Fourier transform optical principles

A General Designs of Optical Instruments 164 7B Sources of Radiation 166 7C Wavelength Selectors 175 7D Sample Containers 190 7E Radiation Transducers 191 7F Signal Processors and Readouts 202 7G Fiber Optics 202 7H Types of Optical Instruments 203 71 Principles of Fourier Transform Optical Measurements 204 Questions and Problems 212... 

Most multiplex analytical instruments depend on the Fourier transform (FT) for signal decoding and are thus often called Fourier transform spectrometers. Such instruments are by no means confined to optical spectroscopy. Fourier transform devices have been described (or nuclear magnetic resonance spectrometry, mass spectrometry, and microwave spectroscopy. Several of these instruments are discussed in some detail in subsequent chapters. The section that follows describes the principles of operation of Fourier transform optical spectrometers. 

Interferometry is difficult in the uv because of much greater demands on optical alignment and mechanical stabiUty imposed by the shorter wavelength of the radiation (148). In principle any fts interferometer can be operated in the uv when the proper choice of source, beam spHtter, and detector is made, but in practice good performance at wavelengths much shorter than the visible has proved difficult to obtain. Some manufacturers have claimed operating limits of 185 nm, and Fourier transform laboratory instmments have reached 140 nm (145). 

In the mid-IR, routine infrared spectroscopy nowadays almost exclusively uses Fourier-transform (FT) spectrometers. This principle is a standard method in modem analytical chemistry45. Although some efforts have been made to design ultra-compact FT-IR spectrometers for use under real-world conditions, standard systems are still too bulky for many applications. A new approach is the use of micro-fabrication techniques. As an example for this technology, a miniature single-pass Fourier transform spectrometer integrated on a 10 x 5 cm optical bench has been demonstrated to be feasible. Based upon a classical Michelson interferometer design, all... 

Fourier transform methods have revolutionized many fields in physics and chemistry, and applications of the technique are to be found in such diverse areas as radio astronomy [52], nuclear magnetic resonance spectroscopy [53], mass spectroscopy [54], and optical absorption/emission spectroscopy from the far-infrared to the ultraviolet [55-57]. These applications are reviewed in several excellent sources [1, 54,58], and this section simply aims to describe the fundamental principles of FTIR spectroscopy. A more theoretical development of Fourier transform techniques is given in several texts [59-61], and the interested reader is referred to these for details. 

Spectroscopy has become a powerful tool for the determination of polymer structures. The major part of the book is devoted to techniques that are the most frequently used for analysis of rubbery materials, i.e., various methods of nuclear magnetic resonance (NMR) and optical spectroscopy. One chapter is devoted to (multi) hyphenated thermograviometric analysis (TGA) techniques, i.e., TGA combined with Fourier transform infrared spectroscopy (FT-IR), mass spectroscopy, gas chromatography, differential scanning calorimetry and differential thermal analysis. There are already many excellent textbooks on the basic principles of these methods. Therefore, the main objective of the present book is to discuss a wide range of applications of the spectroscopic techniques for the analysis of rubbery materials. The contents of this book are of interest to chemists, physicists, material scientists and technologists who seek a better understanding of rubbery materials. 

See for example R. R. Ernst, G. Bodenhausen and A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Oxford University Press, Oxford, 1988. A. G. Marshall and F. R. Verdun, Fourier Transforms in NMR, Optical, and Mass Spectrometry — A User s Handbook, Elsevier, Amsterdam, 1990. E. Fukushima and S. B. W. Roeder, Experimental Pulse NMR. A Nuts and Bolts Approach, Addison-Wesley Publishing Company, Reading, MA, 1981. 

Fourier transform methods have come into their own as a means of studying the optical spectra of gas-phase radicals. Both infrared (FTIR) and ultraviolet/visible spectroscopy (FTUV/VIS) are now used to scrutinize these reactive molecules. We discuss the underlying principles of Fourier transform spectroscopy (FTS) with particular emphasis on the advantages and drawbacks of FTIR and FTUV/VIS measurements. Extensive tables are presented of metastable molecules that have been studied by Fourier transform methods. 

For readers interested in greater detail, Fourier transform techniques are treated in the following references (a) Marshall, A.G. Verdun, F.R. Fourier Transforms in NMR, Optical, and Mass Spectrometry Elsevier Amsterdam, 1986 (b) Griffiths, P.R., DeHaseth, J.A. Fourier Transform Infrared Spectrometry Wiley-Interseience New York, 1986 (c) Chamberlain, J. The Principles of Interferometric Spectroscopy Wiley-Interscience Chichester, 1979 (d) Bell, R. J. Introductory Fourier Transform Spectrometry Academic Press New York, 1972. 

The concept of a repeated distribution is important because it can be shown (we will forego a painful formal proof here) that the Fourier transform (or diffraction pattern) of the convolution of two spatial functions is the product of their respective Fourier transforms. This was demonstrated physically using optical diffraction in Figure 1.8 of Chapter 1. In principle, this means that if we can formulate an expression for the Fourier transform of a single unit cell, and if we can do the same for a lattice, then if we multiply them together, we will have a mathematical statement for how a crystal diffracts waves, its Fourier transform. 

M. (2007) Variable-temperature rheo-optical Fourier-transform infrared spectroscopy of polymers, in Vibrational Spectroscopy of Polymers Principles and Practice (eds N.J., Everall, J.M. 

Fig. 32. Optical arrangement (principle) for asymmetric Fourier transform spectroscopy. For further details see Ref. o>...

In principle and also in practice, the small quantity can be viewed as a legitimate means for introducing an optical potential that is used in practice to avoid the artificial boundary reflection. Such a view is promoted by Seideman and Miller (56). Thus (7 , ) can be calculated by a half Fourier transform on the time-dependent wave function evaluated at a large distance R,, ... 

Discuss the principles of Fourier transform infrared spectroscopy and nonlinear laser optics [74, 75], and of second harmonic and sum frequency generation. Compare the relative advantages of both techniques for the study of the bonding, orientation, and location of adsorbed molecules either on metal or on insulator surfaces. 

In the case of coherent laser light, the pulses are characterized by well-defined phase relationships and slowly varying amplitudes (Haken, 1970). Such quasi-classical light pulses have spectral and temporal distributions that are also strictly related by a Fourier transformation, and are hence usually refered to as Fourier-transform-limited. They are required in the typical experiments of coherent optical spectroscopy, such as optical nutation, free induction decay, or photon echoes (Brewer, 1977). Here, the theoretical treatments generally adopt a semiclassical procedure, using a density matrix or Bloch formalism to describe the molecular system subject to a pulsed or continuous classical optical field, which generates a macroscopic sample polarization. In principle, a fully quantal description is possible if one represents the state of the field by the coherent or quasi-classical state vectors (Glauber, 1965 Freed and Villaeys, 1978). For our purpose, however. 

Mathematically, integral Kramers-Kronig relations have very general character. They represent the Hilbert transform of any complex function s(co) = s (co) + s"(co) satisfying the condition s (co) = s(—co)(here the star means complex conjugate). In our particular example, this condition is applied to function n(co) related to dielectric permittivity s(co). The latter is Fourier transform of the time dependent dielectric function s(f), which takes into account a time lag (and never advance) in the response of a substance to the external, e.g. optical, electric field. Therefore the Kramers-Kronig relations follow directly from the causality principle. 

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