Fourier Transform Spectrometry

By: Sumner P. Davis, Mark C. Abrams, James W. Brault

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Hardcover | 21 May 2001

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276 Pages

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22.86 x 15.88 x 2.54

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Fourier Transform Spectrometry is of immediate use to those who use Fourier transform spectrometers in their research, or are considering their use. The authors' presentations enable readers to obtain a clear understanding of FTS, which is crucial to their studies and research.

Due to the increasing complexity and commercialization of instrumentation, achieving optimum performance in research applications and automated usage can be challenging. For example, a thorough understanding of the instrument can dramatically affect the outcome of the experiment and the generation of reliable data in applications where conditions are not ideal and resulting signals are weak. This book provides a comprehensive discussion of FTS from the ground up, covering basic concepts, instrumentation, data-processing algorithms, and techniques for computerized spectral analysis.

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Non-Fiction Science Chemistry Analytical Chemistry Spectrum Analysis Physical Chemistry Quantum & Theoretical Chemistry

Preface	p. xiii
Introduction	p. 1
Spectra and Spectroscopic Measurement	p. 5
The Classical Michelson Interferometer	p. 10
Precision, Accuracy, and Dynamic Range	p. 12
Units	p. 13
A Glance Ahead and to the Side	p. 15
Why Choose a Fourier Transform Spectrometer?	p. 17
Quantity	p. 18
Quality	p. 20
Resolution and Line Shape	p. 20
Fixed and Variable Quantities in Experiments	p. 21
Cost	p. 24
Summary	p. 25
Theory of the Ideal Instrument	p. 29
Equation for the Balanced Output	p. 31
The Unbalanced Output	p. 32
From Monochromatic to Broadband Light	p. 33
Generalization to Polychromatic Light	p. 35
Extension to Plus and Minus Infinity	p. 35
The Fourier Transform Spectrometer as a Modulator	p. 36
Summary	p. 37
Fourier Analysis	p. 41
Linear Systems and Superposition	p. 42
A Practical Approach to Fourier's Theorem	p. 43
Fourier Decomposition	p. 46
Representations of Functions and Their Transforms	p. 47
Practical Representations	p. 49
Linear Systems and Convolution	p. 49
Cross-Correlation	p. 52
Definition of a Signal-to-Noise Ratio	p. 53
Generalized Functions	p. 54
The Dirac Delta Function	p. 54
The Dirac Comb and Sampling of Continuous Functions	p. 55
The Essential Theorems	p. 57
Addition (Superposition)	p. 57
Similarity (Stretching)	p. 58
Shift	p. 58
Modulation	p. 58
Convolution (Folding Rule)	p. 59
Autocorrelation	p. 60
Derivative	p. 61
Derivatives of a Convolution Integral	p. 62
Rayleigh Theorem	p. 62
Power	p. 63
Zeroth Moment (Area)	p. 63
Examples of Transform Pairs Fundamental to FTS	p. 63
Nonideal (Real-World) Interferograms	p. 67
Finite Path Difference	p. 68
Finite Entrance Aperture Size	p. 69
Finite Instrumental Function and its Properties	p. 73
Non-uniform or Non-symmetric Irradiation of the Aperture	p. 79
Working with Digital Spectra and Fourier Transforms	p. 80
Signals and Measurement	p. 83
Discrete Transforms	p. 86
Interpolation in the Spectrum	p. 87
Apodization	p. 93
Preparation for Making Transforms	p. 98
Common Artifacts	p. 98
Zero Mean Interferograms, End Effects, and Masking	p. 98
Procedure for Reliable Transforms	p. 98
Phase Corrections and Their Significance	p. 101
The What and Why of Phase	p. 101
Origins of Asymmetries in the Interferogram	p. 102
From Asymmetries to Phase Errors	p. 102
Asymmetric Truncation, Amertization, and Phase Errors	p. 107
More on One-Sided vs. Symmetric Interferograms	p. 112
Determining Phase Shifts	p. 112
Low-Resolution Phase Determination	p. 114
High-Resolution Phase Determination	p. 116
Recommendations	p. 116
Effects of Noise in Its Various Forms	p. 119
Signal and Noise in the Two Domains	p. 120
Noise Classifications	p. 122
Detector Noise (k = 0): The Multiplex Advantage	p. 122
Digitizing Noise (k = 0): Dynamic Range	p. 123
Photon Noise (k = 0.5)	p. 126
Source Noise (k = 1)	p. 131
Unbalance, Misalignment, Modulation Efficiency, and Signal-to-Noise	p. 133
Noise Limited Resolution	p. 134
Localized Noise (Ghosts and Artifacts)	p. 134
Periodic Position Error Ghosts	p. 136
Coherent Ghosts	p. 136
Ringing Ghosts	p. 139
Summary	p. 140
Line Positions, Line Profiles, and Fitting	p. 143
Introduction	p. 143
Line Finding and Line Shapes	p. 144
Emission Lines	p. 144
Absorption Lines	p. 144
Derivative Line Finding	p. 145
Kernel Functions	p. 145
Line Position Accuracy	p. 148
Useful Line-Finding Properties of First and Second Derivatives	p. 149
Techniques of Derivative Line-Finding	p. 150
Noise and Filtered Derivative Line-Finding	p. 150
Resolution and Line-Finding	p. 152
Least Square Fitting of Line Profiles to Voigtian Functions	p. 154
Voigtian Functions	p. 154
Fitting Considerations	p. 155
Special Problems in Fitting Voigtian Functions	p. 157
Fitting Errors from Sampling	p. 158
Fitting Errors from Noise	p. 158
Fitting Errors from the Sampling Grid	p. 160
Fitting Underresolved Spectra	p. 160
Rates of Convergence	p. 163
Areas and Equivalent Widths	p. 165
Wavenumber Calibration	p. 166
Processing of Spectral Data	p. 169
Emission Background Subtraction and Intensity Correction	p. 170
Absorption Background and Intensity Corrections	p. 173
Line Lists and Fitting	p. 175
Discussions, Interventions, Digressions, and Obscurations	p. 179
A Novel Approach to Sampling Systems	p. 181
Introduction	p. 181
Position Measurements	p. 182
Sampling Systems	p. 183
A New Approach to Sampling Systems	p. 184
Practical Realization, Results, and Implications	p. 185
The Imaging Fourier Transform Spectrometer (IFTS)	p. 186
Characterization and Determination of Instrumental Line Shape Functions	p. 189
Apodization	p. 190
Introduction	p. 190
Selected Apodization Functions/Windows	p. 192
Evaluation Criteria and Relative Performance	p. 195
Families of Functions	p. 196
Method of Optimization	p. 196
Some Useful Functions for Optimal Apodization	p. 196
Discussion	p. 198
To Apodize or Not to Apodize--Case Studies	p. 198
The Quest for the Perfect Instrument	p. 199
On Fourier Transform Spectrometry and Digital Signal Processing	p. 204
From Echelle Spectrographs to Echelle Spectrographs--A 50-Year Circle	p. 205
A Final Story	p. 211
Chapter-by-Chapter Bibliography	p. 213
Chronological Bibliography	p. 223
Applications Bibliography	p. 233
Author Bibliography	p. 243
Index	p. 259
Table of Contents provided by Syndetics. All Rights Reserved.

Fourier Transform Spectrometry

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