Frequency and time dependece of signals Frequency Domain

Frequency and time dependece of signals Frequency Domain Spectroscopy – radiant power data are recorded as a function of frequency (or wavelength). Time Domain Spectroscopy – concerned with changes in radiant power with time. Achieved by Fourier transform. 1 Chemistry Department, University of Isfahan

Non-Dispersive Methods § Fourier-Transform Interferometry What if we could measure the oscillating wavefunction of EMR directly? Fourier Transform Time Domain Frequency Domain 2 Chemistry Department, University of Isfahan

Fourier composition of a square wave 3 Chemistry Department, University of Isfahan

Direct Measurement: Feasible? § Suppose we had EMR with λ = 10 μm That’s 1 cycle every 33 x 10 -15 s (33 femtoseconds!) Upshot: we can’t measure the oscillating EMR field directly for optical radiation 4 Chemistry Department, University of Isfahan

Enter Interferometry § We need a signal that is much slower, so that it can be measured. . . How? High Freq. ~ 1013 Hz h Interferometer Low Freq. ~ 102 Hz Detector Computer h @f 5 Chemistry Department, University of Isfahan

Michelson Interferometer Movable mirror Beam splitting mirror Fixed Mirror Sour ce -1 Detector 1 2 3

Resulting Interferogram δ = pathlength difference (retardation) δ = 2(M-F) δ = 2 x (mirror displacement) So, we get maxima when δ = nλ and minima when δ = ½nλ (recall that the actual mirror movement is ½δ) 7 Chemistry Department, University of Isfahan

Modulation Frequency • Moving Mirror moves continuously at a fixed velocity (VM), so the signal at the detector will oscillate at a related frequency (f): f = 2 VM/λ Or: f = (2 VM/c)ν If VM = 0. 1 cm/s, λ = 10 μm EMR will be modulated at: f = 2(1. 0 x 10 -3 m/s)/(10 x 10 -6 m) = 200 Hz 8 Chemistry Department, University of Isfahan

To the Frequency Domain! 9 Chemistry Department, University of Isfahan

Chemistry Department, University of Isfahan From Interferogram to Spectrum 10

Why Bother with FT-Interferometry? 1. Signal-to-Noise Enhancement Ø Multiplex Advantage (“Fellgett’s Advantage”) -All wavelengths viewed simultaneously, so measurement time/resolution element is greater If measurement is limited by detector noise: S/N enhancement ∝ (n)1/2 where n = number of resolution elements 11 Chemistry Department, University of Isfahan

Multiplex Advantage: Time Ø Suppose we spent 6000 seconds acquiring the spectrum and we really don’t need the enhanced S/N: We can get the same S/N as with a dispersive system in 1/(n)1/2 of the time In this case, this means it would take: 6000 s/54. 8 ≈ 110 s So, 100 minutes (dispersive) versus 2 minutes (FT-interferometry)! 12 Chemistry Department, University of Isfahan

Summary of Advantages of Fourier Transform Spectroscopy Fellgett Advantage – all of the resolution elements for a spectrum are measured simultaneously, thus reducing the time required to derive a spectrum at any given signal-tonoise ratio. Jacquinot Advantage – the large energy throughput of interferometric instruments (which have few optical elements and no slits to attenuate radiation. High wavelength precision, making signal averaging feasible. Ease and convenience that data can be computer-manipulated. 13 Chemistry Department, University of Isfahan

Optical instrument 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 4. a radiation detector 5. a signal processor and Fiber Optics 14 Chemistry Department, University of Isfahan

Detectors for spectroscpic instruments , nm 100 200 VAC 400 UV 700 1000 VIS 2000 Near IR 4000 7000 10, 000 20, 000 40, 000 IR Far IR Spectral region Detectors Photographic plate Photomultiplier tube Photon detectors Phototube Photocell Silicone diode Charge transfer detector Photoconductor Thermocouple (voltage) or barometer (resistance) Thermal detectors Golay pneumatic cell Pyroelectric cell (capacitance) 15 Chemistry Department, University of Isfahan

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Radiation Detectors convert light energy to an electrical signal. l In spectroscopy, they are typically placed after a wavelength separator to detect a selected wavelength of light. l Different types of detectors are sensitive in different parts of the electromagnetic spectrum. l 17 Chemistry Department, University of Isfahan

Ideal Detectors l l l 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 S =k. P + kd radiation power (intensity) dark current 18 Chemistry Department, University of Isfahan

