Really Basic Optics ppt by dfhdhdhdhjr

VIEWS: 10 PAGES: 116

									                     6. Really Basic Optics


                                                                               15000



                                                                               10000



                                                                                5000




                                                                   Amplitude
                                                                                   0
                                                                                        0    0.2   0.4      0.6      0.8   1   1.2


                                                                                -5000



                                                                               -10000



                                                                               -15000
                                                                                                          Time (s)




                  Sample      Instrument         Instrument
Sample                                                                                      Signal (Data)
                  Prep                           Out put

    Polychromatic light         Selected        Turn off/diminish intensity
                                light
                                              Sample
                     Select                 interaction
                      light


                    select                 Turn on different wavelength
source                                                                                                   detect
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
                                      6. Really Basic Optics

                                                                    A                     Sin=opp/hyp
                                                                       y
                                                                                          y
                                                                                 sin  
                                                                                          A

                                                                                  y  A sin 
            1.5
                                                                                                radians 
                                                                                                       t  t
              1                                                                                    s 

                                                                                                  y  A sint 
            0.5

                             /2                            3/2            2
Amplitude




              0
                   0    50     100   150       200     250      300         350     400



                                                                                             y '  A sint   
            -0.5


                       90o phase angle
                       /2 radian phase angle
             -1



            -1.5
                                               t (s)
                  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                                                       c
                                               hc
Elo                              E  h 
                                               
                                  Frequency 1/s
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
Theoretical width of an atomic spectral line
                        Natural Line Widths
Line broadens due                               frequency
1. Uncertainty
2. Doppler effect
                                  t  1
3. Pressure
4. Electric and magnetic fields   Lifetime of an excited state is typically 1x10-8 s

                                        1         7 1
                                     8  5x10
                                      10 s          s

                                     c  1

                                     d
                                         1c 2
                                     d
                                      d
                                           d
                                     c2


                                            2
                                         
                                  c2
                                               c
                 1 2
            5x10 7 
                  s       5x10 10  2
                                 
                
            8 m  10 nm
                      9
                          nm 
       3x10          
             s m 


Example: 253.7 nm



      5x10 10 
             253.7nm  3.22 x10 nm
                           2          5

      nm 

     Typical natural line widths are 10-5 nm
Line broadens due
1. Uncertainty
2. Doppler effect
                                         elocity
3. Pressure                            
4. Electric and magnetic fields   0          c
Line broadens due
1. Uncertainty
2. Doppler effect
3. Pressure
4. 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.


                                FWHM                    We use pressure broadening
                                                        On purpose to get a large
            f ( )                          
                    1                2                    Line width in AA for some
                                           2
                           o  
                                    2 FWHM               Forms of background
                                                       correction
                                      2  

      FWHM = full width half maximum
      o is the peak “center” in frequency units
     Line spectra – occur when radiating species are atomic particles which
     Experience no near neighbor interactions



Line broadens due
1. Uncertainty
2. Doppler effect
3. Pressure
4. Electric and magnetic fields


       Line events
       Can lie on top
       Of band events




          Overlapping line spectra lead to band emission
        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
                        Stefan-Boltzmann Law                                          Planck’s Blackbody Law

                I  T4                                                                8h 3 
                                                                                              
                                                                                       c  3
                                                                                               
                                                                                          h
                                                                                      exp   kT
                                                                                                 1
Intensity




                                                                               = Energy density of radiation
                                                                               h= Planck’s constant
                                                                               C= speed of light
                                                                               k= Boltzmann constant
                                                                               T=Temperature in Kelvin
                                                                               = frequency
            0     500       1000   1500        2000   2500   3000       3500
                                          nm
                                                                                    1           8h
                     max   
                              b                                                   3
                              T                                                                  hc
                                                                                             exp   kT   1
                   Wien’s Law
                                                                    1. As  ↓(until effect of exp takes over)
                                                                    2. As T,exp↓, 
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
                    Incoherent radiation
                                 The Multitude of emitters, even if they emit
                                 The same frequency, do not emit at the
                                 Same time


               A              A  A 0 sin( t )
                              or
                              A  A 0 sin(2  ft )

               B
                              0.25


                               0.2


                              0.15



B  B 0 sin( t   )          0.1


                              0.05

Frequency,, is the              0
                                                                                        Series1
                                                                                        Series2
Same but wave from particle   -0.05
                                      0   0.05   0.1   0.15   0.2   0.25   0.3   0.35



B lags behind A by the         -0.1

Phase angle                  -0.15


                               -0.2


                              -0.25
         END: Key Definitions
         Begin
         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
        1. Laser
        2. FT instrument
        3. Can be used to obtain information
          about distances
        4. Interference filter.
        5. Can be used to select wavelengths
  More Intense Radiation can be obtained by Coherent Radiation

                          Lasers




Beam exiting the cavity is in phase (Coherent) and therefore enhanced
In amplitude
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
                   w  BN o                                        w  BN *
                                (idea behind LASERs
                        o       Stimulated Emission)


