Introductory Fourier Transform Spectroscopy

Introductory Fourier Transform Spectroscopy

1st Edition - January 28, 1972

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  • Author: Robert Bell
  • eBook ISBN: 9780323152105

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Description

Introductory Fourier Transform Spectroscopy discusses the subject of Fourier transform spectroscopy from a level that requires knowledge of only introductory optics and mathematics. The subject is approached through optical principles, not through abstract mathematics. The book approaches the subject matter in two ways. The first is through simple optics and physical intuition, and the second is through Fourier analysis and the concepts of convolution and autocorrelation. This dual treatment bridges the gap between the introductory material in the book and the advanced material in the journals. The book also discusses information theory, Fourier analysis, and mathematical theorems to complete derivations or to give alternate views of an individual subject. The text presents the development of optical theory and equations to the extent required by the advanced student or researcher. The book is intended as a guide for students taking advanced research programs in spectroscopy. Material is included for the physicists, chemists, astronomers, and others who are interested in spectroscopy.

Table of Contents


  • Preface

    Acknowledgments

    Chapter One Fourier Transform Spectroscopy

    Introduction

    General Advantages of Fourier Transform Spectrometers

    Specific Advantages and Disadvantages of Interferometers

    Two-Beam Interferometers, the Ultimate in Spectrometers

    Quality Factors

    Spectral Ranges

    Applications of Fourier Transform Spectroscopy

    Conclusions

    References

    Chapter Two Historical Sketch and Crucial Ideas

    Introduction

    Michelson and His Interferometer

    Interferometers

    Fundamentals of Fourier Transform Spectroscopy

    Jacquinot Advantage

    Fellgett Advantage

    Strong's Group

    Other Pioneering Fourier Transform Spectroscopists

    Conclusions

    References

    Chapter Three Fourier Analysis and Interferometry

    Introduction

    Derivation of the Basic Integral for Fourier Transform Spectroscopy

    Short Derivation of the Basic Integral for Fourier Transform Spectroscopy

    Computing Spectra

    Coherence in the Interferometer

    Applicability of the Basic Integral Equation of Fourier Transform Spectroscopy

    Proving that the Interferogram is the Autocorrelation Function of the Electric Field

    Conclusions

    References

    Chapter Four Sample Calculations of Spectra from Interferograms

    Introduction

    Academic Example of the Use of EQ. (3-25)

    Practical Example of the Use of EQ. (3-25): the Doublet Problem

    Conclusions

    References

    Chapter Five Apodization—Mathematical Filtering

    Introduction

    Interferogram Produced by a Monochromatic Source

    Computed Spectrum from Interferograms Using Finite Scans

    Apodization and Resolution

    Instrument Line Shape and Convolutions

    Mathematical Filtering

    Conclusions

    References

    Chapter Six Resolution

    Introduction

    Instrument Broadening of Line (without and with Apodization)

    Separation of Resonances with Apodization

    Separation of Resonances without Apodization

    Comparison of Line Broadening and the Separation of Resonances

    Counting Fringes and Resolution

    Conclusions and General Comments

    References

    Chapter Seven Sampling Intervals

    Introduction

    Why Sample?

    Shah Function

    Relating the Sampled and the Complete Spectra

    Experimental Comments

    Conclusions

    Reference

    Chapter Eight Asymmetric Interferometers and Amplitude Spectroscopy

    Introduction

    General Theory and Reflection Studies: Solids—Single Surface

    Complex Inverse Fourier Transform of the Interferogram

    Transmission Studies-Solids—Single Pass (no Channel Spectra)

    Phase Errors of ±2π (Integer)

    Shifting the Computation Origin to the Grand Maximum Position

    Transmission Studies: Solids—Single Pass (with Channel Spectra)

    Transmission Studies: Gases—Single Pass (Bell's Interferometer)

    Transmission Studies: Gases—Double Pass (Ordinary Michelson Interferometer)

