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.
Inhalt
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 ±2p (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, sc, and Efficiency for s = sc
Cavity Effect, sL, 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