    The rate of stimulated event is described by : w  BN o w  BN
                                                                     *


          Where w =rate of stimulated emission or absorption
              Is the energy density of radiation already present at the frequency of
                                          The more perturbing photons the greater the
               the transition
                                          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
 can be described by the Planck equation for black body radiation at some T

             8h 3                   frequency
                    
             c  3
                     
                 h
             exp   kT
                        1

                             In order to measure absorption it is required that the
                             Rate of stimulated absorption is greater than the
                             Rate of stimulated emission
                        wabsorption  BN o  wenussion  BN *

                                       N o  N *
  If the populations of * and o are the same the net absorption is zero as a photon is
  Absorbed and one is emitted
                Need to get a larger population in the excited state
                Compared to the ground state (population inversion)



                             * g*     
                   N*0    N     N0 
                                g0    



                            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




E       pump                             Serves to “trap” electrons in the excited
                                         State, which allows for a population
                                         inversion
Constructive/Destructive interference
1. Laser
2. FT instrument
3. Can be used to select wavelengths
4. Can be used to obtain information
   about distances
5. Holographic Interference filter.


                                    Radiation not along the
                                    Path is lost



                                                              mirror
                           mirror    Stimulated emission
                                     1. Single phase
                                     2. Along same path
                                     =Constructive Interference
                                     Coherent radiation
    Multiple directions,
    Multiple phase lags
  Incoherent radiation
          1.5
                                       FTIR Instrument
                                                            Constructive/Destructive interference
                                                            1. Laser
                                                            2. FT instrument
            1
                                                            3. Can be used to select wavelengths
                                                            4. Can be used to obtain information
                                                               about distances
          0.5
                                                            5. Holographic Interference filter.
Voltage




            0
                 0           0.2             0.4             0.6             0.8            1   1.2

          -0.5



           -1



          -1.5
                                                            Time

           Measurement  A1 sin2f s,1t   As sin2f S ,2 t .... An sin2f S ,n t 
                                                                                                                                        200000


                                                                                                                                        180000



                                                              Time Domain: 2 frequencies                                                160000


                                                                                                                                        140000
                                    4000
                                                                                                                                        120000




                                                                                                                            amplitude
                                                                                                                                        100000
                                    3000
                                                                                                                                           80000


                                    2000                                                                                                   60000


                                                                                                                                           40000

                                    1000
                                                                                                                                           20000
                        Amplitude




                                                                                                                                                        0
                                       0                                                                                                                     1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
                                                                                                                                                                                                                  frequency
                                            0     0.1   0.2   0.3    0.4    0.5      0.6    0.7       0.8   0.9         1               60000


                                    -1000
                                                                                                                                        50000



                                    -2000
                                                                                                                                        40000



                                    -3000




                                                                                                                            Amplitude
                                                                                                                                        30000




                                    -4000
                                                                                                                                        20000

                                                                            t (s)

                                                                                                                                        10000




            8000

                            1 “beat” cycle
                                                                                                                                                    0
                                                                                                                                                            1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
                                                                                                                                                                                                               Frequency


            6000
                                                                                                                                                    200000


            4000                                                                                                                                    180000


                                                                                                                                                    160000



            2000                                                                                                                                    140000
Amplitude




                                                                                                                                                    120000




                                                                                                                                        amplitude
               0                                                                                                                                    100000



                    0                       0.2         0.4         0.6             0.8           1               1.2                               80000



            -2000                                                                                                                                   60000


                                                                                                                                                    40000


                                                                                                                                                    20000
            -4000
                                                                                                                                                            0
                                                                                                                                                                1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
                                                                                                                                                                                                                  frequency

            -6000




                                                                                           sin A  sin B  2 sin 2  A  B cos 2  A  B
            -8000
                                                                                                                      1                1
                                                                    t (s)
                                   B
                              Fixed mirror


     Moving mirror


 A                             C

                                       Beam         IR source
                                       splitter


                                             detector


Constructive interference occurs when
                              1
                     AC  BC  n
                              2
                              4000


                              3000


                              2000
Light Intensity at Detector




                              1000

                                         -2            -1             0              +1
                                 0


                              -1000


                              -2000


                              -3000


                              -4000
                                                                     Mirror distance

                                      dis tan ce  f mirror velocity   mirror 
                   INTERFEROGRAMS

                 n
                        mirror 
                  2                         mirror  velocitymirror

              n         
                   
            2 mirror  mirror
                         1  2 mirror
         f det ector    
                             n
Remember that:            c
                       
                          
                                                Frequency of light
                        2 mirror  light
        f det ector
                              cn
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?




                 2 mirror  light
  f det ector
                       cn
No need to SELECT
Wavelength by using
Mirror, fiber optics,
Gratings, etc.
                            FOURIER TRANSFORMS
         Advantages

         1. Jaquinot or through-put
                 little photon loss; little loss of source intensity

     2. Large number of wavelengths allows for ensemble averaging
             (waveform averaging)

     3. This leads to Fellget or multiplex advantage

                  multiple spectra in little time implies?


