Homodyne

Since optical fields oscillate too quickly for direct detection, they are measured in quadrahire —as photons (see below). There are two ways to achieve quadrahire. One is homodyne detection in which the new field is measured at... 

Returning to the original pump-probe RRS, it is a simple matter to complete the 4WM WMEL diagrams for any proposed RRS. Usually RRS experiments are of the frill quadrature sort, both spontaneous RRS as well as homodyne detected femtosecond RRS. The latter fit most pump-probe configurations. 

Clip acts in phase (the same Fourier component) with the first action of cii to produce a polarization that is anti-Stokes shifted from oi (see fV (E) and IFj (F) of figure B 1.3.2(b)). For the case of CSRS the third field action has frequency CO2 and acts in phase with the earlier action of CO2 (W (C) and IFj (D) of figure Bl.3.2 (b). Unlike the Class I spectroscopies, no fields in CARS or CSRS (or any homodyne detected Class II spectroscopies) are in quadrature at the polarization level. Since homodyne detected CRS is governed by the modulus square of hs lineshape is not a synmretric lineshape like those in the Class I... 

For homodyne detection, the TR-CRS intensity (for Lorentzian Raman lines) is of the fomi [115]... 

Hirose et al. [26] proposed a homodyne scheme to achieve the background-free detection of the fourth-order field. With pump irradiation in a transient grating configuration, the fourth-order field propagates in a direction different from that of the second-order field because of different phase match conditions. The fourth-order field is homodyned to make ffourth(td. 2 D) and spatially filtered from the second-order response hecond td, 2 D). 

Czoch, R. and Francik, A. 1989. Instrumental Effects in Homodyne Electron Paramagnetic Resonance Spectrometers. Chichester Ellis Horwood. 

Frequency modulated continuous wave (FMCW) radar is most commonly used to measure range R and range (radial) velocity of a target [42, 43]. The most common structure of a homodyne FMCW radar is presented in Figure 2. 

In frequency-domain FLIM, the optics and detection system (MCP image intensifier and slow scan CCD camera) are similar to that of time-domain FLIM, except for the light source, which consists of a CW laser and an acousto-optical modulator instead of a pulsed laser. The principle of lifetime measurement is the same as that described in Chapter 6 (Section 6.2.3.1). The phase shift and modulation depth are measured relative to a known fluorescence standard or to scattering of the excitation light. There are two possible modes of detection heterodyne and homodyne detection. 

In the homodyne mode of detection, the modulation frequency of the excitation light is the same as that of the image intensifier. An example of data is shown in Box 11.1. 

The data in Figure B11.1.1 were acquired with a frequency-domain FLIM instrument working in homodyne mode. In this mode, the modulation frequency of the intensifier (40 MHz) is identical to that of the excitation light (40 MHz). The phase and modulation are calculated from a series of images taken at different phase delays between the excitation light and the intensifier. 

In the simplest (homodyne) detection scheme one measures the time-integrated intensity of the field generated by the sample in a given direction ky ... 

A distinction between homodyne and heterodyne detection must be made in optical scattering and diffraction experiments. Without careful treatment of the background, there is always the risk of mixed or unknown coherence conditions, and the diffusion coefficient determined from such data may be off by a factor of two. At least for the signal and background levels present in TDFRS, heterodyne detection is always superior to homodyne, especially since the heterodyne signal, contrary to the homodyne one, turns out to be very stable against perturbations and systematic errors. Even under nearly perfect homodyne conditions the tail of the decay curve is almost unavoidably heterodyne [34]. 

The intensity / as seen by the detector contains both homodyne and heterodyne contributions [34,38,39] ... 

Es is the electric field amplitude of the diffracted beam. Ec and Einc are the coherent and incoherent electric field amplitudes of the background intensity, respectively. 0 is the phase shift between the signal and the coherent background, and the phase of Ec is arbitrarily chosen to be zero. For convenience, the proportionality factor between E2 and / is set to unity. Sbom = E2 is the homodyne and Sbet = 2 ECES cos 0 the heterodyne signal. The total background is Jb=E2c + Efnc. 

