relatively coarse, having typically 300 or fewer grooves per mm for UV radiation

• The angle of reflection r is much higher in the echelle grating than the echellette and approaches the angle of incidence i,

r i =

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Echelle Grating

Under these circumstances, the Equation we obtained for echellette grating, i.e.

with respect to becomes

and the dispersion which was

becomes

nλ = d[sin(i) + sin(r)]

r i =

nλ = 2d sin

F

βdD

n

cos21-

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Comparison of Performance Characteristics of a Conventional and Echelle Grating

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Performance Specifications

The dispersion is usually given in nanometers per millimeter, where the slit width is expressed in mm.

stray light: light transmitted by the monochromator at wavelengths outside of the chosen wavelength and bandpass.

high efficiency: maximize the ability to detect low lightlevels.

Resolution is usually of secondary importance sinceemission spectra rarely have peaks with linewidths less than 5 nm.

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Dispersion for a Grating

)rcos(d

n

d

)r(d

If the angle r is kept small (<5o):

For a fixed angle of incidence (i):

n dλ = d cos(r) d(r)

So:

Da

wavelength independentd

n

d

)r(d

Chemistry Department, University of Isfahan

nλ = d [ sin (i) ± sin (r) ]

1616

Dispersion of Grating Monochromators

Angular dispersion:

Linear dispersion:

F: focal length of the monochromator

Reciprocal linear dispersion D-1

)rcos(d

n

d

)r(d

dλ

Fdr

dλ

dyD

F

d

F

rd

d

d

nn

)cos(

yD 1

Chemistry Department, University of Isfahan

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Chemistry Department, University of Isfahan

Dispersion of Grating Monochromators

F

d

F

rd

d

d

nn

)cos(

yD 1

☻What is the role of D-1 in wavelength separation?

D-1 ↓ resolution ↑ or

D-1 ↑ resolution ↑

What are the effects of d, n and Fon resolution?

1818

Resolution

Resolution is the separationof wavelengths in a spectrum.

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SpectralResolution/Resolving Power

We define Resolution (or Resolving Power):

R = λavg/Δλ

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2020

Resolving Power for aGrating

We need an instrument with a resolving power of:

R = 4500/2 = 2250 The resolving power of a diffraction grating:

So, in order to just resolve these two spectral lines:

R = nN

λ1 = 4501 Åλ2 = 4499 Å

Spectral Order

No. of grating blazes illuminated by radiation

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2121

Monochromator Slits and ResolutionIllumination of an exit slit by monochromatic radiation 2 at various monochromator settings.

Exit and entrance slits are identical.

Reciprocal linear dispersion

D-1 = ddy

eff = w D-1

Slit widthChemistry Department, University of Isfahan

Detector

Wavelength

Pow

er Exit slit

Illumination of an Exit Slit

Monochromator

2

Wavelength

Effective bandwidth

Slit width= Slit width= 3(

Pow

er

Slit width= (Slit width=

2424

Effect of Slitwidthon Spectrum (Benzene)

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Slit width

• The slit widths are generally variable, and a typical monochromator will have both an entrance and an exit slit.

• The light intensity which passes through a monochromator is approximately proportional to the square of the slit width.

• Larger slit widths yield increased signal, what about resolution?

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How it all fits together

Suppose we want to “just resolve” the following Iron doublet:

λ1 = 3099.90 Å R= 3099.935/0.07 λ2 = 3099.97 Å = 44,000

Suppose that we have a 100-mm wide grating ruledwith 1200 grove/mm ; it has a first-order resolvingpower of: R = nN = (1)(100 mm)(1200 gr/mm) R = 120,000

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2727

But, can we really resolvethe two lines?

Consider, now, the dispersion of the

monochromator in which that grating is located:

D-1 = 16 Å/mm

In order to just resolve the two lines:

Δλeff = 0.07 Å

This requires a slitwidth of:

Δλeff = D-1 × ww = 0.07 Å/16 Å/mm = 0.00438 mmw ≈ 4 μm Chemistry Department, University of

Isfahan

2828

How Can WeImprove Resolution?