                                                                                        x                       
                           sinf inite population   Signal          N measurements
  s population samples                                                                     sample    xblank
                              N measurements       N oise       sinf inite population

Signal       x sample  xblank                               Signal
                                                                           N measurements
N oise            sblank                                     N oise
              DIFFRACTION
Huygen’s principle = individual propagating waves combine
to form a new wave front
                             Constructive/Destructive interference
                             1. Laser
                             2. FT instrument
                             3. Can be used to select wavelengths
                             4. Can be used to obtain information
                                about distances
                             5. Holographic Interference filter.




   Can get coherent radiation if the slit is narrow enough.
   Coherent = all in one phase
June 19, 2008, Iowa Flood




Katrina Levee break
Fraunhaufer diffraction at a single slit
                                                   D
                                                      d         9.     sin CBF  sin 
             B
              F’                                                  opposite   CF DE
 W       O                                         E                           
                               L
                     F
                                                                   hypotenuse BC OD
         C
 1        BD, OD, & CD, big  assume / /
                                                                                         DE 
                                                           10.    n  CF  BC sin        BC
2.        if / /, then BCF                                                            OD 

3.        180  DEO  EOD    90  EOD  

4.           OF ' B  90 o
        5.           if / /, then CFB  90o
6.       180  CFB  FBC  BCF  90    
 From which we conclude                                                  DE        DE 
                                                       11.        n       BC       BC
7.        EOD                                                         OD        OE 
 8.          CF must be n for in                                 12.
                                                                                 d
                                                                           n    W
     phase (constructive int erference)                                           L
                                                                             D         The complete equation for a slit is
                                                                                 d                                2
                                                                                                       sin  
    B                                                                                         I  I0        
                                                                            E                          
W                                                L
                                                                                                  b
                                                                                                 sin  
                                                                                                  2
        b=W/2                                                                          Width of the line depends upon
                                                                                       The slit width!!
                                                                                        Therefore resolution depends
                                                                   1.2                  On slit width

                                                                    1



                                                                   0.8
          Relative Intensity




                                                                   0.6



                                                                   0.4



                                                                   0.2
                                                                                                                      Also “see”
                                                                                                                      This spectra
                                                                    0                                                 “leak” of
                               -800       -600       -400   -200         0       200    400      600    800
                                                                     Beta
                                                                                                                      Our hard won
                                                                                                                      intensity
                     The base (I=0) occurs whenever
                                                       2
                                            sin                 sinβ =0
                                   I  I0        
                                             
                                b
           Which occurs when    sin     n
                                2
                                          W
                                                                                                              W
                              b            2 sin   W sin                                       line width  sin 
         line width  2n  2 sin   2                                                                       2
                              2            2         2 1.2
                                                                                               The smaller the
                                                           1                                   Slit width the
                                                                                               Smaller
                                                       0.8
                                                                                               The line width,
Relative Intensity




                                                       0.6                                     Which leads
                                                                                               To greater
                                                       0.4                                     Spectral
                                                                                               Resolution
                                                       0.2
                                                                                               Remember R is
                                                           0                                   Inversely proportional
                     -800   -600       -400    -200            0     200     400   600   800
                                                           Beta
                                                                                               To the width of
                                                                                               The Gaussian base
                                                                SLIT IMAGE
                                           A           Slit



                                    1 2 3B                           Position number
                                                        1234 5
                                    Image
                                                                               When edge AB at            Detector Sees
                                                                                 Position 1               0% power
                                                                                 Position 2               50% power
                                                                                 Position 3               100% power
                                                                                 Position 4               50% power
                                                                                 Position 5               0 % power
                               Detector output:
                     1.2

                                                                                  Triangle results when
                      1

                                                                                  Effective bandpass = image
                                                 eff
                     0.8
Output of detector




                     0.6
                                                                          To resolve two images that are ∆ apart requires
                     0.4



                     0.2



                      0
                                                                                    2 eff
                           0    1      2         3          4    5    6
                                           Image position

                                                                          Implies want a narrower slit
     Essentially,
     Narrow slit widths
     Are generally better

  2 eff
            GRATINGS

          Gratings   Groves/mm
          UV/Vis     300/2000
          IR         10/20



Points:

1. Master grating formed by diamond tip under ground
    1. Or more recently formed from holographic processes
2. Copy gratings formed from resins
                   +       -
                                                       opp DB
                                           sinDAB      
                                                       hyp   d
                           q               r  DBA  90
                                           DBA  BAD  90  180
                                           DBA  BAD  90
               q                           r  BAD

                                                          DB
                                                sin r 
                      
                                                          d
    n  CB  BD
                                                  
                                            n  CB  BD       
                   opp CB
sinCAB             
                   hyp   d                  n  d sini  d sinr
  i  q  90                   CAB  i
                                             n  d sini  sinr 
                                      CB
   q  CAB  90               sini 
                                       d
                  EXAMPLE
Calculate  for a grating which has
i=45
2000 groves per mm

