1. 6. Really Basic Optics Instrument Sample Sample Prep Instrument
Out put
Signal (Data)
Polychromatic light
Selected
light
Turn off/diminish intensity
Sample
interaction
Select
light
Turn on different wavelength
select
source
detect

2. Really Basic Optics Key definitions Phase angle
Atomic lines vs molecular bands
Atomic Line widths (effective; natural)
Doppler broadening
Molecular bands
Continuum sources Blackbody radiators
Coherent vs incoherent radiation

3. 6. Really Basic Optics A Sin=opp/hyp  y  /2 3/2  2
90o phase angle
/2 radian phase angle

4. Emission of Photons
Electromagnetic radiation is emitted when electrons relax from excited states.
A photon of the energy equivalent to the difference in electronic states
Is emitted
Ehi e
Elo
Frequency 1/s

5. Really Basic Optics Key definitions Phase angle
Atomic lines vs molecular bands
Atomic Line widths (effective; natural)
Doppler broadening
Molecular bands
Continuum sources Blackbody radiators
Coherent vs incoherent radiation

7. Theoretical width of an atomic spectral line

8. Natural Line Widths frequency Line broadens due Uncertainty
Doppler effect
Pressure
Electric and magnetic fields
frequency
Lifetime of an excited state is typically 1x10-8 s

9. Typical natural line widths are 10-5 nm
Example: nm
Typical natural line widths are 10-5 nm

10. Line broadens due
Uncertainty
Doppler effect
Pressure
Electric and magnetic fields

11. Line broadens due
Uncertainty
Doppler effect
Pressure
Electric and magnetic fields
The lifetime of a spectral event is 1x10-8 s
When an excited state atom is hit with another high energy atom
energy is transferred which changes the energy of the
excited state and, hence, the energy of the photon emitted.
This results in linewidth broadening.
The broadening is Lorentzian in shape.
We use pressure broadening
On purpose to get a large
Line width in AA for some
Forms of background
correction
FWHM = full width half maximum
o is the peak “center” in frequency units

12. Line spectra – occur when radiating species are atomic particles which
Experience no near neighbor interactions
Line broadens due
Uncertainty
Doppler effect
Pressure
Electric and magnetic fields
Line events
Can lie on top
Of band events
Overlapping line spectra lead to band emission

13. Continuum emission – an extreme example of electric and magnetic
effects on broadening of multiple wavelengths
High temperature solids emit Black Body Radiation
many over lapping line and band emissions influenced by
near neighbors

14. Stefan-Boltzmann Law
Planck’s Blackbody Law
= Energy density of radiation
h= Planck’s constant
C= speed of light
k= Boltzmann constant
T=Temperature in Kelvin
= frequency
Wien’s Law
As  ↓(until effect of exp takes over)
As T,exp↓, 

15. Really Basic Optics Key definitions Phase angle
Atomic lines vs molecular bands
Atomic Line widths (effective; natural)
Doppler broadening
Molecular bands
Continuum sources Blackbody radiators
Coherent vs incoherent radiation

16. Incoherent radiation
The Multitude of emitters, even if they emit
The same frequency, do not emit at the
Same time A B
Frequency,, is the
Same but wave from particle
B lags behind A by the
Phase angle 

17. Begin END: Key Definitions Using Constructive and Destructive
Interference patterns based on phase lag
By manipulating the path length can cause an originally coherent beam
(all in phase, same frequency) to come out of phase can accomplish
Many of the tasks we need to control light for our instruments
Constructive/Destructive interference
Laser
FT instrument
Can be used to obtain information about distances
Interference filter.
Can be used to select wavelengths

18. More Intense Radiation can be obtained by Coherent Radiation
Lasers
Beam exiting the cavity is in phase (Coherent) and therefore enhanced
In amplitude

19. Argument on the size of signals that follows is from Atkins, Phys. Chem. p. 459, 6th Ed
Stimulated Emission
Light Amplification by Stimulated Emission of Radiation
Photons can stimulate
Emission just as much
As they can stimulate
Absorption
(idea behind LASERs
Stimulated Emission) * o
The rate of stimulated event is described by :
Where w =rate of stimulated emission or absorption
Is the energy density of radiation already present at the frequency of the transition
The more perturbing photons the greater the
Stimulated emission
B= empirical constant known as the Einstein coefficient for stimulated absorption or emission
N* and No
are the populations of upper state and lower states

20. can be described by the Planck equation for black body radiation at some T
frequency
In order to measure absorption it is required that the
Rate of stimulated absorption is greater than the
Rate of stimulated emission
If the populations of * and o are the same the net absorption is zero as a photon is
Absorbed and one is emitted

