Heterodyne scattering

Figure 1 shows the experimental time-dependent correlation flmctions obtained at k = 1030 cm for various values of the temperature gradient VT in a solution of polystyrene in toluene with a polymer concentration of w = 2.50%. The data are relative to the intensity of the stray light that serves as a local oscillator in the heterodyne scattering experiments. The correlation functions obtained for all values of VT can be represented by a single exponential... 

The capillary wave frequency is detected by an optical heterodyne technique. The laser beam, quasi-elastically scattered by the capillary wave at the liquid-liquid interface, is accompanied by a Doppler shift. The scattered beam is optically mixed with the diffracted beam from the diffraction grating to generate an optical beat in the mixed light. The beat frequency obtained here is the same as the Doppler shift, i.e., the capillary wave frequency. By selecting the order of the mixed diffracted beam, we can change the wavelength of the observed capillary wave according to Eq. (11). 

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. 

For very accurate line profile measurements, a heterodyne technique has been developed 240) which can be briefly explained as follows the light, scattered into a cone within the angle 0 b9 (50< 1 °). is focused onto the cathode of a photomultiplier. The photocurrent is proportional to the square of the incoming light amplitude but cannot follow the rapid light frequency. Any beat frequencies, however, resulting from interference between the... 

Potma, E. O., Evans, C. L., and Xie, X. S. 2006. Heterodyne coherent anti-Stokes Raman scattering (CARS) imaging. Opt. Lett. 31 241 3. 

Greve, M., Bodermann, B., Telle, H. R., Baum, P, and Riedle, E. 2005. High-contrast chemical imaging with gated heterodyne coherent anti-Stokes Raman scattering microscopy. AppZ. Phys. B-Lasers Opt. 81(7) 875-79. 

Pastirk, I., DelaCruz, J. M., Walowicz, K. A., Lozovoy, V. V., andDantus, M. 2003. Selective two-photon microscopy with shaped femtosecond pulses. Opt. Exp. 11(14) 1695-1701. Potma, E. O., Evans, C. L., and Xie, X. S. 2006. Heterodyne coherent anti-Stokes Raman scattering (CARS) imaging. Opt. Lett. 31(2) 241M 3. 

Vacano, B. V., Buckup, T., and Motzkus, M. 2006. Highly sensitive single-beam heterodyne coherent anti-Stokes Raman scattering. Opt. Lett. 31 2495-97. 

Before melting and for some time after only the band at 625 cm of the AA [C4CiIm]+ cation was observed in the 600-630 cm i region. Gradually 603 cm i band due to the GA conformer became stronger. After about 10 min the AA/GA intensity ratio became constant. The interpretation [50] is that the rotational isomers do not interconvert momentarily at the molecular level. Most probably it involves a conversion of a larger local structure as a whole. The existence of such local structures of different rotamers has been found by optical heterodyne-detected Raman-induced Kerr-effect spectroscopy (OHD-RIKES) [82], Coherent anti-Stokes Raman scattering (CARS) [83],... 

The direct measurement of the g(1,(x) can be achieved by either the interference between the scattered field and a reference beam (heterodyne) or the interference... 

The description of pump-probe signals presented in the preceding section can be immediately generalized to heterodyne-detected transient grating spectroscopy as well as to other four-wave mixing techniques. Heterodyne detection involves mixing the scattered field with an additional heterodyne field 4(r). The signal in the ks direction can then be written in terms of the polarization Ts(t) as... 

In addition to the intrinsic lack of stationarity, many of the fluctuations in the glass relax so slowly that they appear to be static sources of light scattering on the time scale of the data collection. These static contributions will introduce a heterodyne component into the observed relaxation function. If the fraction of the light which is quasi-static exceeds 90%, then the observed relaxation function can be interpreted as a heterodyne case and an analysis can be carried out. However, it is not clear that this limit is ever reached in practice. Only 60% of the light was slowly relaxing at all in polystyrene. If at least 90% of the slowly relaxing part becomes quasi-static the heterodyne case will still apply to the observed part of the relaxation function. For PMMA and PEMA this is unlikely to be the case at any temperature near Tg. 

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]. 

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. 

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