Multiple frequency

Probes may be absolute, differential, reflection or array and may work at single, dual and multiple frequencies. 

In the previous section we discussed light and matter at equilibrium in a two-level quantum system. For the remainder of this section we will be interested in light and matter which are not at equilibrium. In particular, laser light is completely different from the thennal radiation described at the end of the previous section. In the first place, only one, or a small number of states of the field are occupied, in contrast with the Planck distribution of occupation numbers in thennal radiation. Second, the field state can have a precise phase-, in thennal radiation this phase is assumed to be random. If multiple field states are occupied in a laser they can have a precise phase relationship, something which is achieved in lasers by a teclmique called mode-locking Multiple frequencies with a precise phase relation give rise to laser pulses in time. Nanosecond experiments... 

LB Films of Porphyrins and Phthalocyanines. The porphyrin is one of the most important among biomolecules. The most stable synthetic porphyrin is 5,10,15,20-tetraphenylporphyrin (TPP). Many porphyrin and phthalocyanine (PC) derivatives form good LB films. Both these molecules are important for appHcations such as hole-burning that may allow information storage using multiple frequency devices. In 1937 multilayers were built from chlorophyll (35). 

Ground acceleration This is the time history of ground acceleration as a result of an earthquake, where multiple frequency excitation predominates (Figure 14.12(b). A ground response spectrum (GRS) can be derived from this history. 

With time-domain data, the analyst must manually separate the individual frequencies and events that are contained in the complex waveform. This effort is complicated tremendously by the superposition of multiple frequencies. Note that, rather than overlaying each of the discrete frequencies as illustrated theoretically in Figure 43.18(a), actual time-domain data represents the sum of these frequencies as was illustrated in Figure 43.17. 

Overall, it can be summarized that, use of multiple frequency irradiations based on the use of multiple transducers gives much higher cavitational activity in the reactor and hence enhanced results. It is also recommended that a combination of low frequency irradiation (typically 20 kHz) with other frequencies in the range of 50-200 kHz should be used for obtaining maximum benefits from the cavitational reactors. 

Overall, it can be said that for single frequency operation an optimum intensity of irradiation should be selected, whereas for multiple frequency operation, existence of optimum intensity has not been observed but this cannot be generalized. 

The position of the transducers in reactors based on the multiple frequency arrangement should be done in such a way that maximum and uniform cavita-tional activity is obtained. Theoretical analysis of the cavitational activity distribution as discussed earlier aids in arriving at an optimum location of the transducers. Similar argument holds true for the geometry of the reactor. 

Design of sonochemical reactors is a very important parameter in deciding the net cavitational effects. Use of multiple transducers and multiple frequencies with possibility of variable power dissipation is recommended. Theoretical analysis for predicting the cavitational activity distribution is recommended for optimization of the geometry of the reactor including the transducer locations in the case of multiple transducer reactors. Use of process intensifying parameters at zones with minimum cavitational intensity should help in enhancing the net cavitational effects. 

A. Klein, E.J.L. Mclnnes, T. Scheiring and S. Zalis, Electronic structure of radical anionic binuclear organoplatinum complexes. A multiple frequency EPR investigation, J. Chem. Soc., Faraday Trans., 1998, 94, 2979. 

Figure 75-2 shows third-order data or a hyperspectral data cube where the spectral amplitude is measured at multiple frequencies (spectrum) with X and Y spatial dimensions included. Each plane in the figure represents the amplitude of the spectral signal at a single frequency for an X and Y coordinate spatial image. 

Figure 75-1 (a) Second order data (amplitude, multiple frequencies, time) (b) Second order data (amplitude at one frequency, with X and Y spatial dimensions). 

Meyer M, Hermand JP, Asch M et al (2006) An analytic multiple frequency adjoint-based inversion algorithm for parabolic-type approximations in ocean acoustics. Inverse Probl Sci Eng 14 245-265... 

In order to implement frequency domain based sensing systems capable of monitoring the temporal luminescence of sensors, in few seconds, data must be collected at multiple frequencies simultaneously. Single-frequency techniques have been used to make frequency domain measurements of luminescent decays. 14, 23 28) This approach is unsuitable for real-time applications since data must be acquired at several frequencies in order to precisely and accurately determine the temporal variables of luminescent systems. 1 Each frequency requires a separate measurement, which makes the single frequency approach too slow to monitor the evolution... 

In the case of a single lifetime with no interference from ambient or backscattered light only a single frequency is necessary to determine the lifetime of the luminescence. Determination of the phase and modulation at multiple frequencies is necessary to characterize complex decays in fiberoptic sensors. 

K. Hadener, S. Bergamasco and G. Calzaferri, Conversion and amplification of photomultiplier anode current in multiple-frequency phase fluorometry, Rev. Sci. Instrum. 59, 1924-1927 (1988). 

The multiexponential decay law of the emission from a mixture of fluorophores can be recovered from phase and modulation measurements over a range of multiple frequencies by... 

Infrared methods measure the absorbance of the C-H bond and most methods typically measure the absorbance at a single frequency (usually, 2930 cm Q that corresponds to the stretching of aliphatic methylene (CH2) groups. Some methods use multiple frequencies, including 2960 cm (CH3 groups) and 2900 to 3000 cm (aromatic C-H bonds). 

The development of simple, multiple-frequency solvent suppression techniques has greatly improved the quality of data that can be obtained using LC-NMR. One of the most useful methods for multiple resonance solvent suppression in LC-NMR is... 

In the first part of this contribution the general principle of multiple frequency selective excitation is explained, followed by a short presentation of correspondingly updated selective ID and 2D pulse sequences and by a few applications and results for demonstration. The contribution concludes with a critical discussion of advantages and limitations for this kind of experiments and the perspectives for further developments. Readers interested in a more detailed description and in experimental details such as spectrometer settings are referred to the corresponding publications [2-6]. 

Fig. 8. Normal HMBC spectrum (expansion of the ring carbons and ring protons) of the trisaccharide 1 dissolved in CDCI3 (b). Equivalent spectrum obtained with the multiple frequency selective experiment further modified to discriminate between "Jch and Jch (c). Additional spectra acquired within the same experiment, which show Jch connectivities between the ring protons and the carbonyl carbons (a), and which show the Jch connectivities between the ring protons and the ring carbons (d).

The interference process in this collinear approach is, however, different from the interference realized by mixing the local oscillator and the CARS field on a beam splitter. Interference takes place in the sample, which, in the presence of multiple frequencies, mediates the transfer of energy between the beams that participate in the nonlinear process. The local oscillator mixes with the anti-Stokes polarization in the focal volume, and is thus coherently coupled with the pump and Stokes beams in the sample through the third-order polarization of the material. In other words, the material s polarization, and its ability to radiate, is directly controlled in this collinear interferometric scheme. Under these conditions, energy from the local oscillator may flow to the pump and Stokes fields, and vice versa. For instance, when the local oscillator field is rout of phase with the pump/Stokes-induced anti-Stokes polarization in the focal interaction volume, complete depletion of the local oscillator may occur. The energy of the local oscillator field is not redistributed in terms... 

The AC Sweep is used for Bode plots, gain and phase plots, and phasor analysis. The circuit can be analyzed at a single frequency or at multiple frequencies. In this part we will illustrate its use at a single frequency for magnitude and phase results (phasors), and at multiple frequencies for Bode plots. 

The results can be obtained for a single frequency or multiple frequencies. 

For multiple frequencies, the results can be viewed graphically using Probe. For a single frequency, the results can be viewed as text in the output file. Use the Print part to generate text output. 

Advantages Applicable for multiple frequency input signals ... 

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