1) Get d
                   1mm       500nm
                           
                2000 groves grove

  2) Use grating equation to solve for    n  d sini  sinr 


                          
           n  500nm sin 45o  sinr     
Inputs that can be varied are in pink
                                                                              Czerny-Turner        440.3
                                                                              construction         220.1
                           d                         nlambda = d(sin+sinr)
grooves/mm         2000      500                                                                   146.8
i in degrees         45 0.785398 i in radians                                                      88
                                                                                                   73
r in degrees         -40            -20        -10           0       10       20       40          All come
radians         -0.69813       -0.34907   -0.17453           0 0.174533 0.349066 0.698132
                                                                                                   through
order n
            1   32.15959   182.5433       266.7293    353.5534   440.3775    524.5635   674.9472
            2   16.07979   91.27166       133.3647    176.7767   220.1887    262.2817   337.4736
            3   10.71986   60.84777       88.90977    117.8511   146.7925    174.8545   224.9824
            4   8.039896   45.63583       66.68233    88.38835   110.0944    131.1409   168.7368
            5   6.431917   36.50866       53.34586    70.71068    88.0755    104.9127   134.9894
            6   5.359931   30.42389       44.45488    58.92557   73.39625    87.42724   112.4912


                                                                                        Multiple wavelengths
                                 You get light of 674.9 nm                              Are observed
                                                    ½; 1/3; 1/4; 1/5; etc.              At a single angle
                                                                                        Of reflection!!
Physical Dimensions:                  89.1 mm x 63.3 mm x 34.4 mm
Weight:            190 grams
Detector:          Sony ILX511 linear silicon CCD array
Detector range:    200-1100 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                                        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)
                                                                                                 construction
Grating options: 14 different gratings, UV through Shortwave NIR
Detector collection lens option:      Yes, L2
OFLV filter options:                  OFLV-200-850; OFLV-350-1000
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:                   ~0.3-10.0 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:        90 mA @ 5 VDC
Data transfer speed:                  Full scans to memory every 13 ms with USB 2.0 or 1.1 port, 300 ms with serial port
 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
                                            Hit grating second time
                    Time to get 440.3
                                 220.1
                                 146.8
                                 88
                                 73                            220.1 nm
                                 All come
                                 through
                            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
                                                    d           nlambda = d(sin+sinr)
               grooves/mm             2000         500
               i in degrees            45       0.785398 i in radians

                  order                 1           2           3          4        5

Light of 100                                 Reflection Angle
               wavelength
Nm shows up       100               -30.47131   -17.88496   -6.148561   5.330074 17.03125
At -30.4          125               -27.20057   -11.95286    2.458355   17.03125 32.88081
AND               150               -24.02322   -6.148561    11.12168   29.53092 52.45672
                  175               -20.92262   -0.407192    20.05324   43.85957 #NUM!
-17.88            200               -17.88496    5.330074    29.53092   63.23909 #NUM!
And               225               -14.89846    11.12168     40.0079    #NUM!    #NUM!
-6.1              250               -11.95286    17.03125    52.45672    #NUM!    #NUM!
                  275               -9.039003    23.13464    70.54325    #NUM!    #NUM!
And               300               -6.148561    29.53092     #NUM!      #NUM!    #NUM!
5.3               325               -3.273759    36.36259     #NUM!      #NUM!    #NUM!
Etc.              350               -0.407192    43.85957     #NUM!      #NUM!    #NUM!
                  375                2.458355    52.45672     #NUM!      #NUM!    #NUM!
                  400                5.330074    63.23909     #NUM!      #NUM!    #NUM!
                  425                8.215299    83.16511     #NUM!      #NUM!    #NUM!
                  450                11.12168     #NUM!       #NUM!      #NUM!    #NUM!
                  475                14.05736     #NUM!       #NUM!      #NUM!    #NUM!
                  500                17.03125     #NUM!       #NUM!      #NUM!    #NUM!
              GRATING DISPERSION

D-1 = Reciprocal linear dispersion

 1 d dis tan ce between  d cos r
D                         
    dy dis tan ce on screen   nF


      Where n= order
            F = focal length
             d= distance/groove

        1      d
      D r 0 
               nF


POINT = linear dispersion
What is (are) the wavelength(s) transmitted at 45o
reflected AND incident light for a grating of 4000
groves/mm?
          ave
        1 2                     RESOLUTION




                                   
                                    1    2

                                   2      ave
                             R         
                                2  1   

The larger R the greater the spread between the two wavelengths, normalized by
The wavelength region

  R  nF

   Where n = order and N = total grooves exposed to light
    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 489.2 nm resolved?




               
              1   2

               2      ave
         R         
R  nF      2  1   
      Constructive/Destructive interference
      1. Laser
      2. FT instrument
      3. Can be used to select wavelengths
      4. Can be used to obtain information
         about distances
      5. Holographic Interference filter.




