Raman: theory andRaman: theory andinstrumentationinstrumentation

Kit Kit UmbachUmbach

Dept. of MS&EDept. of MS&E

CCMR,NBTC facilitiesCCMR,NBTC facilities

OutlineOutline

oo 1. Introduction1. Introduction

oo 2. Theory2. Theoryoo Role of Role of polarizabilitypolarizability; mathematical models; mathematical models

oo Depolarization ratioDepolarization ratio

oo TemperatureTemperature correctioncorrection

oo 3. System instrumentation3. System instrumentationoo ComponentsComponents

oo FT-RamanFT-Raman

oo Raman microscopyRaman microscopy

Light as a probe of molecular structureLight as a probe of molecular structureoo light is light is absorbedabsorbed excitation of molecule excitation of molecule

de-excitation of de-excitation of molecule molecule light is light is emittedemitted

oo visible/UV:visible/UV:

excitation of valence electronsexcitation of valence electrons

oo infrared (IR):infrared (IR):

excitation of vibrationsexcitation of vibrations

oo microwave/IR:microwave/IR:

excitation of rotationsexcitation of rotations

ApplicationsApplications Raman SpectroscopyRaman Spectroscopy is a method of determining modes of molecular is a method of determining modes of molecular

motions, especially motions, especially vibrationsvibrations. It is predominantly applicable to the. It is predominantly applicable to thequalitative and quantitative analyses of covalently bonded molecules.qualitative and quantitative analyses of covalently bonded molecules.

Characteristic regions for different groups as in IR

Raman databases available

Good for aqueous based samples

Useful for a variety of samples, organic, inorganic & biological

Identification of phasesIdentification of phases

Molecular and crystalline symmetriesMolecular and crystalline symmetries

Identification of crystalline polymorphsIdentification of crystalline polymorphs

Measurement of stressMeasurement of stress

HistoryHistory

Chandrasekhara Venkata Chandrasekhara Venkata RamanRaman

oo 1888-19701888-1970

oo Discovered the inelastic scatteringDiscovered the inelastic scatteringphenomenon in 1928phenomenon in 1928

oo Was awarded the Nobel Prize for PhysicsWas awarded the Nobel Prize for Physicsin 1930in 1930

a.k.a. SirChandra

Predicted in 1923, demonstrated 1928 by C.V.Raman

Ramans experiment:

sunlight(white)

violetfilter

violet

Scattering liquid

Raman-scattered light

observer

green

green filter

Rayleigh-scattered

light

violet green

Prof. Sir C V Raman

oo Infrared and Raman spectroscopy are two kindsInfrared and Raman spectroscopy are two kindsof spectroscopyof spectroscopy

oo a spectrum is a graph of light intensity as aa spectrum is a graph of light intensity as afunction of light frequencyfunction of light frequency

oo peaks in the spectrum give information about molecularpeaks in the spectrum give information about molecularstructurestructure

oo from molecular structure, the compound can be identifiedfrom molecular structure, the compound can be identified

frequency

intensity

Sample

I0() I()

0

0 - Rayleigh

Sample

0 - Raman

IR Spectrography - Absorption

Raman Spectrography - Scattering

Laser detector

Laser detector

oo examples of characteristic examples of characteristic stretching frequenciesstretching frequencies (group frequencies) (group frequencies)

O-HO-H 3600 cm3600 cm-1-1

N-HN-H 3400 cm3400 cm-1-1

C-HC-H 3000 cm3000 cm-1-1

C-O/C-N/C-C 1100-1200 cmC-O/C-N/C-C 1100-1200 cm-1-1

oo spectra showsspectra shows vibrational vibrational frequency infrequency in wavenumbers wavenumbers (cm(cm-1-1))

oo peaks are used to identify chemical "groups", i.e. types of bondspeaks are used to identify chemical "groups", i.e. types of bonds

C-C C-C 1200 cm1200 cm-1-1

aromatic C-C aromatic C-C 1450-1600 cm1450-1600 cm-1-1

C=CC=C 1650 cm1650 cm-1-1

CCCC 2200 cm2200 cm-1-1

C C C C C C2150 cm1 1650 cm1 1200 cm1

increasing K

C H C C C O C Cl C Br3000 cm1 1200 cm1 1100 cm1 800 cm1 550 cm1

increasing ?

Raman based on inelastic scattering of a monochromatic excitationsource

- Routine energy range: 200 - 4000 cm1

- The Raman effect comprises a very small fraction,about 1 in 107 of the incident photons.

