Heterodyne-beat method

An important and precise traditional method of measuring capacitance for dipole moment determinations is the heterodyne beat method, a particular form of the null method mentioned above. The output of an LC oscillator incorporating the capacitance... 

Measurements of e,.—Stability under pressure is the prime requirement for capacitance cells used to determine dielectric virial coefiScients. Cells of both parallel-plate and cylinder-within-a-cjirnder design, stable to a few parts in 10 and usable to over 200 atm, have been described by a number of authors. " Cells for use in the microwave region and cells for measuring refractivity > have also been described. Early measuremoits at radio frequencies relied on the heterodyne beat method, " but more recent work " has utilized the three-terminal transform ratio-aim technique developed by Cole and Gross. This second method eliminates difficulties due to stray capacitances and provides accuracies of better than 1 part in 10 . For an exceUent review of techniques at both ratfio and microwave frequencies see ch. 2 of ref. 53. For refractivity methods see refs. 45,46, and 54. 

The overall dipole moments of many covalent azides were obtained from measurements of the dielectric constants of their benzene solutions by the heterodyne beat method (Table 9). 

The dipole moment of D-fructose was studied by the heterodyne beat method, with pyridine or p-dioxane as the solvent, and a value of 15 Debye units was obtained, whereas other hexoses showed values in the range of 11 to 12. 

The dielectric constants needed for the determination of dipole moments are obtained by a heterodyne beat method or the resonance and bridge methods. The instrument specifically adapted for measurements of dielectric constants for dipole moments is a dipole meter model DM-01 manufactured by Wissenschaflich-Technische Werkstatten, Weilheim, Germany, equipped with two different thermostatted cells for two ranges of dielectric constants (cell DFL-1, e 1.0 to 3.4, cell DFL-2, e 2 0 to 6.9). The other dipole meter which used to be available from Toshniwal Brothers, Ltd., Madras, India, is not sufficiently sensitive for measurements of dielectric constants of diluted solutions and is better suited for measurements of large differences, such as the dielectric constants and dipole moments of different solvents. 

Equations 5.446 and 5.450 are applicable in the so-called homodyne method (or self-beating method), where only scattered light is received by the detector. In some cases, it is also desirable to capture by the detector a part of the incident beam that has not undergone the scattering process. This method is called heterodyne (or method of the local oscillator) and sometimes provides information that is not accessible by the homodyne method. It can be shown that if the intensity of the scattered beam is much lower than that of the detected nonscattered (incident) beam, the detector measures the autocorrelation function of the electrical held of the scattered light, dehned as... 

A laser whose frequency is unknown can be compared to a reference laser by heterodyne methods to high precision. Beat frequency measurements up to 2.5 THz in the visible spectrum have already been made. An alternative to simple heterodyne schemes is harmonic mixing by use of synthesis chains. 

The literature [61,63-82] r rs to QELS by many differoit names, some of which are spediic methods of implemratation. The.se include dynamic light scattering, laser scattering, laser Doppler velocimeby, intensity fluctuation spectroscopy, photon correlation spectroscopy (PCS), light beating spectroscopy and homo- and heterodyne spectroscopy. Most of the techniques discussed here are based on PCS. 

An instmmental alternative to microelectrophoresis is electrophoretic light scattering (ELS). The light scattering at migrating particles leads to phase shift (Doppler effect), which can be detected by a heterodyne DLS set-up (i.e. reference-beating with frequency shift). The method yields an intensity weighted distribution of the zeta-potential. 

A third group of methods is based on heterodyning (light beats). For this a frequency difference is introduced between the two beams in the interferometer, usually by means of a pair of acoustooptic modulators operated at sUghtly different frequencies. The output from a detector... 

The spectral distribution and frequency stability of the output of these stabilized lasers cannot be studied by the methods of conventional high-resolution spectroscopy. Instead it is usually necessary to construct two stabilized lasers, one of which may be regarded as a local oscillator, and to investigate the frequency stability using optical heterodyne techniques. As shown in Fig.13.17 the outputs of both lasers are superimposed coherently on the surface of a square-law detector, such as a photodiode or photomultiplier. The detector output signal then contains a component corresponding to the beat note or frequency difference between the two lasers. The power spectrum of this optical heterodyne signal may be "displayed directly on an r.f. spectrum analyser and its mean frequency determined pre-... 

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