                    Change in path length results
                    In phase lag




                                             
 E0  x, y  Eo0  x, y cos 2ft  0  x, y
The photo plate contains all the information
Necessary to give the depth perception when
decoded
     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
               1. Laser
               2. FT instrument
               3. Can be used to obtain information
                 about distances
               4. Interference filter.
               5. Can be used to select wavelengths
End
Section on Using Constructive
and Destructive
Interference patterns based on
phase lags
   Constructive/Destructive interference
   1. Laser
   2. FT instrument
   3. Can be used to obtain information
     about distances
   4. Interference filter.
   5. Can be used to select wavelengths
         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
Move electrons around (polarize)
Re-radiate




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




                   This phenomena causes:
                           1. scattering
                           2. change in the velocity of light
                           3. absorption
First consider propagation of light in a vacuum


      1               c is the velocity of the electromagnetic wave in free space
c
      0 0            0   Is the permittivity of free space which describes the
                            Flux of the electric portion of the wave in vacuum and
                            Has the value
                                                          capacitance
                                                 C2
                       0  8.8552 x10 12
                                                N  m2
                                                      kg  m
                                          force    N
                                                        s

                     It can be measured directly from capacitor measurements

              0    Is the permeablity of free space and relates the current
                    In free space in response to a magnetic field and is defined as
                                       N  s2
                    0  4  x10  7
                                        C2
      1                             N  s2                                  C2
c               0  4  x10  7                 0  8.8552 x10 12
      0 0                          C2                                    N  m2


                                        1
         c                                                            
                            12  C   2
                                                   7 N  s
                                                                  2

                8.8552 x10          2   4  x10       2 
                                N m                C 


                          1                         1
              c                        
                                s   2
                                                          9   s
                   111x10 17
                    .                        3.33485x10
                                                               m
                                m2
                                     m
                       c  2.9986x10         8
                                     s
                                                                                                        sqrt dielectric

              1                                                                   1.000034        1.000131           1.000294      1.00E+00


  c
                                                                            1.8                                                                1.0005


              0 0                                                         1.6

                                                                            1.4
                                                                                                                                               1.0004


                                                                                                                                               1.0003




                                                      Index of refraction




                                                                                                                                                        Index of refraction
                                                                            1.2
                 1
velocity                                                                    1                                                                 1.0002


                                                                          0.8                                                                1.0001

                                                                            0.6
                                                                                                                                               1
                                                                            0.4

             c                                                                                                                              0.9999

r                          Ke
                                                                            0.2


       vvelocity       0 0      0                                         0
                                                                                  1.51       4.63E+00        5.04           5.08    8.96E+00
                                                                                                                                               0.9998


                                                                                                        sqrt dielectric



                                      Dielectric constant
       Typically       ~0           so                                      This works pretty well for gases (blue line)


                         c
             r                      Ke
                      v elocity     Says: refractive index is proportional to the dielectric
                 Maxwell’s relation constant
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
                                                                                 vol molecule2 
             SCATTERING                                                 Is  Io                  
                                                                                
                                                                                       4
                                                                                                  
                                                                                                  
                                                                          Most important parameter is the
Light in            particle                                              relationship to wavelength



            8 4 2         
 I s  I o  4 2 1  cos  
                         2          Angle between incident and scattered
            r                    light
                                                         1.2
     Polarizability of electrons
       a) Number of electrons                             1

       b) Bond length
                                    Relative Intensity   0.8
       c) Volume of the molecule,
          which depends upon                             0.6

          the radius, r
                                                         0.4


= vacuum                                               0.2

Io = incident intensity
                                                          0
                                                               0   45     90   135       180      225     270   315   360
                                                                               Angle of Scattered Light
         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
                                          vol molecule2 
                                 Is  Io                  
                                         
                                                4
                                                           
                                                           



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)
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
             c
   r                      Refractive index = relative speed of radiation
          v elocity

                            Refractive index is related to the relative permittivity
                            (dielectric constant) at that Frequency


     2  1  Pm             Where  is the mass density of the sample, M is the molar
                            mass of the molecules and Pm is the molar polarization
     1
      2
             M         0    Is the permittivity of free space which describes the
                             Flux of the electric portion of the wave in vacuum and
                             Has the value
     NA       2            Where  is the electric dipole moment operator
Pm             
     3 o     3kT              is the mean polarizabiltiy

                                                                   Point – refractive index
       1 N A 
      2
                          N A 2
                                                                   Is related to polarizability
                        
       1 3 0 M 
      2
                       3kT  3 0 M
             2  1  N A
                              Clausius-Mossotti equation
              1 3 0 M
               2
    1  N A
    2                                      2e 2 R 2
                                       
   2  1 3 0 M                            3 E
                        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

 2  1   N A   2e 2 R 2 
                         
  1  3 0 M   3 E 
  2




   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
2  1       N A   2e 2 R 2 
                            
 1
 2
            3 0 M   3 E 

  An alternative expression for a single atom is
                      2
                                                              Transition probability that
             Ne                        fj
                          
                                                              Interaction will occur
       1
       2
             o me        j
                               2
                               0j     2j  i j 