The homodyne and heterodyne signals can be separated if two measurements with a phase shift of n between background and signal are combined according to... 

Fig. 3. Homodyne/heterodyne separation measured intensities for step excitation and phase angles 0=0 and 0 =n, together with extracted homodyne and heterodyne signals. Left 90° rotation of the polarization, sample PS/toluene. Right 180° rotation of the polarization, sample toluene/n-hexane From Ref. [34]...

Figure 3 shows the signals measured for 0 = 0 and 0 = 7ras well as the separation into homodyne and heterodyne components for 90° and 180° rotation of the polarization. The superior quality of the heterodyne signal is obvious, and the homodyne signal is only usable in the case of 90° rotation. 

Chet(t) can be complex to account for phase shifts. The homodyne diffraction efficiency, which is measured in the absence of coherent background, is proportional to nq(t) 2. 

Once the scaling relation of Eq. (39) is known, the molar mass distribution can, at least in principle, be obtained from a Laplace inversion of the multi-exponential decay function as defined in Eq. (40). At this point, the differences between PCS and TDFRS stem mainly from the different statistical weights and from the uniform noise level in heterodyne TDFRS, which does not suffer from the diverging baseline noise of homodyne PCS caused by the square root in Eq. (38). 

Pseudostochastic random binary sequences are noise-like time patterns. They are defined at times n A t and assume only two different values, corresponding to the grating amplitudes -1 and +1, if 180°-phase modulation is used for switching off the optical grating. Only software modifications, and no changes in the hardware of the TDFRS setup, are necessary in order to utilize pseudostochastic excitation sequences. The timing for heterodyne/homodyne separation is identical to the one already described for pulsed excitation. 

The main problem with periodic TDFRS is, that the different frequencies are measured at different times. This requires a long-time stability, especially of the heterodyne reference, lasting about as long as the entire experiment. Time domain experiments, on the other hand, are frequency multiplexed, and stability of the heterodyne background is only required for one homodyne/heterodyne separation cycle as described in the experimental section, which is only of the order of seconds, not hours. No stability of the signal amplitude is required for the averaging of C lel(t) over arbitrary times. 

We have outlined how TDFRS not only provides a useful tool for the study of the Ludwig-Soret effect in multicomponent liquids, but can also contribute valuable pieces of information towards solving the puzzles encountered in polymer analysis. Though TDFRS is conceptually simple, real experiments can be rather elaborate because of the relatively low diffraction efficiencies, which require repetitive exposures and a reliable homodyne/heterodyne signal separation. As an optical scattering technique it has much in common with PCS, and the diffusion coefficients obtained in the hydrodynamic limit (q —> 0) for monodisperse solutions are indeed identical. 

Z c of the intensity fluctuations. In a homodyne light scattering experiment, 7 c is related to the translational diffusion coefficient, Dy, of the particles by the relationship... 

It is important to note that the homodyne autocorrelation function is independent of the mean velocity within the scattering volume and is influenced only by the diffusion and velocity gradient induced motions of the particles. Furthermore, if there is no velocity gradient, the result is that the correlation function is the following, familiar result,... 

Equation (6.29) is the governing equation for the use of homodyne, dynamic light scattering for measurement of velocity gradients. What is left is to specify the shape of the intensity distribution of the incident light within the scattering volume. As an example, if... 

The other geometric consideration is the relative orientation of the scattering vector, q, and an applied field, such as a flow or electric field. For example, as seen in Chapter 6, the use of homodyne dynamic light scattering to measure velocity gradients requires that q be oriented parallel to the component of the velocity of interest. This is simply accomplished by having that velocity component directed parallel to the vector bisecting k(. and k [44],... 

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