Library of Congress Cataloging-in-Publication Data

Ball, David W. (David Warren), 1962-

Field guide to spectroscopy / David W. Ball.

p. cm. -- (SPIE field guides)

Includes bibliographical references and index.

ISBN 0-8194-6352-3

1. Spectrum analysis. I. Title. II. Series.

QC451.B183 2006

535.8′4--dc22

2006008336

Published by

SPIE—The International Society for Optical Engineering

P.O. Box 10

Bellingham, Washington 98227-0010 USA

Phone: +1360 676 3290

Fax: +1 360 647 1445

Email: spie@spie.org

Web: http://spie.org

The content of this book reflects the work and thought of the author. Every effort has been made to publish reliable and accurate information herein, but the publisher is not responsible for the validity of the information or for any outcomes resulting from reliance thereon.

Printed in the United States of America.

Second printing

## Introduction to the Series

Welcome to the * SPIE Field Guides*—a series of publications written directly for the practicing engineer or scientist. Many textbooks and professional reference books cover optical principles and techniques in depth. The aim of the

*is to distill this information, providing readers with a handy desk or briefcase reference that provides basic, essential information about optical principles, techniques, or phenomena, including definitions and descriptions, key equations, illustrations, application examples, design considerations, and additional resources. A significant effort will be made to provide a consistent notation and style between volumes in the series.*

**SPIE Field Guides**Each * SPIE Field Guide* addresses a major field of optical science and technology. The concept of these

*is a format-intensive presentation based on figures and equations supplemented by concise explanations. In most cases, this modular approach places a single topic on a page, and provides full coverage of that topic on that page. Highlights, insights, and rules of thumb are displayed in sidebars to the main text. The appendices at the end of each*

**Field Guides***provide additional information such as related material outside the main scope of the volume, key mathematical relationships, and alternative methods. While complete in their coverage, the concise presentation may not be appropriate for those new to the field.*

**Field Guide**The * SPIE Field Guides* are intended to be living documents. The modular page-based presentation format allows them to be easily updated and expanded. We are interested in your suggestions for new

*topics as well as what material should be added to an individual volume to make these*

**Field Guide***more useful to you. Please contact us at*

**Field Guides****fieldguides@SPIE.org.**

John E. Greivenkamp, **Series Editor**

Optical Sciences Center

The University of Arizona

## The Field Guide Series

Keep information at your fingertips with all of the titles in the * Field Guide* series:

* Field Guide to Geometrical Optics*, John E. Greivenkamp (FG01)

* Field Guide to Atmospheric Optics*, Larry C. Andrews (FG02)

* Field Guide to Adaptive Optics*, Robert K. Tyson & Benjamin W. Frazier (FG03)

* Field Guide to Visual and Ophthalmic Optics*, Jim Schwiegerling (FG04)

* Field Guide to Polarization*, Edward Collett (FG05)

* Field Guide to Optical Lithography*, Chris A. Mack (FG06)

* Field Guide to Optical Thin Films*, Ronald R. Willey (FG07)

* Field Guide to Spectroscopy*, David W. Ball (FG08)

## Field Guide to Spectroscopy

Of all the Field Guides published to date, this one may stand out due to its relatively broad topic: the field of spectroscopy. Indeed, entire field guides can be written on what is covered here in one or two pages (witness the two pages on polarization here versus an entire * Field Guide* devoted to that topic published previously). Whatever limitations this may impart on this volume, I accept them and expect that the reader will understand them, too.

This material is derived from several sources, including my own training in infrared and circular dichroism spectroscopy from Rice University and the Lawrence Berkeley Laboratory; from courses I have taught in spectroscopy at Cleveland State University; and from personal research I conducted in the course of authoring “The Baseline” column in * Spectroscopy* magazine since 1994. Writing is a form of self-education, and I have been blessed with fast (though not always accurate) typing skills with which I can benefit by increased writing and, as a result, learning.

Thanks go to my colleague, John F. Turner II, for his review of the initial Table of Contents. I would also like to thank reviewers Brad Stone of San Diego State University and Vidi Saptari of MKS Instruments, Inc., for their thoughtful comments on the manuscript, and John E. Greivencamp of the University of Arizona, series editor, for leadership in the * Field Guides* series. Thanks are also due to Dr. Koji Masutani of Micro Science Inc. for corrections made while preparing the Japanese translation of this book.

This * Field Guide* is dedicated to my family: my wife, Gail, and my sons, Stuart and Casey.