Types of radiation detectors Two major types: one responses to photons, the other to heat l photon detectors: UV, visible, IR used for 3 µm or longer , cooling to dry ice or liquid nitrogen is necessary to avoid interference with thermal signal) l signal results from a series of individual events l shot noise limited l (when l thermal detectors: IR l signal responds to the average power of the incident radiation l thermal noise limited 19 Chemistry Department, University of Isfahan

Photon detectors (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 (d) Photoconductivity detectors: absorption of radiation by a (e) Silicon photodiods: photons increase the conductance as several additional surfaces that emit a cascade of electrons when struck by electrons from the photosensitive area; semiconductor produces electrons and holes, thus leading to enhanced conductivity; across a reverse biased pn junction. Used as diode array to observe the entire spectrum simultaneously (f) Multichannel photon detector 20 Chemistry Department, University of Isfahan

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

Photoelectric Effect V

Cathode Wire anode 90 Vdc

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. 24 Chemistry Department, University of Isfahan

Photomultiplier Tube Dynode Potential(V) Number of electrons 1 90 10 2 180 100 3 270 103 4 360 104 5 450 105 9 6 540 106 Quartz envelope 7 630 107 8 720 108 810 900 V 109 Gain =108 5 7 3 6 4 2 1 8 Anode Grill Photoemissive Cathode 9 Anode 900 V dc Photoemissive Cathode Dynodes 1 -9 Anode + _ To readout

Features of Photomplier Tubes • High sensitivity in UV, Vis, and NIR – Limited by dark current – Cooling to -30 o. C improves response • Extremely fast time response • Limited to measuring low-level signals

Silicon Diode pn junction Metal contact Lead wire p region n region Fig. 7. 30

Silicon diode under Revese Bias Reverse bias Depletion layer

Silicon Diode under Forward Bias Forward bias e e

Photodiode and Photovoltaic Detectors l When a photon strikes a semiconductor, it can promote an electron from the valence band (filled orbitals) to the conduction band (unfilled orbitals) creating an electron(-) - hole(+) pair. l The concentration of these electron-hole pairs is dependent on the amount of light striking the semiconductor, making the semiconductor suitable as an optical detector. 30 Chemistry Department, University of Isfahan

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Semiconductor Detector A reverse-biased linear diode-array detector: (a) cross section and (b) top view. Chemistry Department, University of Isfahan 33

Multichannel Photon Detector Photodiode Arrays Charge-injection devices Charge-coupled devices (CCDs) 34 Chemistry Department, University of Isfahan

Photodiode Array Detectors (PDA) l l A photodiode array (PDA) is a linear array of discrete photodiodes on an integrated circuit (IC) chip. For spectroscopy it is placed at the image plane of a spectrometer to allow a range of wavelengths to be detected simultaneously. In this regard it can be thought of as an electronic version of photographic film. Array detectors are especially useful for recording the full uv-vis absorption spectra of samples that are rapidly passing through a sample flow cell, such as in an HPLC detector. 35 Chemistry Department, University of Isfahan

Diode Array Detectors Advantage speed sensitivity The Multiplex advantage Disadvantage resolution is 1 nm, vs 0. 1 nm for normal UV 36

Optical instrument 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 4. a radiation detector 5. a signal processor and Fiber Optics 37 Chemistry Department, University of Isfahan

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Signal processing An electronic device that amplifies the electric signal from the detector photon counting: • has a number of advantages over analog signal: • improved S/N • sensitivity to low radiation level • improved precision for a given time measurement time 39 Chemistry Department, University of Isfahan

Fiber Optics The field of fiber optics depends upon the total internal reflection of light rays traveling through tiny optical fibers. Once the light is introduced into the fiber, it will continue to reflect almost losslessly off the walls of the fiber and thus can travel long distances in the fiber. Bundles of such fibers can accomplish imaging of otherwise inaccessible areas. 40 Chemistry Department, University of Isfahan

Fiber optic • • • Optical fibers are circular dielectric waveguides that can transport optical energy and information. They have a central core surrounded by a concentric cladding with slightly lower (about 1%) refractive index. Fibers are typically made of silica with index modifying dopants such as Ge. O 2. • total internal reflection • incident angle larger than critical angle • core material: n 1; cladding material: n 2 • n 1 > n 2 for total internal reflection • numerical aperture: a measure of the magnitude of the light gathering ability of the fiber. It also indicates how easy it is to couple light into a fiber. 41 Chemistry Department, University of Isfahan

Fiber Optics • Good for transmission of light over long distances • Flexible 42 Chemistry Department, University of Isfahan

Fiber Optics Chemistry Department, University of Isfahan 43