Interferometric techniques applications

This Fourier transform process was well known to Michelson and his peers but the computational difficulty of making the transformation prevented the application of this powerful interferometric technique to spectroscopy. An important advance was made with the discovery of the fast Fourier transform algorithm by Cooley and Tukey 29) which revived the field of spectroscopy using interferometers by allowing the calculation of the Fourier transform to be carried out rapidly. The fast Fourier transform (FFT) has been discussed in several places 30,31). The essence of the technique is the reduction in the number of computer multiplications and additions. The normal computer evaluation requires n(n — 1) additions and multiplications whereas the FFT method only requires (n logj n) additions and multiplications. If we have a 4096-point array to Fourier transform, it would require (4096) (4095) or 16.7 million multiplications. The FFT allows us to reduce this to... 

Improvements in the single side-band performance of a mixer-based receiver can be made by filtering the unwanted side band before it is down-converted in the mixer. Such a scheme, which is described in detail by Goldsmith (1982) is based on interferrometric techniques. We will not discuss single side-band filtering any further, except to note that it is a particularly apposite demonstration of the use of optical techniques to process the radiation in the spectrometer. We will discuss the use of interferometric techniques in Section IX as a means to realize a reflection mode spectrometer. These few examples indicate the flexibility of application of optical techniques to problems of instrument design in the FIR. 

In this chapter we explore several aspects of interferometric nonlinear microscopy. Our discussion is limited to methods that employ narrowband laser excitation i.e., interferences in the spectral domain are beyond the scope of this chapter. Phase-controlled spectral interferometry has been used extensively in broadband CARS microspectroscopy (Cui et al. 2006 Dudovich et al. 2002 Kee et al. 2006 Lim et al. 2005 Marks and Boppart 2004 Oron et al. 2003 Vacano et al. 2006), in addition to several applications in SHG (Tang et al. 2006) and two-photon excited fluorescence microscopy (Ando et al. 2002 Chuntonov et al. 2008 Dudovich et al. 2001 Tang et al. 2006). Here, we focus on interferences in the temporal and spatial domains for the purpose of generating new contrast mechanisms in the nonlinear imaging microscope. Special emphasis is given to the CARS technique, because it is sensitive to the phase response of the sample caused by the presence of spectroscopic resonances. 

We first review the essentials of the phase distribution of the electric fields at the focus of a high numerical aperture lens in Section II. After discussing the phase properties of the emitted signal, in Section HI we zoom in on how the information carried by the emitted held can be detected with phase-sensitive detection methods. Interferometric CARS imaging is presented as a useful technique for background suppression and signal enhancement. In Section IV, the principles of spatial interferometry in coherent microscopy are laid out and applications are discussed. The influence of phase distortions in turbid samples on phase-sensitive nonlinear microscopy is considered in Section V. Finally, in Section VI, we conclude this chapter with a brief discussion on the utility of phase-sensitive approaches to coherent microscopy. 

The ability to control the phase of focal fields at different locations in the interaction volume has interesting applications when combined with interferometric mixing techniques. When a local oscillator field is focus engineered and overlapped with... 

In contrast to the relatively limited number of experimental approaches utilized to determine electron collisional information for C02 laser species, many different types of experiments have been employed in the determination of heavy particle rates as a function of temperature, for temperatures slightly below room temperature up to several thousand degrees. At room temperature, measurements have been obtained using sound absorption and/or dispersion as well as impact-tube and spectrophone techniques. High temperature rate data have been obtained primarily from shock tube experiments in which electron beam, infrared emission, schlieren, and interferometric diagnostic techniques are employed. For example, as many as 36 separate experiments have been conducted to determine the relaxation rate of the C02 bending mode in pure C02 [59]. The reader is referred to the review by Taylor and Bitterman [59] of heavy-particle processes of importance to laser applications for a detailed description and interpretation of available experimental and theoretical data. 

For volumetric measurements with DACs high precision can only be obtained using interferometric and video control, and the primary applications may be for thermal pressure measurements at constant volume. The techniques need still further development. 

Photon correlation spectroscopy (PCS) is a well estabhshed technique that exploits the fluctuations coherent radiation scattered by small particles in order to determine their size. Its formulation, implementation and exploitation have been treated thoroughly in two previous NATO Advanced Study Institutes [1,2]. The concepts upon which the technique is foimded are not unique to metrological applications however, for they also underpin interferometric methods used in radio astronomy. The original formulation of PCS was for... 

Probably the most important instruments in laser spectroscopy are interferometers, which are applicable in various modifications to numerous problems. We therefore treat these devices in somewhat more detail. Recently, new techniques of measuring laser wavelengths with high accuracy have been developed they are mainly based on interferometric devices. Because of their relevance in laser spectroscopy they will be discussed in a separate section. 

With the ultrahigh resolution, which can, in principle, be achieved with singlemode tunable lasers (Vol. 2, Chaps. 1-5), the accuracy of absolute wavelength measurements attainable with conventional techniques may not be satisfactory. New methods have been developed that are mainly based on interferometric measurements of laser wavelengths. For applications in molecular spectroscopy, the laser can be stabilized on the center of a molecular transition. Measuring the wavelength of such a stabihzed laser yields simultaneously the wavelength of the molecular... 

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