David W. Ball

Department of Chemistry

Cleveland State University

## Table of Contents

**Glossary x**

**Basics 1**

Spectroscopy Defined 1

Spectrometer, Spectroscope, and Spectrograph 2

Light as a Wave 3

Light as a Particle 5

The Electromagnetic Spectrum 6

Maxwell’s Equations of Electromagnetism 7

Maxwell’s Equations: General Form 8

Spectroscopy and the Regions of the Spectrum 9

Polarization 10

Polarization and Reflection 11

Interactions of Light with Matter 12

Index of Refraction 13

Internal Reflection 14

Dichroism 15

**Instrumental Aspects 16**

Light Sources 16

Prisms 17

Gratings 18

Absorption Filters 19

Interference Filters 20

Types of Lenses: Convex 21

Other Types of Lenses 22

Mirrors 23

Lens and Mirror Equations 24

Modulators: Mechanical Choppers and Shutters 25

Electro-Optical Modulators 26

Magneto- and Acousto-Optical Modulators 27

Other Components 28

Grating Monochromators 29

Prism Monochromators 30

Michelson Interferometer 31

Fabry-Perot Interferometer 32

Detectors 33

Photon Detectors 34

Photomultiplier Tubes 35

Multichannel Photon Detectors 36

Multichannel Detectors: Charge-Transfer Devices 37

Thermal Detectors 38

**Theory and Methods 39**

Fourier Transform 39

Fourier Transform Spectroscopy 40

Absorption 41

Emission 42

Magnetic Resonance 43

Quantum Theory 44

Quantum Theory of Light and Its Application 45

Quantum Mechanics—Postulates 46

Quantum Mechanics—More Postulates 47

QM—Particle-in-a-Box 48

QM—Harmonic Oscillator 49

QM—Two-Dimensional Rotations 50

QM—Three-Dimensional Rotations 51

QM—The Hydrogen Atom: Setup 52

QM—The Hydrogen Atom: Solutions 53

QM—Other Systems 54

Spin 55

Approximation Methods—Variation Theory 56

Approximation Methods—Perturbation Theory 57

Approximation Methods Applied to Spectroscopy 58

The Transition Moment 59

Quantum-Mechanical Selection Rules 60

Group Theory 61

Plotting a Spectrum—The Ordinate 62

Plotting a Spectrum—The Abscissa 63

Baselines 64

Beer’s Law 65

Linewidths 66

Types of Line Broadening 67

Noise 68

Resolution 69

Resolution in Fourier Transform Spectrometers 70

Atomic Electronic Spectroscopy 71

Atomic Term Symbols 72

Electronic Spectra Selection Rules 73

Atomic Emission Spectroscopy 74

Atomic Absorption Spectroscopy 75

The Born-Oppenheimer Approximation 76

Molecular Spectroscopy 77

Diatomic Term Symbols 78

Molecular Electronic Spectroscopy 79

Hückel Approximations 80

The Zeeman Effect 81

The Anomalous Zeeman Effect 82

Nuclear Magnetic Resonance: Theory 83

NMR: The Chemical Shift 84

NMR: Spin-Spin Splitting 85

Electron Spin Resonance 86

Rotational Spectroscopy 87

Vibrational Spectroscopy 88

Near- and Far-Infrared Spectroscopy 89

Overtones and Combination Bands 90

Rovibrational Spectroscopy 91

Vibronic Spectroscopy 92

Raman Spectroscopy 93

Lasers 94

Fluorescence 95

Phosphorescence 96

Photoelectron Spectroscopy 97

**Appendix 98**

Equation Summary 98

**Bibliography 102**

**Index 103**

#### Glossary

**a**

Absorptivity

**a**

Hyperfine coupling constant

**a**

Width

A

Ammeter

**A**

Einstein coefficient of spontaneous emission

* A*(λ)

Absorbance at some wavelength λ

ATR

Attenuated total reflection

**b**

Path length

B

Beamsplitter

B

Magnetic flux strength

**B**

Einstein coefficient of stimulated absorption

**B**

Rotational constant

**B**

Magnetic flux density

BE

Binding energy of electron

**c**

Concentration

**c**

Speed of light in vacuum

**c’**

Speed of light in transparent medium

**c _{n}**

Linear combination expansion coefficient

C

Compensator

CCD

Charge coupled device

CD

Circular dichroism

CID

Charge injection device

**d**

Distance between grating grooves

**D**_{a}

Angular dispersion

**D**_{1}

Linear dispersion

D1, etc.

Dynode 1, etc.