21. Need to get a larger population in the excited state
Compared to the ground state (population inversion)
Degeneracies of the different energy levels
Special types of materials have larger excited state degeneracies
Which allow for the formation of the excited state population inversion
Serves to “trap” electrons in the excited
State, which allows for a population
inversion E
pump

22. Constructive/Destructive interference
Laser
FT instrument
Can be used to select wavelengths
Can be used to obtain information about distances
Holographic Interference filter.
Radiation not along the
Path is lost
mirror
mirror
Stimulated emission
Single phase
Along same path
=Constructive Interference
Coherent radiation
Multiple directions,
Multiple phase lags
Incoherent radiation

23. FTIR Instrument Constructive/Destructive interference Laser
FT instrument
Can be used to select wavelengths
Can be used to obtain information about distances
Holographic Interference filter.

24. Time Domain: 2 frequencies
1 “beat” cycle

25. B
Fixed mirror A C
Moving mirror
Beam
splitter
IR source
detector
Constructive interference occurs when

26. -2
-1
+1

27. INTERFEROGRAMS
Remember that:
Frequency of light

28. An interferometer detects a periodic wave with a frequency of 1000 Hz when moving at a velocity of 1 mm/s. What is the frequency of light impinging on the detector?

29. No need to SELECT
Wavelength by using
Mirror, fiber optics,
Gratings, etc.

30. FOURIER TRANSFORMS Advantages Jaquinot or through-put
little photon loss; little loss of source intensity
Large number of wavelengths allows for ensemble averaging
(waveform averaging)
3. This leads to Fellget or multiplex advantage
multiple spectra in little time implies?

31. DIFFRACTION
Huygen’s principle = individual propagating waves combine to form a new wave front
Constructive/Destructive interference
Laser
FT instrument
Can be used to select wavelengths
Can be used to obtain information about distances
Holographic Interference filter.
Can get coherent radiation if the slit is narrow enough. Coherent = all in one phase

33. June 19, 2008, Iowa Flood
Katrina Levee break

34. Fraunhaufer diffraction at a single slit

35. D d B F’ E W O L F C
From which we conclude

36. D
The complete equation for a slit is d B E W L
b=W/2
Width of the line depends upon
The slit width!!
Therefore resolution depends
On slit width
Also “see”
This spectra
“leak” of
Our hard won
intensity

37. The base (I=0) occurs whenever
sinβ =0
Which occurs when
The smaller the
Slit width the
Smaller
The line width,
Which leads
To greater
Spectral
Resolution
Remember R is
Inversely proportional
To the width of
The Gaussian base

38. SLIT IMAGE
Slit A
1 2 3 B
Position number
Image
When edge AB at Detector Sees
Position 1 0% power
Position 2 50% power
Position % power
Position 4 50% power
Position 5 0 % power
Detector output:
Triangle results when
Effective bandpass = image
To resolve two images that are ∆ apart requires
Implies want a narrower slit

39. Essentially,
Narrow slit widths
Are generally better

41. GRATINGS Points: Master grating formed by diamond tip under ground
Gratings Groves/mm
UV/Vis 300/2000
IR 10/20
Points:
Master grating formed by diamond tip under ground
Or more recently formed from holographic processes
Copy gratings formed from resins

42. + - q q

43. EXAMPLE Calculate  for a grating which has i=45 2000 groves per mm
Get d
2) Use grating equation to solve for 

44. Czerny-Turner
construction
440.3
220.1
146.8 88 73
All come
through
Multiple wavelengths
Are observed
At a single angle
Of reflection!!
You get light of nm
½; 1/3; 1/4; 1/5; etc.

45. Czerny-Turner construction
Physical Dimensions: mm x 63.3 mm x 34.4 mm
Weight: 190 grams
Detector: Sony ILX511 linear silicon CCD array
Detector range: nm
Pixels: 2048 pixels
Pixel size: 14 μm x 200 μm
Pixel well depth: ~62,500 electrons
Sensitivity: 75 photons/count at 400 nm; 41 photons/count at 600 nm
Design: f/4, Symmetrical crossed Czerny-Turner
Focal length: 42 mm input; 68 mm output
Entrance aperture: 5, 10, 25, 50, 100 or 200 µm wide slits or fiber (no slit)
Grating options: 14 different gratings, UV through Shortwave NIR
Detector collection lens option: Yes, L2
OFLV filter options: OFLV ; OFLV
Other bench filter options: Longpass OF-1 filters
Collimating and focusing mirrors: Standard or SAG+
UV enhanced window: Yes, UV2
Fiber optic connector: SMA 905 to 0.22 numerical aperture single-strand optical fiber
Spectroscopic Wavelength range: Grating dependent
Optical resolution: ~ nm FWHM
Signal-to-noise ratio: 250:1 (at full signal)
A/D resolution: 12 bit
Dark noise: 3.2 RMS counts
Dynamic range: 2 x 10^8 (system); 1300:1 for a single acquisition
Integration time: 3 ms to 65 seconds
Stray light: <0.05% at 600 nm; <0.10% at 435 nm
Corrected linearity: >99.8%
Electronics Power consumption: VDC
Data transfer speed: Full scans to memory every 13 ms with USB 2.0 or 1.1 port, 300 ms with serial port
Czerny-Turner
construction

