Interferometric techniques calculations

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... 

Since, however, each model involves some assumptions, the calculation of h2 always renders certain inaccuracy. The most important problem in the three-layer model concerns the position of the plane that divides the hydrophobic and hydrophilic parts of the adsorbed surfactant molecule. In some cases it seems reasonable to have this plane passing through the middle of the hydrophilic head of the molecule, in others the head does not enter into the aqueous core. That is why it is worth comparing film thicknesses determined by the interferometric technique using the three-layer model, to those estimated by other methods. An attempt for such a comparison is presented in [63]. Discussed are phospholipid foam films the thickness of which was determined by two optical techniques the microinterferometric and FT-IR (see Section 2.2.5). The comparison could be proceeded with the results from the X-ray Reflectivity technique that deals not only with the foam film itself but also with the lamellar structures in the solution bulk, the latter being much better studied. Undoubtedly, this would contribute to a more detailed understanding of the foam film structure. 

A completely different behaviour exhibit NBF from NaDoS solutions. They do not change their thickness with pa and Cei alterations. However, their properties depend on the composition of the initial surfactant solution (see 0(Cei) and ta(Cei) dependences in Section 3.4.1.1). The thickness of NBF determined from h(Cei) dependence is approximately equal to the doubled thickness of the adsorption layer as assumed by Perrin [318]. This is confirmed by NBF obtained from other surfactants. It should be bom in mind that the interferometric technique employed to measure film thickness gives directly the optical difference in the path of the beams reflected by the two film surfaces. When the thickness is calculated from optical measurements a refractive coefficient, being a function of film structure, should be chosen (see Sections 2.1.3 and 3.4.1). 

Methods for the analysis of phosgene in the presence of HCl have involved interferometric techniques [1235,1967]. In one example, the refractive index of the gas mixture was measured by use of an interferometer, in order to calculate the composition of the mixture [1967]. In another example, a rapid method for the continuous analysis of phosgene (in the off-gases from the production of alkyl isocyanates) involved an interferometric technique in which the number of interference iines were correlated as a function of phosgene concentration [1235]. 

Ultrasonic transducers can excite various wave modes, eg, guided Lamb waves that may be suitable for specific apphcations (143). Ultrasonic excitation is also used to detect the so-called acoustic nonlinearity associated with defects, eg, in PMC (144,145). The combination of recording guided ultrasonic waves with numerical back-calculation of wave propagation for detecting indications of defects in PMC pipes also looks promising (146). Surface-bonded fiber optics can detect ultrasonic waves via interferometric techniques (147). Beyond frequencies of 1 GHz, ultrasonics is called acoustic microscopy, for details, the reader is referred to Reference 148. This technique can be applied to polymers or PMC (149), specifically to polymeric microelectronics packaging (150). 

Measurements of lateral strains in thin films can be carried out using interferometric techniques [43]. Alternatively, methods have been developed for measuring the appropriate compliance coefficients to enable 21, 031 and 0 2 fo be calculated [41]. For PVDF, values of a again depend on the manufacturer one set of results reported values of 0.25, 0.57 and 0.45 for O21, 0 1 and 0 2 respectively [43]. 

The laser interferometry technique is widely used for the study of the detonation wave time profile and structure due to its exceptionally good time resolution. The laser interferometry operating principle is based on the Doppler effect. The technique records the position and time dependence of the interferometric fields obtained due to the Doppler shift in wavelength of the reflected laser beam, resulting from the thin metal shim motion. The metal shim, 15-25 pm thick, is placed between the explosive charge and windows that are made of an inert optically transparent material, such as water, lithium fluoride, or polymethylmethacrylate. On the basis of the velocity of the explosive/metal shim interface as a function of time, it is possible to calculate the values of detonation parameters of the explosive (Gimenez et al., 1985, 1989 Hemsing, 1985 Leeetal., 1985). 

Neu et al. [23] have compiled their A factors measured by laser fluorescence spectroscopy with values obtained earlier by interferometric measurements [27, 28] and compared their results with the values for the 5d 6s and 5d 6s levels calculated by the effective operator technique of Sandars and Beck [24], see Table 2/25. 

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