Complementary selection rules to IR spectroscopy

- Selection rules dictate which molecular vibrations are probed

- Some vibrational modes are both IR and Raman active

Great for many real-world samples

- Minimal sample preparation (gas, liquid, solid)

- Compatible with wet samples and normal ambient

- Sample fluorescence is problematic

Polarizability Polarizability in an electric fieldin an electric field

oo An electric field will distort the molecular orbitalAn electric field will distort the molecular orbital

oo This is a weak effect that grows with the square of the intensityThis is a weak effect that grows with the square of the intensity

+ +

E +-

Induced electric dipoleInduced electric dipolemomentmoment

oo An electric field can distort the electron cloudAn electric field can distort the electron cloudof a molecule, thereby creating an of a molecule, thereby creating an inducedinducedelectric dipole momentelectric dipole moment

oo The oscillating electric field associated withThe oscillating electric field associated withEM radiation will therefore create anEM radiation will therefore create anoscillating induced electric dipole momentoscillating induced electric dipole momentwhich in turn will emit, i.e. scatter, EMwhich in turn will emit, i.e. scatter, EMradiationradiation

Raman scatteringRaman scattering

oo Rayleigh Rayleigh scattering: elastic interaction, no non-kineticscattering: elastic interaction, no non-kinetictransfer of energy between molecule and photon, transfer of energy between molecule and photon, scsc exex

oo Raman scattering: inelastic interaction, transfer ofRaman scattering: inelastic interaction, transfer ofenergy between molecule and photon, energy between molecule and photon, scsc exex

oo Stokes lines: Energy of molecule increases, Stokes lines: Energy of molecule increases, scsc < < exexoo Anti-stokes lines: Energy of photon increases, Anti-stokes lines: Energy of photon increases, scsc >>exex

Molecule

Excitation photon hex

Scattered photon hsc

oo Vibrational energy levelsVibrational energy levelsoo vv == 11oo Polarisability Polarisability must must changechange during particular vibration during particular vibration

oo Rotational energy levelsRotational energy levelsoo J =J = 22oo Non-isotropic Non-isotropic polarisability polarisability ((ie ie molecule must not bemolecule must not be

spherically symmetric like CHspherically symmetric like CH44, SF, SF66, etc.), etc.)

oo CombinedCombined

Raman selection rulesRaman selection rules

Vibrational RamanVibrational Raman

oo Symmetric stretching vibration of COSymmetric stretching vibration of CO22oo Polarisability Polarisability changeschanges

oo therefore Raman band at 1,340 cmtherefore Raman band at 1,340 cm-1-1

oo Dipole moment does Dipole moment does notnotoo no absorption at 1,340 cmno absorption at 1,340 cm-1-1 in IR in IR

Vibrational RamanVibrational Raman

oo Asymmetric stretching vibration of COAsymmetric stretching vibration of CO22oo Polarisability Polarisability does does notnot change during vibration change during vibration

oo No Raman band near 2,350 cmNo Raman band near 2,350 cm-1-1

oo Dipole moment does changeDipole moment does changeoo COCO22 absorbs at 2,349 cm absorbs at 2,349 cm

-1-1 in the IR in the IR

Raman Spectroscopy: Classical Treatment Number of peaks related to degrees of freedom

DoF = 3N - 6 (bent) or 3N - 5 (linear) for N atoms

Energy related to harmonic oscillator

Selection rules related to symmetryRule of thumb: symmetric=Raman active, asymmetric=IR active

Raman: 1335 cm1

IR: 2349 cm1

IR: 667 cm1

CO2

or = c2k(m1+m2)m1m2

Raman + IR: 3657 cm1

Raman + IR: 3756 cm1

Raman + IR: 1594 cm1

H2O

ElectronicGround State

1st ElectronicExcited State

Excit

ation

Ene

rgy,

(cm

1 )

Vib.states

4,000

25,000

0 IR

2nd ElectronicExcited State

emit

fluore

scenc

eIm

purit

y

emit

fluore

scenc

e

UV/VisFluorescence

emit

ElasticScattering(Raleigh)

Main Optical Transitions: Absorption, Scattering, and Fluorescence

ElectronicGround State

1st ElectronicExcited State

Excit

ation

Ene

rgy,

(cm

1 )