    Interferograms for Transmission Studies

    Transmission Studies: Limits on Sample Thickness

    Transmission Studies: Solid—Two Passes

    Transmission Studies: Liquids—Double Pass

    Accurate Low-Transmittance Measurements

    Conclusions

    References

    Chapter Nine Beamsplitters

    Introduction

    Self-Supporting Dielectric Beamsplitters

    Polarization in Dielectric-Sheet Beamsplitters

    Dielectric Beamsplitters on Substrates

    Phase Errors due to Absorption

    Wire-Grid Beamsplitters

    Conclusions

    References

    Chapter Ten Spectral Filtering

    Introduction

    Spectral Filters for below 400 CM-1

    Spectral Filters for below 5000 CM-1

    Spectral Filters for below, 16,000 CM-1

    Spectral Filtering with Choppers

    Spectral Filtering by Electronic Means

    Conclusions

    References

    Chapter Eleven Field of View

    Introduction

    Interferogram due to an Extended Source

    General Treatment

    Applying the General Treatment to the Extended Source Problem

    Discussion of the Instrumental Profile

    Interference Fringes and an Extended Source

    Conclusions

    References

    Chapter Twelve Phase Error and Sampling Problems

    Introduction

    Sampling Phase Errors

    Sampling Phase Errors and Two-Sided Interferograms

    General Phase Errors

    Origin Shifts Corrected by Curve Fitting

    Conclusions

    References

    Chapter Thirteen Procedures for Choosing Experimental Parameters

    Introduction

    Experimental Parameters

    Conclusions

    References

    Chapter Fourteen Sample Interferograms and Spectra

    Introduction

    Reproducibility of Scans and Signal Averaging

    Reading Interferograms

    Transmission Studies of Solids

    Transmission Studies of Liquids

    Transmission Studies of Gases

    Reflection Studies

    Emission Studies

    Planetary Atmospheres and Astronomy

    Conclusions

    References

    Chapter Fifteen Lamellar Grating Interferometers

    Introduction

    Plane, Lamellar Grating Interferometers and Efficiency of the Beamsplitter

    Diffraction Theory and Lamellar Gratings

    High-Order Diffraction Problems, σc, and Efficiency for σ ≥ σc

    Cavity Effect, σL, and Resolution

    Shadowing

    Wavenumber Shift due to Off-Axis Optical System

    Sample Spectra from Plane, Lamellar Grating Interferometers

    Spherical, Lamellar Grating Interferometers

    Effects of Noncollimation on the Computed Spectrum

    Sample Spectra from a Spherical, Lamellar Grating Interferometer

    Conclusions

    References

    Chapter Sixteen Computation Techniques

    Introduction

    Conventional Computation Techniques

    Conventional versus Cooley-Tukey Computations

    Conclusions

    References

    Chapter Seventeen The Cooley-Tukey Algorithm

    Introduction

    Introduction to the Binary Number System

    Preparing for the Cooley-Tukey Algorithm

    Cooley-Tukey Algorithm for N = 8

    Generalization for N = 2n

    Special Case of S(j) Real

    Special Case of S(j) Real and Even

    Special Case of a Real, Odd Function

    Conclusions

    References

    Chapter Eighteen Minicomputers and Real-Time Fourier Analysis

    Introduction

    Real-Time Fourier Analysis of a One-Sided Interferogram

    Initialization

    Parabolic Fit

    Computation of the Fourier Transform

    Calculation of S(j) cos[2πσK(jΔδ + ε)]

    Example: Commercial Real-Time Systems

    Choice of a Computer

    Conclusion

    References

    Chapter Nineteen Commercial Instruments

    Introduction

    RIIC or Beckman Instruments, INC. (3-500 CM-1)

    Digilab, INC. (5-10,000 CM-1)

    Grubbs-Parsons (10-675 CM-1)

    Coderg (10-800 CM-1)

    Idealab (10-10,000 CM-1)

    Polytec GmbH (10-1000 CM-1)

    Conclusions

    References

    Appendix A Optical Alignment of a Michelson Interferometer

    Introduction

    Coarse Adjustment

    Intermediate and Fine Adjustment

    Appendix B Computer Programs

    Program using Cooley-Tukey Algorithm

    Table of Symbols

    Program for Real-Time Analysis

    Appendix C Mirror Tilt, the Cat's-Eye Retroreflector

    Introduction

    Cat's-Eye Retroreflector (Convex Secondary)

    Cat's-Eye Retroreflector (Concave Secondary)

    References

    Appendix D Rapid-Scan Fourier Transform Spectroscopy

    References

    Author Bibliography

    Subject Bibliography

    Author Index

    Subject Index


Product details

  • No. of pages: 400
  • Language: English
  • Copyright: © Academic Press 1972
  • Published: January 28, 1972
  • Imprint: Academic Press
  • eBook ISBN: 9780323152105

About the Author

Robert Bell

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