46. Monochromator we looked inside
Ocean Optics
For fluorescence lab
440.3
220.1
146.8 88 73
All come
through
Monochromator we looked inside
440.3
Only
Hit grating first
Time to get
Hit grating second time
440.3
220.1
146.8 88 73
All come
through
220.1 nm

47. Another way to look at it is to say
We Lose some of the light
Not all of it ends up at the intended angle of reflection
Light of 100
Nm shows up
At -30.4
AND
-17.88
And
-6.1
5.3
Etc.

48. GRATING DISPERSION D-1 = Reciprocal linear dispersion
Where n= order
F = focal length
d= distance/groove
POINT = linear dispersion

49. What is (are) the wavelength(s) transmitted at 45o reflected AND incident light for a grating of 4000 groves/mm?

50. RESOLUTION
The larger R the greater the spread between the two wavelengths, normalized by
The wavelength region
Where n = order and N = total grooves exposed to light

51. What is the resolution of a grating in the first order of 4000 groves/mm if 1 cm of the grating is illuminated?
Are 489 and nm resolved?

52. Constructive/Destructive interference
Laser
FT instrument
Can be used to select wavelengths
Can be used to obtain information about distances
Holographic Interference filter.
Change in path length results
In phase lag
The photo plate contains all the information
Necessary to give the depth perception when
decoded

53. Interference Filter
Holographic Notch Filter
Can create a filter using
The holographic principle
To create a series of
Groves on the surface
Of the filter. The grooves
Are very nearly perfect
In spacing
Constructive/Destructive interference
Laser
FT instrument
Can be used to obtain information about distances
Interference filter.
Can be used to select wavelengths

54. End Section on Using Constructive and Destructive
Interference patterns based on phase lags
Constructive/Destructive interference
Laser
FT instrument
Can be used to obtain information about distances
Interference filter.
Can be used to select wavelengths

55. Interaction with Matter
Begin Section
Interaction with Matter
In the examples above have assumed that there is no interaction with
Matter – all light that impinges on an object is re-radiated with it’s
Original intensity

57. Move electrons around (polarize)
Re-radiate
“virtual state”
Lasts ~10-14s

58. This phenomena causes:
Move electrons around (polarize)
Re-radiate
This phenomena causes:
1. scattering
2. change in the velocity of light
3. absorption

59. First consider propagation of light in a vacuum
c is the velocity of the electromagnetic wave in free space
Is the permittivity of free space which describes the
Flux of the electric portion of the wave in vacuum and
Has the value
capacitance
force
It can be measured directly from capacitor measurements
Is the permeablity of free space and relates the current
In free space in response to a magnetic field and is defined as

61. Dielectric constant
Typically so
This works pretty well for gases (blue line)
Says: refractive index is proportional to the dielectric
constant
Maxwell’s relation

62. Our image is of electrons perturbed by an electromagnetic field which causes
The change in permittivity and permeability – that is there is a “virtual”
Absorption event and re-radiation causing the change
It follows that the re-radiation event should be be related to the ability to
Polarize the electron cloud
10-14 s to polarize the electron cloud and re-release electromagnetic
Radiation at same frequency

63. SCATTERING Most important parameter is the relationship to wavelength
Light in
particle
Angle between incident and scattered
light
Polarizability of electrons
Number of electrons
Bond length
Volume of the molecule, which depends upon the radius, r
= vacuum 
Io = incident intensity

64. At sunset the shorter wavelength is
Scattered more efficiently, leaving the
Longer (red) light to be observed
Better sunsets in polluted regions
Blue is scattered
Red is observed
Long path allow more of the blue light (short wavelength) to be scattered

65. What is the relative intensity of scattered light for 480 vs 240 nm?
What is the relative intensity of scattered light as one goes from Cl2 to Br2? (Guess)