Vib.states

4,000

25,000

0 IR

emit

2nd ElectronicExcited State

Raman=emit

Resonance Raman=emit

Raman Spectroscopy: Absorption, Scattering, and Fluorescence

Stokes Anti-Stokes

ElectronicGround State

1st ElectronicExcited State

Excit

ation

Ene

rgy,

(cm

1 )

Vib.states

4,000

25,000

0

fluore

scenc

e

IR

emit

2nd ElectronicExcited State

Raman=emit-

flu

oresce

nce

Impu

rity

Fluorescence = Trouble

Raman Spectroscopy: Absorption, Scattering, and Fluorescence

Stokes Anti-Stokes

Raman SpectrumRaman SpectrumA Raman spectrum is a plot of the intensity of Raman scattered radiation as a functionof its frequency difference from the incident radiation (usually in units of wavenumbers,cm-1). This difference is called the Raman shift.

At the very most, the intensities of Raman lines are 0.001 % of the intensity of thesource; as a consequence, their detection and measurement are somewhat moredifficult than are infrared spectra

Raman Spectrum of CCl4

The intensity or power of a normal Raman peakdepends in a complex way upon thepolarizability of the molecule, the intensity of thesource, and the concentration of the activegroup.

The power of Raman emission increases withthe fourth power of the frequency of the source

Raman intensities are usually directlyproportional to the concentration of the activespecies.

Stokes and anti-StokesStokes and anti-Stokes

As you can see, theStokes peaks correspondto lower photonfrequencies and lowerenergies. The anti-Stokes side is symmetricbut corresponds tohigher frequencies andenergies. The Stokeslines are strongerbecause the populationof molecules at =0 ismuch larger than at=1 by the Maxwell-Boltzmann distributionlaw.

Advantages of RamanAdvantages of Raman

oo Selection rules allow for some vibrations (normallySelection rules allow for some vibrations (normallysymmetric) to be seen only by Ramansymmetric) to be seen only by Ramanspectroscopy.spectroscopy.

oo Measurements of depolarization ratios yieldMeasurements of depolarization ratios yieldinformation about molecular symmetry.information about molecular symmetry.

oo Only a small sample area is needed (laser spot).Only a small sample area is needed (laser spot).oo Water is a weak Raman Water is a weak Raman scattererscatterer, allowing for the, allowing for the

use of aqueous solutions. Can also sample throughuse of aqueous solutions. Can also sample throughglass container walls.glass container walls.

oo The region 4000 cmThe region 4000 cm-1-1 to 50 cm to 50 cm-1-1 can be covered in can be covered ina single scan without changing gratings, splitters,a single scan without changing gratings, splitters,detectors, etc.detectors, etc.

The simplest real vibrating system:The simplest real vibrating system:a diatomic moleculea diatomic molecule

( )2122

2

21

2

21

21 xxKdt

xd

dt

xdmmmm

+=

+

+

qKdt

qd2

2

=Reduced mass displacement

( )t2cosqq m0 =

=

K21

mWhere:

Just likeHookeslaw: F=kX

x1 x2

m1 m2

K

Scattering of radiation from a diatomicScattering of radiation from a diatomicmoleculemolecule

( )t2cosEE 00 =

( )t2cosqq m0 =

?

( )t2cosEEP 00 ==Induced dipole moment:

For a small amplitude of vibration, thepolarizability is a linear function of q: K+

+==

qq 0q

0

( ) ( ) ( )

( ) { }( ) { }( )[ ]t2cost2cosEqq2

1t2cosE

t2cosEt2cosqq

t2cosEP

m0m0000q

000

00m00q

000

++

+=

=

+=

=

=

Rayleighscattering

Stokesscattering

Anti-Stokesscattering

Selection rules for vibrationsSelection rules for vibrations

oo IR absorption: electric dipole moment of molecule changes during vibrationIR absorption: electric dipole moment of molecule changes during vibration

oo electric dipole moment is net separation of + and electric dipole moment is net separation of + and charge charge

oo tends to show peaks for polar bonds and non-symmetric vibrationstends to show peaks for polar bonds and non-symmetric vibrations

oo NO for HNO for H22 stretch and CO stretch and CO22 symmetric stretch symmetric stretch

oo YES for COYES for CO22 asymmetric stretch and bend asymmetric stretch and bend

oo Raman scattering:Raman scattering: polarisability polarisability ofofmolecule changes during vibrationmolecule changes during vibration

oo polarisability is related to how easily apolarisability is related to how easily amolecule can be deformedmolecule can be deformed

oo tends to show peaks fortends to show peaks for homopolar homopolar bondsbondsand symmetric vibrationsand symmetric vibrations

oo NO for CONO for CO22 asymmetric stretch and asymmetric stretch andbendbend

oo YES for HYES for H22 stretch and CO stretch and CO22 symmetric symmetricstretchstretch