                                                      A damping force term that account for
                                                      Absorbance (related to delta E in prior
    Molecules per         Natural                     Expression)
    Unit volume           Frequency of
    Each with             The oscillating electrons
    J oscillators         In the single atom j



                                              Frequency of incoming electromagnetic
                                              wave
    If you include the interactions between atoms and ignore absorbance you get
2  1       N A   2e 2 R 2 
                            
 1
 2
            3 0 M   3 E 



2  1   Ne 2                  fj
 2     
  2 3 o me
                    
                     j
                          2
                                 2j
                          0j



           when           2 j   2
                           0        j
                                          The refractive index is constant


           when             2   2j
                             j     0
                                            The refractive index depends on omega

    c
r         Ke            And the difference    2j   2
                                                  0      j
                                                             Gets smaller so the
    v                                                        Refractive index rises
     REFRACTIVE INDEX VS 


Anomalous dispersion near absorption bands
which occur at natural harmonic frequency of
material


Normal dispersion is required for lensing materials
       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?



                 c
 r 
           v elocity
                         c
 frequency 
                     vacuum
   frequency      c
                       vacuum


   frequency      v
                       media    elocity ,media


            c            frequency vacuum vacuum
r                                       
         velocity        frequency media   media
                                     Filters can be constructed
                                     By judicious combination of the
                                     Principle of constructive and
                                     Destructive interference and

                          t  2 '
                              1      Material of an appropriate refractive
                                     index


                 t                            n
Wavelength
In media             '                    t  '
                                              2
                           t  '            vacuum
                                          
                                               '
             t
                                               n   vacuum 
                                          t               
                                               2   
                          t  2 '
                              3

                                          2t
                                               vacuum
             t                             n
         What is (are) the wavelength(s) selected from
         an interference filter which has a base width
         of 1.694 m and a refractive index of 1.34?

2t
     vacuum
 n
Holographic filters are better
INTERFERENCE WEDGES

                                2t1
                           1 
                                 n
                                 2t2
                            2 
                                   n
                                 2t3
                            3 
                                   n
                                 2t4
                            4 
                                   n
           AVAILABLE WEDGES
 Vis        400-700 nm
 Near IR    1000-2000 nm
 IR         2.5 -14.5 m
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.
              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
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




                                                                         Glass
The two polarization components are                                      n=1.5
reflected and transmitted with
Different amplitudes depending                            T
Upon the angle of reflection, r,
And the angle of transmittence, t
                                                          Let’s start by examing
                                                          The Angle of transmittence
                                                        c
                                             i 
                                                    velocity 1
                                          Snell’s Law
                                               sin  i  t
                                                       
                         2                    sin  t   i
               1



Less dense 1
                              More dense 1
Lower refractive index
                              Higher refractive index
Faster speed of light
                              Slower speed of light


      sin 1 sin i velocityi t
                           
      sin 2 sin t velocityt i
     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?




sin  i  t
        
sin  t   i
                                                                              PRISM
                                                            1.535




Crown Glass                                                  1.53
(nm)     




                          refractive index of crown glass
400nm 1.532
                                                            1.525
450 nm 1.528
550 nm 1.519
590 nm 1.517                                                 1.52


620 nm 1.514
650 nm 1.513                                                1.515




                                                             1.51
                                                                    0   100     200   300         400   500   600   700
                                                                                       wavelength nm


                                                                                Uneven spacing = nonlinear




POINT, non-linear dispersive device
Reciprocal dispersion will vary with wavelength, since refractive index varies with
wavelength
  The intensity of light (including it’s component polarization) reflected as compared
  to transmitted (refracted) can be described by the Fresnel Equations




Angle of transmittence
Is controlled by
The density of
Polarizable electrons                                       T
In the media as
Described by Snell’s Law
                       i cosi  t cost 
                                                       2
                                                                                           2i cosi
                                                                                                            2
                                                                                                       
R  r            
                        cos   cos                     T  t  
                 2

                                                                                       cos   cos 
                                                                                    
                                                                            2
                                                                                                       
                       i      i    t     t                                         i     i    t  t 



                                                                                           2i cosi
                                                       2                                                        2
                        t cos  i   i cos  t                                                    
R/ /  r/ /           cos    cos  
                                                            T/ /  t / /           cos   cos 
                                                                                    
                 2                                                              2
                                                                                                       
                       i         i     t       t                                   i     t    t  i 




       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
                             sin  i  t
                                     
                             sin  t   i

Since the total amount of light needs to remain constant we also know that

                              R/ /  T/ /  1              Therefore, given the two refractive
                              R  T  1                  Indices and the angle of incidence can
                                                           Calculate everything
                          Consider and air/glass interface
                i
                    0.8

                    0.7
                                                                 Perpendicular
                    0.6
Transmittance




                    0.5

                    0.4

                    0.3

                                        Here the transmitted parallel light is
                    0.2
                                        Zero! – this is how we can select
                                        For polarized light!
                    0.1                                                 Parallel