**e**

Charge on the electron

**E**

Electric field

**E**

Energy

Δ**E**

Change in energy

〈* E*〉

Average energy

EPR

Electron paramagnetic resonance

ESR

Electron spin resonance

**f**

Focal length

* f*(

*)*

**t**Time-dependent function

F

Focal point

**F**

Force

* F*(ω),

*(ν)*

**F**Fourier transform

* F*(

*)*

**v**Lineshape function

FID

Free induction decay

FIR

Far infrared

FT

Fourier transform

FTIR

Fourier transform infrared spectroscopy

FT-NMR

Fourier transform nuclear magnetic resonance spectroscopy

FWHM

Full width at half maximum

**g _{e}**

Electron * g* factor

**g _{J}**

Landé * g* factor

gN

Nuclear * g* factor

G

Grating

**h**

Planck’s constant

$\hslash $

Planck’s constant divided by 2π

HCL

Hollow-cathode lamp

**H**

Magnetic field

$\widehat{H}$

Hamiltonian operator for energy

* H*(α

^{½}

*)*

**x**Hermite polynomial

**i**

The square root of–1

**I**

Intensity

**I**

Moment of inertia

**I**

Nuclear spin quantum number

**I**_{a}

Intensity of absorbed light

**I**_{p}

Intensity of p-polarized light

**I**_{r}

Intensity of reflected light

**I**_{s}

Intensity of s-polarized light

**I**_{t}

Intensity of transmitted light

ICP

Inductively coupled plasma

IR

Infrared

**J**

Free current density

**J**

Rotational quantum number

**J**

Total (spin + orbital) angular momentum

Δ**J**

Change in rotational quantum number

**k**

Boltzmann’s constant

**k**

Force constant

**l**

Length

**l**

(3D) Angular momentum quantum number

LED

Light-emitting diode

**L, L _{tot}**

Total angular momentum

**L**_{Z}

Z-component angular momentum

${\widehat{L}}_{z}^{2}$

* Z*-component angular momentum operator

${\widehat{L}}_{\text{tot}}^{2}$

Squared total angular momentum operator

**m**

Mass

**m**

Order of refraction

**m**_{e}

Mass of the electron

**m _{l}**

(2D) Angular momentum quantum number

**m**_{s}

* Z*-component of spin angular momentum quantum number

M

Mirror

M

Transition moment

**M _{I}**

* Z*-component of nuclear spin angular momentum

**M _{J}**

* Z*-component of total angular momentum

**n**

Index of refraction

**n**

Quantum number (principal)

Δ**n**

Change in quantum number

NIR

Near infrared light

NMR

Nuclear magnetic resonance

**〈O〉**

Average value of property **O**

**p**

Momentum, linear

$\widehat{p}$

Momentum operator, linear

* P*(

*)*

**t**Probability, time-based

PDA

Photodiode array

PMT

Photomultiplier tube

QM

Quantum mechanics

**r**

Distance

**R**

Radius of curvature

**R**

Resolution

**R**_{d}

Reciprocal linear dispersion

S

Source

**S**

Spin angular momentum quantum number

2* S*+1

Multiplicity

S1, S2

Slits

SNR

Signal-to-noise ratio

**t**

Time

**T**

Temperature, absolute

**T**

Transmittance

% **T**

Percent transmittance

TDSE

Time-dependent Schrödinger equation

TISE

Time-independent Schrödinger equation

UPS

Ultraviolet photoelectron spectroscopy

UV

Ultraviolet light

UVA

Ultraviolet A

UVB

Ultraviolet B

**v**

Velocity

**V**

Verdet constant

**V**

Potential energy

$\widehat{V}$

Potential energy operator

**x**

Position

$\widehat{x}$

Position operator

XPS

X-ray photoelectron spectroscopy

α

Angle of incoming light

β

Angle of preferential refraction

γ

Blaze angle

γ

Magnetogyric ratio

δ

Chemical shift parameter

Γ

Irreducible representation of point group

ε_{0}

Permittivity of free space

ε(λ)

Molar extinction coefficient

θ

Angle of dispersion

θ

Angle of rotation

θ_{c}

Critical angle

θ, θ_{i}

Angle of incidence

θ_{r}

Angle of reflection

λ

Wavelength of light

λ_{max}

Maximum wavelength

Δλ

Wavelength range

μ

Magnetic permeability

μ

Reduced mass

μ_{0}

Permeability of free space

μ_{B}

Bohr magneton

μ_{N}

Nuclear magneton

$\widehat{\text{\mu}}$

Dipole moment operator

ν

Frequency of light

ν

Larmor frequency

$\tilde{\text{\nu}}$

Wavenumber of light

ρ, ρ(ν)

Radiation density

σ

Screening constant

ϕ

Angle

ϕ

Angle of refraction

ϕ

Work function

ϕ, Φ

Trial wave function

Ψ

Wavefunction

Ψ*

Wavefunction, complex-conjugated

ω

Angular frequency