More mathMore math

In actual molecules, the nice linear relationship does not hold since both P and E are vectors. Then the equation must be written asPxPyPz

=

xx xy xzyx yy yzzx zy zz

ExEyEz

The matrix is called the

polarizability tensor. Wecan plot

i ( in the i

direction) in all directions

we get a 3D surface.

Conventionally we plot

instead, and get a

polarizability ellipsoid.

1/ i

Selection rulesSelection rules

dVxdVI 1i01i0i =

= dVxxdVI 1ji01ij0ij

i ( i = x,y,z ) are the components of the dipole moment.

If one of the integrals i 0, than the transition is IR active

ij ( i,j = x,y,z ) are the components of the polarizability tensor.

If one of the integrals ij 0, than the transition is Raman active

0 and 1 are the wavefunctions of a molecule before and after avibrational transition, respectively.

=

z

y

x

zzzyzx

yzyyyx

xzxyxx

z

y

x

E

E

E

P

P

P

COCO22 Polarizability Polarizability ellipsoidsellipsoids

Raman active

IR active

IR active

Modes ofModes of H H22OO

All the modes are bothRaman & IR Active

The simplest Raman active crystal:The simplest Raman active crystal:1D chain with 2 atoms in the unit cell1D chain with 2 atoms in the unit cell

m1 m2K

( )( )1n2n22n2n22

n21n21n2n21

u2uuKum

u2uuKum

++

+

+=

+=

&&

&&

u2n u2n+1

=

21

22

2

2

22

mmkasinK4KK

4

1

[ ]( )[ ]ka1n2t2iexpAunka2t2iexpAu

21n2

1n2

++=

+=

+

Equations of motion:

Assume the solutions:

Obtain the frequencies:

The The phononphonon spectrum spectrum

IR & Raman Active

ScatteringScattering

ooClassically, the observed intensity of RamanClassically, the observed intensity of Ramanscattering is proportional toscattering is proportional to

IIRR = = ((00jj))44jj

22QQjj22

where where 00 is the laser light frequency, is the laser light frequency, jj is theis the

frequency of the frequency of the jjthth mode, mode, QQjj the displacement,the displacement,and and is the is the polarizability polarizability of that mode. of that mode. NoteNote

the dependence on the fourth power of thethe dependence on the fourth power of thelaser lightlaser light, typical for dipole scattering., typical for dipole scattering.

PolarizationPolarization

oo Incident laser light is plane-polarizedIncident laser light is plane-polarized

oo Scattered light may become de- polarizedScattered light may become de- polarized

Depolarization occurs forthe less symmetricalvibrational modes

DepolarizationDepolarizationoo Put a (plane) polarizing filter between sample andPut a (plane) polarizing filter between sample and

detectordetector

oo Acquire spectrum with polarizing filter parallel to laserAcquire spectrum with polarizing filter parallel to laserplane polarizationplane polarization

oo Rotate polarizing filter 90Rotate polarizing filter 90, reacquire spectrum, reacquire spectrum

oo Compare relative intensities of bands in the two spectraCompare relative intensities of bands in the two spectra

DepolarizationDepolarization

oo Define Define depolarization ratiodepolarization ratio

||

=II

0 < < 0.75, band is said to be polarized

= 0.75, band is said to be depolarized

PolarizationPolarization

oo Raman: Raman:

- totally symmetric vibrations produce polarized bands,- totally symmetric vibrations produce polarized bands,0 < 0 < < 0.75 < 0.75

- non-totally symmetric vibrations produce depolarized- non-totally symmetric vibrations produce depolarizedbands, bands, = 0.75 = 0.75

- polarization measurements can help identify (symmetry)- polarization measurements can help identify (symmetry)type of vibration producing a bandtype of vibration producing a band

Depolarization ratioDepolarization ratiooo The depolarization ratioThe depolarization ratio

is defined as the ratio ofis defined as the ratio ofthe light scattered at 90the light scattered at 90degrees that isdegrees that isperpendicular (perpendicular (IIyy) to the) to thelight that is parallel (Ilight that is parallel (I||||))with respect to thewith respect to theincident light.incident light.

oo TheThe incident laser lightincident laser lightis already polarized.is already polarized.But the scrambler isBut the scrambler isrequired becauserequired becausemonochromator monochromator gratingsgratingsshow differentshow differentefficiencies for theefficiencies for thedifferent polarizations.different polarizations.