                     0
                          0             10              20              30         40   50
                                                       Angle of incidence

This is referred to as the polarization
angle
                Total Internal Reflection



Here consider                               Glass
Light propagating                           n=1.5
In the DENSER
Medium and
Hitting a
Boundary with
The lighter
medium

                    Air, n=1

                                     T
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
                                   1.2

                                                             Parallel
                                    1
   Reflectance and Transmittence




                                             Perpendicular
                                   0.8


                                   0.6


                                   0.4


                                   0.2


                                    0
                                         0           20          40            60      80          100
                                                                Angle of incidence
                                           t
                                                                    All of the light is reflected
                                                                    internally
                     ic
                                                                                         2
                                                          i cos  i   t cos  t 
                                 RT  r                cos    cos  
                                                       
                                                   2
                                                                                     
                                                         i         i     t       t 
Set R to 1 &  to 90
The equation can be solved for the critical angle of incidence

                        transmitted ,less dense
             sin c 
                           incident ,dense
                                                  1
           For glass/air                sin c      0.666
                                                  .
                                                 15
                                        c  a sin(0.666)  0.7297rads
                                          0.7297rads180
                                                                     418o
                                                                        .
                                                       
                                           The angle at which the discontinuity occurs:
                                           1. 0% Transmittance=100% Reflectance
                                           2. Total Internal Reflectance
                                           3. Angle = Critical Angle – depends on refractive index
                  0.8
                                                1.69/1
                  0.7                                             1.3/1

                  0.6                                    1.5/1
                                                                      ni/nt          Critical Angles
% Transmittence




                  0.5
                                                                               1.697              36.27
                  0.4                                                            1.5               41.8
                                                                                 1.3              50.28
                  0.3

                  0.2

                  0.1

                   0
                        0   10   20        30        40          50       60        70    80     90
                                      37         Angle of Incidence            51
                                           42
   Numerical Aperture

            NA  sinc        2
                                incident ,dense    transmitted ,less dense
                                                      2
                                                                               
The critical angle here is defined differently because we have to LAUNCH the
beam
sin  i  t
                                                              Shining light directly through our sample
sin  t   i                                                      i=0

                 Using Snell’s Law the angle of transmittance is

                t 
           0    sin  t
                i 

           sin 1 0   t  0

     cos0  1



                                                           2
                        i cos  i   t cos  t 
 RT  r              cos    cos  
                     
                 2
                                                   
                       i         i     t       t 

                                                       2                 T
                        t cos  i   i cos  t 
R/ /  r/ /           cos    cos  
                     
                 2
                                                   
                       i         i     t       t 
cos0  1
                                          2
                           i  t 
 RT  r 
                     2
                                  
                           i  t 
                                                        same
                                      2
                       t  i 
R/ /  r/ / 
                 2
                              
                       i  t 


                                  2
                t  i                     The amount of light reflected depends
        R/ /           
                i  t                     Upon the refractive indices of the medium
          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?

                                                      2
            I reflected        t  i 
R/ /                                 
                I initial      i  t 
                                                          2
                                 t  i 
   I reflected       I initial          
                                 i  t 

 I transmitted  I initial  I reflected
                                                      2
                                           i 
I transmitted  I initial    I initial  t       
                                         i  t 

                               2
I transmitted    I initial 1   t     i
                                            
                            
                                 i  t  
                                             
                        Water,
                        refractive index
                        1.33
                                It’ = I’’o                   It’’ =     It’’’
    Io         It=I’o                                         I’’’o
                                                                      Air, refractive index 1
    Air
                        Glass, refractive index 1.5


 Final exiting light
                                                                                      15  1 2    133  15 2 
                                                                                            .              .    .
                       15  1 2 
                             .                  15  1 2 
                                                    .                   I t '  I o 1           1          
   I t '''  I ''' o 1            I t 1  
                                           ''
                                                                                       15  1    133  15 
                                                                                            .              .    . 
                     
                          15  1 
                             .               
                                                 15  1 
                                                    .       
                                                                                                  

                  15  133 2               15  133 2 
                                                                                                                           2
                        .    .                       .    .                           15  1 2    133  15 2 
                                                                                            .               .   .
I t ''  I o '' 1                I t ' 1                    I t ''  I o 1           1          
                
                     15  133 
                        .    .              
                                                  15  133 
                                                     .    .                              15  1    133  15 
                                                                                    
                                                                                           .             .   . 
                133  15 2 
                       .       .             133  15 2 
                                                    .       .
I t '  I ' o 1                  I t 1                
              
                    133  15 
                       .       .          
                                                 133  15 
                                                    .       .                                         2                        2
                                                                                      15  1 2 
                                                                                            .                133  15 2 
                                                                                                                  .     .
            15  1 2                                              I t '''  I o 1                 1            
I t  I o 1  
                  .
                                                                                    
                                                                                         15  1 
                                                                                            .             
                                                                                                               133  15 
                                                                                                                  .     . 
                        
