1 Dispersion (Terminology)   How do we quantify the spatial separation of wavelengths on the exit focal plane? Angular Dispersion : D a = dθ/dλ (property of dispersive element) Linear Dispersion: D = dy/dλ (property of dispersive device) F Dispersive Element λ1λ1 λ2λ2 θ1θ1 θ2θ2 y1y1 y2y2 Chemistry Department, University of Isfahan

2 More Dispersive Terminology   If dθ is small, it can be shown that: More commonly, we will use: Reciprocal Linear Dispersion (D -1 ) = 1/D -typically around Å/mm in UV/Vis Effective Bandwidth: D = F × D a Δλ eff = D -1 × w Slit-width D -1 = 16 Å/mm w = 100 μm Δλ eff = 1.6 Å Chemistry Department, University of Isfahan Sin d  = d  = dy/F

3 Prism   As we saw in the previous chapter, refraction of light is given by Snell's law: n 1 sin θ 1 = n 2 sin θ 2 A prism is a transparent optic that is shaped to bend light. Since the refractive index of a material varies with wavelength, prisms are useful for dispersing different wavelengths of light. Chemistry Department, University of Isfahan

4 Dispersion of white light by a prism Dispersed light Incident White light Chemistry Department, University of Isfahan

5 Dispersion by a prism (a) quartz Cornu types and (b) Littrow type Chemistry Department, University of Isfahan

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7 Rainbow

8 Diffraction Gratings   Typically, a series of closely spaced facets ruled onto a reflecting surface Spacing of facets must be comparable to λ of EMR Parallel EMR rays striking adjacent facets will travel different distances Constructive interference occurs if the difference in the distance travelled by the two rays is an integer multiple of λs Constructive interference will be a function of the angles (incident and reflection) and the wavelength Chemistry Department, University of Isfahan

9 Let’s see how it works! i r D C B A Grating normal Monochromatic Beam at incident Angle i Diffraction beam at Reflected angle r d Chemistry Department, University of Isfahan Wave front

10 Dispersion by Echelle Grating Echelle grating: i = angle of incidence; r = angle of reflection; d = groove spacing. In usual practice, i  r =  = 63  26. Chemistry Department, University of Isfahan

11 Echelle Grating   Provides high dispersion and high resolution   Difference with echellette grating Its blaze angle is significantly greater The short side of the blaze is used rather than the long side which is used in echellette grating The grating is relatively coarse, having typically 300 or fewer grooves per mm for UV radiation The angle of reflection r is much higher in the echelle grating than the echellette and approaches the angle of incidence i, r  i =  Chemistry Department, University of Isfahan

12 Echelle Grating   Under these circumstances, the Equation we obtained for echellette grating, i.e. with respect to becomes and the dispersion which was becomes nλ = d[sin(i) + sin(r)] r  i =  nλ = 2d sin  Chemistry Department, University of Isfahan

13 Comparison of Performance Characteristics of a Conventional and Echelle Grating Chemistry Department, University of Isfahan

14 Performance Specifications The dispersion is usually given in nanometers per millimeter, where the slit width is expressed in mm. stray light: light transmitted by the monochromator at wavelengths outside of the chosen wavelength and bandpass. high efficiency: maximize the ability to detect low light levels. Resolution is usually of secondary importance since emission spectra rarely have peaks with linewidths less than 5 nm. Chemistry Department, University of Isfahan

15 Dispersion for a Grating If the angle r is kept small (<5 o ):  For a fixed angle of incidence (i): n dλ = d cos(r) d(r) So: DaDa wavelength independent Chemistry Department, University of Isfahan nλ = d [ sin (i) ± sin (r) ]

16 Dispersion of Grating Monochromators Angular dispersion: Linear dispersion: F: focal length of the monochromator Reciprocal linear dispersion D -1 Chemistry Department, University of Isfahan

17 Chemistry Department, University of Isfahan Dispersion of Grating Monochromators ☻What is the role of D -1 in wavelength separation? D -1 ↓ resolution ↑ or D -1 ↑ resolution ↑ What are the effects of d, n and F on resolution?

18 Resolution Resolution is the separation of wavelengths in a spectrum. Chemistry Department, University of Isfahan

19 Spectral Resolution/Resolving Power  We define Resolution (or Resolving Power): R = λ avg /Δλ Chemistry Department, University of Isfahan

20 Resolving Power for a Grating We need an instrument with a resolving power of: R = 4500/2 = 2250  The resolving power of a diffraction grating:  So, in order to just resolve these two spectral lines: R = nN λ 1 = 4501 Å λ 2 = 4499 Å Spectral Order No. of grating blazes illuminated by radiation Chemistry Department, University of Isfahan

21 Monochromator Slits and Resolution Illumination of an exit slit by monochromatic radiation 2 at various monochromator settings. Exit and entrance slits are identical. Reciprocal linear dispersion D -1 = d dy  eff = w D -1 Slit width Chemistry Department, University of Isfahan

Detector    Wavelength Power Exit slit Illumination of an Exit Slit Monochromator   2

  Wavelength Effective bandwidth Slit width=  Slit width= 3(  Power Slit width= (  Slit width=

24 Effect of Slitwidth on Spectrum (Benzene) Chemistry Department, University of Isfahan

25 Slit width The slit widths are generally variable, and a typical monochromator will have both an entrance and an exit slit. The light intensity which passes through a monochromator is approximately proportional to the square of the slit width. Larger slit widths yield increased signal, what about resolution? Chemistry Department, University of Isfahan