Ez

Incident laser beam

y

z

x

Scrambler

Analyzer

Iz (I||)

Iy (I )

Direction ofobservation

(Original diagram from J.R. Ferraro, in References)

Depolarization ratioDepolarization ratio

Since the ratio is defined as

p =IyIz

, and it can be shown that this is related to the

polarizability matrix by

p =3gs + 5ga10g0 + 4gs , where

g0 = 13 xx + yy + zz( )2

gs = 13 ( xx yy )2 + ( yy zz)2 + ( zz xx )2[ ]

+12 ( xy +yx )

2 + ( yz + zy )2 + (xz + zx )2[ ]

ga = 12 ( xy yx )2 + ( xz zx )2 + ( yz zy )2[ ]

In normal Raman scattering, ga = 0 from symmetry. For totally symmetric vibration, we

then get

0 p twist () > twist ())

458 cm-1 790 cm-1

218 cm-1314 cm-1

CClCCl44 modes and Raman modes and Raman

ooAnimation fromAnimation fromhttp://http://fyfy..chalmerschalmers.se/~b.se/~brodin/MolecularMotions/rodin/MolecularMotions/CCl4molecule.htmlCCl4molecule.html

Temperature correctionTemperature correction

oo The thermal population factor can maskThe thermal population factor can maskpeakspeaks or bands in the low-frequency regionor bands in the low-frequency regionof the spectrum. The corrected (reduced)of the spectrum. The corrected (reduced)Raman intensity can be calculated fromRaman intensity can be calculated from

Ireduced =Iobserved

Exp hkT

+1

This needs to be done before any peakassignments are made

Temperature correctionTemperature correction

oo The effect of theThe effect of thetemperaturetemperaturecorrection can becorrection can beseen at left, whereseen at left, wherethe most dramaticthe most dramaticchange occurs atchange occurs atlow low wavenumberswavenumbers..

Modern Raman SpectrometersModern Raman Spectrometersoo FT-Raman spectrometers FT-Raman spectrometers also make use of Michelson also make use of Michelson

interferometersinterferometersoo Use IR (1 Use IR (1 m) lasers, almost no problem with fluorescence form) lasers, almost no problem with fluorescence for

organic moleculesorganic molecules

oo Have many of the same advantages of FT-IR over dispersiveHave many of the same advantages of FT-IR over dispersive

oo But, there is much debate about the role of But, there is much debate about the role of shot noiseshot noise and andwhether signal averaging is really effectivewhether signal averaging is really effective

oo CCD-Raman spectrometers CCD-Raman spectrometers dispersive spectrometers that use a dispersive spectrometers that use aCCD detectorCCD detector

oo Raman is detected at optical frequencies!Raman is detected at optical frequencies!

oo Generally more sensitive, used for microscopyGenerally more sensitive, used for microscopy

oo Usually more susceptible to fluorescence, also more complexUsually more susceptible to fluorescence, also more complex

oo Detectors - Detectors - GaAs GaAs photomultiplier tubes, diode arrays, in addition tophotomultiplier tubes, diode arrays, in addition tothe above.the above.

Dispersive and FT-Dispersive and FT-RamanRaman

SpectrometrySpectrometry

McCreeryMcCreery, R. L., , R. L., RamanRamanSpectroscopy for ChemicalSpectroscopy for Chemical

Analysis, 3rd ed.Analysis, 3rd ed., Wiley, New, Wiley, NewYork: 2000York: 2000

Sample Illumination SystemSample Illumination Systemoo Liquid Samples:Liquid Samples: A major advantage of sample A major advantage of sample

handling in Raman spectroscopy compared withhandling in Raman spectroscopy compared withinfrared arises because water is a weak Ramaninfrared arises because water is a weak Ramanscatterer scatterer but a strong absorber of infrared radiation.but a strong absorber of infrared radiation.Thus, aqueous solutions can be studied by RamanThus, aqueous solutions can be studied by Ramanspectroscopy but not by infrared. This advantage isspectroscopy but not by infrared. This advantage isparticularly important for biological and inorganicparticularly important for biological and inorganicsystems and in studies dealing with water pollutionsystems and in studies dealing with water pollutionproblems.problems.

oo Solid Samples:Solid Samples: Raman spectra of solid samples are Raman spectra of solid samples areoften acquired by filling a small cavity with the sampleoften acquired by filling a small cavity with the sampleafter it has been ground to a fine powder. Polymersafter it has been ground to a fine powder. Polymerscan usually be examined directly with no samplecan usually be examined directly with no samplepretreatment.pretreatment.