Decrease Slitwidth (w)

-limits light throughput

Operate in Higher Spectral Orders

-limits light throughput (decreased efficiency)

D-1 ∝ 1/n Increase Focal Length

-limits light throughput (inverse square law)

D-1 ∝ 1/F

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Five components

1. a stable source of radiant energy

2. a transparent container for holding the sample

3. a device that isolates a restricted region of the spectrum for measurement

5. a signal processor and Fiber Optics

Optical instrument

4. a radiation detector

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Detectors for spectroscpic instruments

VAC UV VIS Near IR IR Far IRSpectral region

Detectors

Photondetectors

Thermaldetectors

Photographic plate

Photomultiplier tube

Phototube

Photocell

Silicone diode

Photoconductor

Thermocouple (voltage) or barometer (resistance)

Golay pneumatic cell

Pyroelectric cell (capacitance)

Charge transfer detector

, nm 100 200 400 700 1000 2000 4000 7000 10,000 20,000 40,000

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Detectors convert light energy to an Detectors convert light energy to an electrical signal. electrical signal.

In spectroscopy, they are typically placed In spectroscopy, they are typically placed after a wavelength separator to detect a after a wavelength separator to detect a selected wavelength of light. selected wavelength of light.

Different types of detectors are sensitive in Different types of detectors are sensitive in different parts of the electromagnetic different parts of the electromagnetic spectrum. spectrum.

Radiation Detectors

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3333

high sensitivity high S/N ratio constant response over a considerable range of fast response minimum output signal in the absence of

illumination (low dark current) electric signal directly proportional to the radiation

power

Ideal Detectors

?

radiation power (intensity)dark current

S =kP + kd

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Two major types: one responses to photons, the other to heat

photon detectors: UV, visible, IR(when used for 3 µm or longer , cooling to dry ice

or liquid nitrogen is necessary to avoid interference with thermal signal)

signal results from a series of individual eventsshot noise limited

thermal detectors: IRsignal responds to the average power of the

incident radiationthermal noise limited

Types of radiation detectors

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(a) Photovoltaic cells: radiant energy generates a current atthe interface of a semiconductor layer and a metal;

(b) Phototubes: radiation causes emission of electrons from a photosensitive solid surface;

(c) Phtomultiplier tubes: contain a photoemissive surface as well as several additional surfaces that emit a cascade of electrons when struck by electrons from the photosensitive area;

(d) Photoconductivity detectors: absorption of radiation by a semiconductor produces electrons and holes, thus leading

to enhanced conductivity;

(e) Silicon photodiods: photons increase the conductance across a reverse biased pn junction. Used as diode array to observe the entire spectrum simultaneously

(f) Multichannel photon detector

Photon detectors

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Plastic case

Glass Thin layer of silver

Selenium

Iron

+ -

Barrier Layer Cell

3737

Vacuum Phototubes

• The number of electrons ejected from a photoemissive surface is directly proportional to the radiant power of the beam striking that surface;

• As the potential applied across the two electrodes of the tube increases, the fraction of the emitted electrons reaching the anode rapidly increases;

• when the saturation potential is achieved, essentially

all the electrons are collected at the anode.

• The current then becomes independent of potential and directly proportional to radiation power. Chemistry Department, University of

Isfahan

90 Vdc

Wire anodeCathode

3939

Photomultiplier Tube (PMT)

Photomultiplier Tubes (PMTS) are light detectors that are useful in low intensity applications such as fluorescence spectroscopy.

Due to high internal gain, PMTs are very sensitive detectors.

PMTs are similar to phototubes. They consist of a photocathode and a series of dynodes in an evacuated glass enclosure.

Photons that strikes the photoemissive cathode emits electrons due to the photoelectric effect.

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4040

Photomultiplier Tube (PMT)

Instead of collecting these few electrons at an anode like in the phototubes, the electrons are accelerated towards a series of additional electrodes called dynodes.

These electrodes are each maintained at a more positive potential.

Additional electrons are generated at each dynode.

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Photomultiplier Tube (PMT)

This cascading effect creates 105 to 107 electrons for each photon hitting the first cathode depending on the number of dynodes and the accelerating voltage.

This amplified signal is finally collected at the anode where it can be measured.

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Dynode Potential(V) Number of electrons

1 90 1

2 180 10

3 270 100

4 360 103

5 450 104

6 540 105

7 630 106

8 720 107

9 810 108

Anode 900V Gain =108

12

3

4

5

6

8

7

9

Anode

PhotoemissiveCathode

GrillQuartz envelope

+_

900V dc

Anode

PhotoemissiveCathodeDynodes 1-9

To readout