Fourier Transform Spectrometry

Fourier Transform Spectrometry provides essential background in Fourier analysis, systematically develops the fundamental concepts governing the design and operation of Fourier transform spectrometers, and illustrates every concept pictorially. Methods for transforming the interferogram and phase correcting the resulting spectrum are presented, with a focus on understanding the capabilities and limitations of the algorithms. Techniques of computerized spectrum analysis are discussed in a way that enables spectroscopists to understand the numerical processing algorithms without becoming computer programmers. Methods for determining the accuracy of numerical algorithms are detailed and compared pictorially and quantitatively. Algorithms for line finding, fitting spectra to voigtian profiles, filtering, Fourier transforming, and spectrum synthesis are a basis for spectrum analysis tools from which complex signal-processing procedures can be constructed.

This book is of immediate value to those who use Fourier transform spectrometers in their research or are considering their use. It gives the mathematical and physical background for understanding the operation of an ideal interferometer, illustrates those ideas with example interferograms obtained via ideal and nonideal interferometers, and shows how the maximum amount of information can be extracted from the interferograms. Finally, it shows how sampling and noise affect the spectrum.

Contents

• Preface
• 1 Introduction 1
• 2 Why Choose a Fourier Transform Spectrometer? 17
• 3 Theory of the Ideal Instrument 29
• 4 Fourier Analysis 41
• 5 Nonideal (Real World) Interferograms 67
• 6 Working with Digital Spectra and Fourier Transforms 80
• 7 Phase Corrections and Their Significance 101
• 8 Effects Noise in its Various Forms 119
• 9 Line Positions, Line Profiles, and Fitting 143
• 10 Processing of Spectral Data 169
• 11 Discussions, Interventions, Digressions, and Obscurations 179
• 12 Chapter-by-Chapter Bibliography 213
• 13 Chronological Bibliography 223
• 14 Applications Bibliography 233
• 15 Author Bibliography 243
• 16 Index