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
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