26 How it all fits together  Suppose we want to “just resolve” the following Iron doublet: λ 1 = Å R= /0.07 λ 2 = Å = 44,000 Suppose that we have a 100-mm wide grating ruled with 1200 grove/mm ; it has a first-order resolving power of: R = nN = (1)(100 mm)(1200 gr/mm) R = 120,000 Chemistry Department, University of Isfahan

27 But, can we really resolve the two lines?  Consider, now, the dispersion of the monochromator in which that grating is located: D -1 = 16 Å/mm In order to just resolve the two lines: Δλ eff = 0.07 Å This requires a slitwidth of: Δλ eff = D -1 × w w = 0.07 Å/16 Å/mm = mm w ≈ 4 μm Chemistry Department, University of Isfahan

28 How Can We Improve Resolution?  Decrease Slitwidth (w) -limits light throughput  Operate in Higher Spectral Orders -limits light throughput (decreased efficiency) D -1 ∝ 1/n  Increase Focal Length -limits light throughput (inverse square law) D -1 ∝ 1/F Chemistry Department, University of Isfahan

29 Five components 1. a stable source of radiant energy 2. a transparent container for holding the sample 3. a device that isolates a restricted region of the spectrum for measurement 5. a signal processor and Fiber Optics Optical instrument 4. a radiation detector Chemistry Department, University of Isfahan

30 Detectors for spectroscpic instruments VAC UV VIS Near IR IR Far IR Spectral region Detectors Photon detectors Thermal detectors Photographic plate Photomultiplier tube Phototube Photocell Silicone diode Photoconductor Thermocouple (voltage) or barometer (resistance) Golay pneumatic cell Pyroelectric cell (capacitance) Charge transfer detector, nm ,000 20,000 40,000 Chemistry Department, University of Isfahan

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32 Detectors convert light energy to an electrical signal. Detectors convert light energy to an electrical signal. In spectroscopy, they are typically placed after a wavelength separator to detect a selected wavelength of light. In spectroscopy, they are typically placed after a wavelength separator to detect a selected wavelength of light. Different types of detectors are sensitive in different parts of the electromagnetic spectrum. Different types of detectors are sensitive in different parts of the electromagnetic spectrum. Radiation Detectors Chemistry Department, University of Isfahan

33 high sensitivity high S/N ratio constant response over a considerable range of fast response minimum output signal in the absence of illumination (low dark current) electric signal directly proportional to the radiation power Ideal Detectors ? radiation power (intensity) dark current S =kP + k d Chemistry Department, University of Isfahan

34 Two major types: one responses to photons, the other to heat photon detectors: UV, visible, IR (when used for 3 µm or longer, cooling to dry ice or liquid nitrogen is necessary to avoid interference with thermal signal) signal results from a series of individual events shot noise limited thermal detectors: IR signal responds to the average power of the incident radiation thermal noise limited Types of radiation detectors Chemistry Department, University of Isfahan

35 (a) Photovoltaic cells : radiant energy generates a current at the interface of a semiconductor layer and a metal; (b) Phototubes : radiation causes emission of electrons from a photosensitive solid surface; (c) Phtomultiplier tubes : contain a photoemissive surface as well as several additional surfaces that emit a cascade of electrons when struck by electrons from the photosensitive area; (d) Photoconductivity detectors : absorption of radiation by a semiconductor produces electrons and holes, thus leading to enhanced conductivity; (e) Silicon photodiods : photons increase the conductance across a reverse biased pn junction. Used as diode array to observe the entire spectrum simultaneously (f) (f) Multichannel photon detector Photon detectors Chemistry Department, University of Isfahan

Plastic case Glass Thin layer of silver Selenium Iron + - Barrier Layer Cell

37 Vacuum Phototubes The number of electrons ejected from a photoemissive surface is directly proportional to the radiant power of the beam striking that surface; As the potential applied across the two electrodes of the tube increases, the fraction of the emitted electrons reaching the anode rapidly increases; when the saturation potential is achieved, essentially all the electrons are collected at the anode. The current then becomes independent of potential and directly proportional to radiation power. Chemistry Department, University of Isfahan

90 Vdc Wire anode Cathode

39 Photomultiplier Tube (PMT) Photomultiplier Tubes (PMTS) are light detectors that are useful in low intensity applications such as fluorescence spectroscopy. Due to high internal gain, PMTs are very sensitive detectors. PMTs are similar to phototubes. They consist of a photocathode and a series of dynodes in an evacuated glass enclosure. Photons that strikes the photoemissive cathode emits electrons due to the photoelectric effect. Chemistry Department, University of Isfahan

40 Photomultiplier Tube (PMT) Instead of collecting these few electrons at an anode like in the phototubes, the electrons are accelerated towards a series of additional electrodes called dynodes. These electrodes are each maintained at a more positive potential. Additional electrons are generated at each dynode. Chemistry Department, University of Isfahan

41 Photomultiplier Tube (PMT) This cascading effect creates 10 5 to 10 7 electrons for each photon hitting the first cathode depending on the number of dynodes and the accelerating voltage. This amplified signal is finally collected at the anode where it can be measured. Chemistry Department, University of Isfahan

Dynode Potential(V) Number of electrons Anode 900V Gain = Anode Photoemissive Cathode Grill Quartz envelope + _ 900V dc Anode Photoemissive Cathode Dynodes 1-9 To readout