Frequency and time dependece of signals

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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.

Chemistry Department, University of Isfahan

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Non-Dispersive Methods Fourier-Transform Interferometry

What if we could measure the oscillatingwavefunction of EMR directly?

Frequency DomainTime Domain

FourierTransform


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Fourier composition of a square Fourier composition of a square wave wave


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Direct Measurement:Feasible?

Suppose we had EMR with λ = 10 μm

Hz 103

m 1010

m/s 1000.3

13

6

8

c

Freq

That’s 1 cycle every 33 x 10-15 s(33 femtoseconds!)

Upshot: we can’t measure the oscillatingEMR field directly for optical radiation


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Enter Interferometry

We need a signal that is much slower, so that it can be measured . . . How?

Interfer-ometer

Detector Computer

High Freq.~ 1013 Hz

h h@ f

Low Freq.~ 102 Hz


Source

Fixed Mirror

Movable mirror

Beam splitting mirror

21 3-1

Detector

Michelson Interferometer

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Resulting Interferogram

δ = pathlength difference (retardation)

δ = 2(M-F)

δ = 2x (mirror displacement)

So, we get maxima when δ = nλ and minima whenδ = ½nλ (recall that the actual mirror movement is ½δ)


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Modulation Frequency• Moving Mirror moves continuously at a fixed velocity (VM), so the signal at the detector will oscillate at a related frequency (f):

If VM = 0.1 cm/s, λ = 10 μm EMR will be modulatedat: f = 2(1.0 x 10-3 m/s)/(10 x 10-6 m) = 200 Hz

f = 2VM/λ

f = (2VM/c)ν

Or:


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To the Frequency Domain!


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From Interferogram toSpectrum


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Why Bother withFT-Interferometry?

1. Signal-to-Noise Enhancement 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 elementsChemistry Department, University of

Isfahan

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Multiplex Advantage: Time Suppose we spent 6000 seconds acquiring the

spectrum and we really don’t need the enhancedS/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)!


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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-to-noise ratio.

Jacquinot Advantage – the large energy throughput ofinterferometric instruments (which have few optical elementsand no slits to attenuate radiation.

High wavelength precision, making signal averaging feasible.

Ease and convenience that data can be computer-manipulated.

Summary of Advantages of Fourier Transform Spectroscopy


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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


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Detectors for spectroscpic instruments

VAC UV VIS Near IR IR Far IRSpectral region

Detectors

Photondetectors

Thermaldetectors

Photographic plate

Photomultiplier tube

Phototube

Photocell

Silicone diode

Photoconductor

Thermocouple (voltage) or barometer (resistance)

Golay pneumatic cell

Pyroelectric cell (capacitance)

Charge transfer detector

, nm 100 200 400 700 1000 2000 4000 7000 10,000 20,000 40,000


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Detectors convert light energy to an Detectors convert light energy to an electrical signal. electrical signal.

In spectroscopy, they are typically placed In spectroscopy, they are typically placed after a wavelength separator to detect a after a wavelength separator to detect a selected wavelength of light. selected wavelength of light.

Different types of detectors are sensitive in Different types of detectors are sensitive in different parts of the electromagnetic different parts of the electromagnetic spectrum. spectrum.

Radiation Detectors


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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 + kd


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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 eventsshot noise limited

thermal detectors: IRsignal responds to the average power of the

incident radiationthermal noise limited

Types of radiation detectors


2020

(a) Photovoltaic cells: radiant energy generates a current atthe 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) Multichannel photon detector

Photon detectors


Plastic case

Glass Thin layer of silver

Selenium

Iron

+ -

Barrier Layer CellBarrier Layer Cell

V

Photoelectric EffectPhotoelectric Effect

90 Vdc

Wire anodeCathode

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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

Dynode Potential(V) Number of electrons

1 90 10

2 180 100

3 270 103

4 360 104

5 450 105

6 540 106

7 630 107

8 720 108

9 810 109

Anode 900V Gain =108

12

3

4

5

6

8

7

9

Anode

PhotoemissiveCathode

GrillQuartz envelope

+_

900V dc

Anode

PhotoemissiveCathodeDynodes 1-9

To readout

Photomultiplier Tube

Features of Photomplier Tubes

• High sensitivity in UV, Vis, and NIR– Limited by dark current – Cooling to -30oC improves response

• Extremely fast time response

• Limited to measuring low-level signals

p region n region

pn junction

Metal contactLead wire

Fig. 7.30

Silicon DiodeSilicon Diode

Depletion layer

Reverse bias

Silicon diode under Revese BiasSilicon diode under Revese Bias

Forward bias

ee

Silicon Diode under Forward BiasSilicon Diode under Forward Bias

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Photodiode and Photovoltaic Detectors

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.

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. Chemistry Department, University of Isfahan

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3232

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Semiconductor Detector

A reverse-biased linear diode-array detector:

(a) cross section and

(b) top view.


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Multichannel Photon Detector

Photodiode Arrays

Charge-injection devices

Charge-coupled devices (CCDs)


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Photodiode Array Detectors (PDA)

A photodiode array (PDA) is a linear array of discrete A photodiode array (PDA) is a linear array of discrete photodiodes on an integrated circuit (IC) chip. photodiodes on an integrated circuit (IC) chip.

For spectroscopy it is placed at the image plane of a For spectroscopy it is placed at the image plane of a spectrometer to allow a range of wavelengths to be spectrometer to allow a range of wavelengths to be detected simultaneously. detected simultaneously.

In this regard it can be thought of as an electronic In this regard it can be thought of as an electronic version of photographic film. version of photographic film.

Array detectors are especially useful for recording the Array detectors are especially useful for recording the full uv-vis absorption spectra of samples that are full uv-vis absorption spectra of samples that are rapidly passing through a sample flow cell, such as in rapidly passing through a sample flow cell, such as in an HPLC detector.an HPLC detector.


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Diode Array DetectorsDiode Array Detectors

Advantage

speed

sensitivity

The Multiplex advantage

Disadvantage

resolution is 1 nm, vs 0.1 nm for normal UV

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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

Optical instrument

5. a signal processor and Fiber Optics


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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


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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.


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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 GeO2.

• total internal reflection• incident angle larger than critical angle• core material: n1; cladding material: n2

• n1 > n2 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.


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Fiber Optics

• Good for transmission of light over long distances• Flexible


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Fiber OpticsChemistry Department, University of Isfahan

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Frequency and time dependece of signals

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