Heterodyne method

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. 

Here, the unknown laser frequency is compared (via heterodyne methods) to a harmonic of some well known reference line such as the methane stabilized He-Ne laser at 3.39 pm.- -... 

Precise frequencies relative to a frequency standard (at frequency oiq) can be provided by comb generation. If we amplitude or frequency modulate (at frequency 2) a source at the standard frequency, then spectral components at frequencies ioq n 2 (n an integer) are generated. If n and 2 are chosen so that ioq + n 2 a w(unknown) then w(unknown) can be precisely determined by heterodyne methods. The challenge is to make (n 2) very large. 

In conclusion, the rather straightforward one-color pump-probe scheme of the self-heterodyne method seems particularly appropriate for smaller coupled systems where the vibrational spectra are less congested. The main content of the present approach and the frequency domain method described in Section IV.C are the same, namely the existence and magnitudes of cross peaks and their relationship to couplings between... 

It should be noted that a recent paper by Mumma et al. [11] using-a ground-based ir heterodyne method to measure the concentration of the important species CIO failed totally to observe any CIO, putting a limit of a factor of 1/7 of the accepted value, based upon in situ measurements. Professor Anderson will comment on this. 

A heterodyne method first suggested by Preuner and Pungs was used to determine the dielectric constants. The apparatus is shown diagrammatically in fig. I. 

If charged parhcles are placed in an external, constant electrical held (e.g., in electrophorehc equipment), they acquire a drift velocity, Vg, which is superimposed upon the diffusion. The respective power spectrum in the heterodyne method is ... 

The term Ie(co) can be measured directly either by filter experiments or b heterodyne methods using a spectrum analyzer instead of a correlator. As we have noted before, the technique of choice depends upon the time scale of the fluctuations. 

In the heterodyne method, a small portion of the unscattered laser light (local oscillator) is mixed with the scattered light on the photomultiplier cathode (see Fig. 1.2.2c). We assume below that the local oscillator varies at the laser frequency.2 The PM output may then be analyzed with an autocorrelator or a spectrum analyzer. 

Although homodyne is the most used method in PCS, we describe shortly also the heterodyne method, which is widely used for Doppler velocimetry experiments or when the Siegert relation is not applicable. Heterodyning means that we mix in the detector the scattered light with a strong nonscattered signal (named commonly as the local oscillator), that is. 

In the heterodyne method, there is frequency offset between test and reference beams, given for example, by an acousto-optical modulator in the source. The frequency of the intensity fluctuations when test and reference beams are recombined depends on the relative direction and velocity of motion. With appropriate data processing, sub-nm position resolution and tens of kHz bandwidth can be obtained. 

Various instruments have been constructed for measurement of the capacity or capacity increase. In the early research, primarily instruments based on electrostatic methods were employed, e.g., those utilizing Coulomb s law [Fu 24] or static capacity measurement [Op 33]. Later, instruments based on alternating current capacity measurement gained preference. Among these can be listed the instruments based on the classical bridge method [Ad 64, Ga 50], the resonance methods [Im 65, So 64] and the heterodyne method [Ba 51, We 51]. All of these can be used only for relative measurements. The dielectric data sought are obtained by comparison with known calibration substances. Instruments based on the... 

In the heterodyne method (Forre.ster et ah, 1947 Gorelik, 1947 Cummins et ah, 1964 13crnc and Pecora, 1976) the time correlation function... 

The longitudinal and transversal fluctuations of the shear modulus cause time correlation functions of the electric Held, which are measured by the heterodyne method (dynamic scattering of polarized and iinpolarized light) (see Kqiialion 2..S-32). 

Several well-known experimental techniques are employed in laser light scattering. Here we describe the homodyne and heterodyne methods. Both methods use a laser source for incident radiation. Both use a photomultiplier as a detector followed by an autocorrelator for computer analysis. The autocorrelator is defined as... 

I2 u = 12 127j -510(5) 79CHU LIF excited state ) heterodyne method ) strong correlation between both parameters ... 

A very precise method of measuring the frequency separation of two closely spaced spectral lines is based on a heterodyne technique. In this method, two single-mode lasers are used. Each laser is stabilized onto the centers Vp V2 of two spectral lines. The output of both lasers is superimposed onto a detector with nonlinear response generating the difference frequency - V2 which is electronically filtered from the frequencies Vp V2 and + V2 and which directly yields the desired line separation. This heterodyne method is illustrated by several examples in Sect.10.6. 

Frequencies associated with infrared radiation, that is, from approximately 3 x 10 to 3 X 10 " Hz, cannot be detected directly by radio frequency techniques. One exception exists in the heterodyne method discussed in Section 5.9, but, in general, infrared frequencies are too high for a direct application of microwave technology. On the other hand, the frequencies and, therefore, the energies of infrared photons are too low to liberate electrons from surfaces by the photoelectric effect. Consequently, standard photomultipliers and all devices based on photoelectric phenomena are also unsuitable as detectors above about 1 m. For all practical purposes only two classes of phenomena provide infrared detection mechanisms. 

A straightforward approach with heterodyne treatment was proposed by Fang and Brown, which is a modification of the partial heterodyne method, where the instmmental coherent factor p is taken into account. Then, we can rewrite eqn [140] as... 

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