Simplified RamanSimplified Ramanspectrometer layoutspectrometer layout

LasersLasers

For a long time the most common laser for a Ramansystem was the Ar:ion laser, which provided multiple lines(wavelengths). Cost was significant, however, as weremaintenance costs. Nowadays the selection is muchgreater: Gas Ion, HeNe, DPSS 532 nm, Solid-state visiblelasers, NIR Diode, High power fibre linked, UV lasers

The key is what laser canminimize the fluorescence signalof the sample. On the left wesee a sample irradiated withgreen light (too fluorescent); redlight (still too much), and NIR(785 nm; just right)

A Typical Raman System

Typical geometries for RamanTypical geometries for Ramanscatteringscattering

90o scattering

180o scattering

SpectrographsSpectrographs

oo The most commonThe most commonspetrographspetrographarrangement is thearrangement is theCzerny-Turner, shownCzerny-Turner, shownon the right. Theon the right. Themirrors are used asmirrors are used ascollimators, and thecollimators, and theturret contains planarturret contains planarreflective gratings.reflective gratings.

SpectrographsSpectrographs

oo For higher resolutionFor higher resolutionand rejection ofand rejection ofunwanted (readunwanted (readRayleighRayleigh) wavelengths,) wavelengths,one can use a doubleone can use a doubleor tripleor triplemonochromatormonochromator. This. Thisadds to the price andadds to the price anddiminishes the overalldiminishes the overalllight signal.light signal.

CCD DetectorsCCD Detectors

oo Most of the current dispersive Raman set-upsMost of the current dispersive Raman set-upsare now equipped with are now equipped with multichannel multichannel two-two-dimensional CCD detectors. The maindimensional CCD detectors. The mainadvantages of these detectors are the highadvantages of these detectors are the highquantum efficiency, the extremely low level ofquantum efficiency, the extremely low level ofthermal noise (when effectively cooled), lowthermal noise (when effectively cooled), lowread noise and the large spectral rangeread noise and the large spectral rangeavailable. Many CCD chips exist, but one of theavailable. Many CCD chips exist, but one of themost common spectroscopy sensor formats ismost common spectroscopy sensor formats isthe 1024 x 256 pixel array.the 1024 x 256 pixel array.

FT-RamanFT-Raman

Advantages andAdvantages anddisadvantages of FT-Ramandisadvantages of FT-Raman

oo Use of NIR lasers greatly reduces fluorescence problemUse of NIR lasers greatly reduces fluorescence problemoo Relatively inexpensiveRelatively inexpensiveoo High resolution, high throughputHigh resolution, high throughputoo Collects Stokes and Anti-Stokes simultaneouslyCollects Stokes and Anti-Stokes simultaneouslyoo Can be attached to an IR instrumentCan be attached to an IR instrumentButButoo Black body emissions at higher temp swamp RamanBlack body emissions at higher temp swamp Ramanoo Lower scattering intensity due to use of NIR (Lower scattering intensity due to use of NIR (44 effect) effect)oo Absorptions in the NIRAbsorptions in the NIRoo Slow (tens of minutes in some systems)Slow (tens of minutes in some systems)

Michelson interferometerMichelson interferometer

3D viewFTIR

FT-Raman schematicFT-Raman schematic

InteferometersInteferometers For monochromatic

radiation, theinterferogram looks likea cosine curve

For polychromaticradiation, eachfrequency is encodedwith a much sloweramplitude modulation

The relationshipbetween frequencies:

Example: mirror rate = 0.3 cm/s modulates 1000 cm-1 light at 600 Hz Example: mirror rate = 0.2 cm/s modulates 700 nm light at 5700 Hz

cv

f M2

=

Where: is the frequency of the radiationc is the speed of light in cm/svm is the mirror velocity in cm/s

Raman microscopesRaman microscopes

Microscope schematicMicroscope schematic

Conventional Conventional vsvs. . ConfocalConfocal