66. Our image is of electrons perturbed by an electromagnetic field which causes
The change in permittivity and permeability – and therefore, the speed of the
Propagating electromagnetic wave.
It follows that the index of refraction should be related to the ability to
Polarize the electron cloud

67. Refractive index = relative speed of radiation
Refractive index is related to the relative permittivity (dielectric constant) at that Frequency
Where  is the mass density of the sample, M is the molar mass of the molecules and Pm is the molar polarization
Is the permittivity of free space which describes the
Flux of the electric portion of the wave in vacuum and
Has the value
Where  is the electric dipole moment operator
 is the mean polarizabiltiy
Point – refractive index
Is related to polarizability
Clausius-Mossotti equation

68. Where e is the charge on an electron, R is the radius of the molecule and ∆E is the mean energy to excite an electron between the HOMO-LUMO
The change in the velocity of the electromagnetic radiation is a function of
1.mass density (total number of possible interactions)
2. the charge on the electron
3. The radius (essentially how far away the electron is from the nucleus)
4. The Molar Mass (essentially how many electrons there are)
5. The difference in energy between HOMO and LUMO

69. An alternative expression for a single atom is
Transition probability that
Interaction will occur
A damping force term that account for
Absorbance (related to delta E in prior
Expression)
Molecules per
Unit volume
Each with
J oscillators
Natural
Frequency of
The oscillating electrons
In the single atom j
Frequency of incoming electromagnetic
wave
If you include the interactions between atoms and ignore absorbance you get

70. The refractive index is constant
when
The refractive index depends on omega
when
Gets smaller so the
Refractive index rises
And the difference

71. REFRACTIVE INDEX VS 
Anomalous dispersion near absorption bands which occur at natural harmonic frequency of material
Normal dispersion is required for lensing materials

73. What is the wavelength of a beam of light that is 480 nm in a vacuum if it travels in a solid with a refractive index of 2?

74. Filters can be constructed
By judicious combination of the
Principle of constructive and
Destructive interference and
Material of an appropriate refractive
index t
Wavelength
In media t t

75. What is (are) the wavelength(s) selected from an interference filter which has a base width of m and a refractive index of 1.34?

76. Holographic filters are better

77. INTERFERENCE WEDGES AVAILABLE WEDGES Vis 400-700 nm
Near IR nm
IR m

78. Using constructive/destructive interference to select for polarized light
The electromagnetic wave can be described in two components, xy, and
Xy - or as two polarizations of light.

79. Refraction, Reflection, and Transmittance Defined
Relationship to polarization
The amplitude of the spherically oscillating electromagnetic
Wave can be described mathematically by two components
The perpendicular and parallel to a plane that described the advance of
The waveform. These two components reflect the polarization of the wave

80. When this incident, i, wave plane strikes a denser surface with polarizable electrons
at an angle, i, described by a perpendicular to
The plane
It can be reflected
Air, n=1
Or transmitted R T
Glass
n=1.5
The two polarization components are
reflected and transmitted with
Different amplitudes depending
Upon the angle of reflection, r,
And the angle of transmittence, t
Let’s start by examing
The Angle of transmittence

81. Snell’s Law Less dense 1 Lower refractive index More dense 1
Time=4
Time=3
Time=2
Time=1
Time=0
Time=4
Time=3
Less dense 1
Lower refractive index
Faster speed of light
Time=2
More dense 1
Higher refractive index
Slower speed of light
Time=1
Time=0

82. What is the angle of refraction, 2, for a beam of light that impinges on a surface at 45o, from air, refractive index of 1, to a solid with a refractive index of 2?

83. PRISM Crown Glass (nm)  nm 1.532 450 nm 1.528 550 nm 1.519
Uneven spacing = nonlinear
POINT, non-linear dispersive device
Reciprocal dispersion will vary with wavelength, since refractive index varies with wavelength

85. The intensity of light (including it’s component polarization) reflected as compared to transmitted (refracted) can be described by the Fresnel Equations R T
Angle of transmittence
Is controlled by
The density of
Polarizable electrons
In the media as
Described by Snell’s Law

86. The amount of light reflected depends upon the Refractive indices and the angle of incidence.
We can get Rid of the angle of transmittence using Snell’s Law
Since the total amount of light needs to remain constant we also know that
Therefore, given the two refractive
Indices and the angle of incidence can
Calculate everything

87. Consider and air/glass interface
Here the transmitted parallel light is
Zero! – this is how we can select
For polarized light!
This is referred to as the polarization
angle

