Introductory Fourier Transform Spectroscopy

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