          
               15  1 
                  .      
                                        2                            2
                 15  1 2 
                       .                      133  15 2 
                                                    .     .
 I t '''  I o 1                       1             
               
                    15  1 
                       .                   
                                                 133  15 
                                                    .     . 

                                            2                    2
                               05 2 
                                   .              017  2 
                                                        .
I glass/ air 2    I initial 1             1        
                               2.5 
                                              
                                                     2.83 
                                                             

   I glass/ air 2  I initial 0.96 0.99
                                    2           2




     I glass/ air 2  I initial 0.915

    We lose nearly 10% of the light
                            Key Concepts
                      Interaction with Matter

   Light Scattering             vol 2 
                      I s  Io  4 
                                 
                                                          2  1   Ne 2               fj
  Refractive Index
  Is wavelength dependent
                                       r 
                                                 c
                                              v elocity
                                                                 
                                                            2 3 o me
                                                           2               
                                                                            j
                                                                                 2
                                                                                        2j
                                                                                 0j
  Used to separate light by prisms
                                                           2  1   N A   2e 2 R 2 
                                                                                   
                                                            1  3 0 M   3 E 
                                                            2




                           2t
Refractive index based         
Interference filters        n
                                        Key Concepts
                                  Interaction with Matter

                                   sin  i  t
       Snell’s Law                         
                                   sin  t   i
      Describes how light is bent based differing refractive indices


      Fresnell’s Equations describe how polarized light is transmitted and/or reflected
                               at an interface

                       i cosi  t cost 
                                                       2
                                                                                         2i cosi
                                                                                                          2
                                                                                                     
R  r            
                        cos   cos                   T  t  
                 2

                                                                                     cos   cos 
                                                                                  
                                                                          2
                                                                                                     
                       i      i    t     t                                       i     i    t  t 



                                                                                         2i cosi
                                                       2                                                      2
                        t cos  i   i cos  t                                                  
R/ /  r/ /           cos    cos  
                                                          T/ /  t / /           cos   cos 
                                                                                  
                 2                                                            2
                                                                                                     
                       i         i     t       t                                 i     t    t  i 

                 Used to create surfaces which select for polarized light
                                  Key Concepts
                             Interaction with Matter

Fresnell’s Laws collapse to

                         transmitted ,less dense
           sin c 
                               incident ,dense
      Which describes when you will get total internal reflection (fiber optics)

And

                                                  2
                I reflected      t  i 
       R/ /                            
                 I initial       i  t 


Which describes how much light is reflected at an interface
     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
    KEm  h  


                              Work function=minimum energy binding an
                              Electron in the metal
Energy of
Ejected        Frequency of impinging photon
electron       (related to photon energy)
  KEm  h  




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)
           DETECTORS
Ideal Properties
1. High sensitivity
2. Large S/N
3. Constant parameters with wavelength

 Selectrical signal  kPradiant power  kd

       Where k is some large constant           Want low dark current
               kd is the dark current


 Classes of Detectors

    Name            comment
    Photoemissive   single photon events
    Photoconductive “ (UV, Vis, near IR)

    Heat                  average photon flux
                       Very sensitive detector


       Rock to
       Get different
       wavelengths




1. Capture all simultaneously
   = multiplex advantage
2. Generally less sensitive
Sensitivity of photoemissive
Surface is variable

Ga/As is a good one
As it is more or less consistent
Over the full spectral range
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
Photomultiplier tube



        The AA experiment




Photodiodes
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

                                                     1. Set device to accumulate
                                                         charge for some period of
                                                        time. (increase sensitivity)
                                                     2. Charge accumulated near
                                                        electrode



                                                   3. Apply greater voltage
                                                   4. Move charge to “gate”
      +V                                              And Count,
                                                   5. move next “bin” of
                                                      charge and keep on counting
                                                   6. Difference is charge in
                                                     One “bin”
                                                 Requires special cooling, Why?
END
6. Really Basic Optics
 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  r  1
                  
              3 o  r  2

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
                                                          180             65
                                              165                   900

                                       150                         800               -150
                                                                   700
                                135                               600                       -135
2nd   order                                                      500
                                                                400
                          120                                                                       -120
                                                             300
                                                            200
                                                            100                                             -105
                    105
                                                             0
                                                         -100
1st order                                                Grating
                                                         -200                                                - 90
                    90



                                                                                                            - 75
                     75


                                                                                                     - 60
                           60


                                  45                                                         - 45


                                         30                                           -30

                                                                               -15
                                                    15            0
              Angle of
              reflection

        i=45
                                                          180             65
                                              165                   900

                                       150                         800               -150
                                                                   700
                                135                               600                       -135
2nd   order                                                      500
                                                                400
                          120                                                                       -120
                                                             300
                                                            200
                                                            100                                             -105
                    105
                                                             0
                                                         -100
1st order                                                -200                                                - 90
                    90



                                                                                                            - 75
                     75


                                                                                                     - 60
                           60


                                  45                                                         - 45


                                         30                                           -30

                                                                               -15
                                                    15            0
              Angle of
              reflection

        i=45

								
To top