89. Total Internal Reflection
Here consider
Light propagating
In the DENSER
Medium and
Hitting a
Boundary with
The lighter
medium
Glass
n=1.5 R T
Air, n=1

90. Same calculation but made the indicident medium denser so that wave is
Propagating inside glass and is reflected at the air interface
Discontinuity at 42o signals
Something unusual is
happening

91. All of the light is reflected
internally
Set R to 1 &  to 90
The equation can be solved for the critical angle of incidence
For glass/air

92. The angle at which the discontinuity occurs:
0% Transmittance=100% Reflectance
Total Internal Reflectance
Angle = Critical Angle – depends on refractive index
1.69/1
1.3/1
1.5/1 37 51 42

94. Numerical Aperture
The critical angle here is defined differently because we have to LAUNCH the
beam

95. Shining light directly through our sample
Using Snell’s Law the angle of transmittance is
R=? T

96. same
The amount of light reflected depends
Upon the refractive indices of the medium

97. For a typical Absorption Experiment,
How much light will we lose from the cuvette?
Or another way to put it is how much light will get transmitted?

98. Water, refractive index 1.33
It’’ =
I’’’o
It’ = I’’o
It’’’ Io
It=I’o
Air, refractive index 1
Air
Glass, refractive index 1.5
Final exiting light

99. We lose nearly 10% of the light

100. Key Concepts
Interaction with Matter
Light Scattering
Refractive Index
Is wavelength dependent
Used to separate light by prisms
Refractive index based
Interference filters

101. Snell’s Law Key Concepts Interaction with Matter
Describes how light is bent based differing refractive indices
Fresnell’s Equations describe how polarized light is transmitted and/or reflected
at an interface
Used to create surfaces which select for polarized light

102. Key Concepts
Interaction with Matter
Fresnell’s Laws collapse to
Which describes when you will get total internal reflection (fiber optics)
And
Which describes how much light is reflected at an interface

103. PHOTONS AS PARTICLES The photoelectric effect: The experiment:
1. Current, I, flows when Ekinetic > Erepulsive
2. E repulsive is proportional to the applied voltage, V
3. Therefore the photocurrent, I, is proportional to the applied voltage
4. Define Vo as the voltage at which the photocurrent goes to zero = measure of the maximum kinetic energy of the electrons
5. Vary the frequency of the photons, measure Vo, = Ekinetic,max
Work function=minimum energy binding an
Electron in the metal
Energy of
Ejected
electron
Frequency of impinging photon
(related to photon energy)

104. To convert photons to electrons that we can measure with an electrical circuit use
A metal foil with a low work function (binding energy of electrons)

107. DETECTORS Ideal Properties High sensitivity Large S/N
Constant parameters with wavelength
Where k is some large constant
kd is the dark current
Want low dark current
Classes of Detectors
Name comment
Photoemissive single photon events
Photoconductive “ (UV, Vis, near IR)
Heat average photon flux

108. Very sensitive detector
Rock to
Get different
wavelengths
Capture all simultaneously
= multiplex advantage
2. Generally less sensitive

109. Sensitivity of photoemissive
Surface is variable
Ga/As is a good one
As it is more or less consistent
Over the full spectral range

110. Diode array detectors
Great in getting
A spectra all at once!
Background current
(Noise) comes from?
One major problem
Not very sensitive
So must be used
With methods in
Which there is a large
signal

111. Photomultiplier tube
The AA experiment
Photodiodes

112. The fluorescence
experiment
Charge-Coupled Device (CCD detectors)
1. Are miniature – therefore do not need to “slide” the image across
a single detector (can be used in arrays to get a
Fellget advantage)
2. Are nearly as sensitive as a photomultiplier tube
Set device to accumulate
charge for some period of
time. (increase sensitivity)
Charge accumulated near
electrode
Apply greater voltage
Move charge to “gate”
And Count,
move next “bin” of
charge and keep on counting
6. Difference is charge in
One “bin” +V
Requires special cooling, Why?

113. END
6. Really Basic Optics

114. Since polarizability of the electrons in the material also controls the dielectric
Constant you can find a form of the C-M equation with allows you to compute
The dielectric constant from the polarizability of electrons in any atom/bond
N = density of dipoles
= polarizability (microscopic (chemical) property)
r = relative dielectric constant
Frequency dependent
Just as the refractive index is
Typically reported
Point of this slide: polarizability of electrons in a molecule is related to the
Relative dielectric constant

115. 2nd order
1st order
Grating
Angle of
reflection
i=45

116. 2nd order
1st order
Angle of
reflection
i=45