Sensitivity of Polarization Spectroscopy

In the following we briefly discuss the sensitivity and the signal-to-noise ratio achievable with polarization spectroscopy. The amplitude of the dispersion signal in (2.50) for 0 is approximately the difference AIj = It x = +1) — Ij x = — 1) between the maximum and the minimum of the dispersion curve. From (2.50) we obtain (Fig. 2.29) 

Under general laboratory conditions the main contribution to the noise comes from fluctuations of the probe-laser intensity, while the principal limit set by shot noise 

Because the crossed polarizers greatly reduce the background level, we can expect a better signal-to-noise ratio than in saturation spectroscopy, where the full intensity of the probe beam is detected. 

In this case of ideal windows (Z r = = 0) the quality of the two polarizers, given by 

For comparison, in saturation spectroscopy the S/N ratio is, according to (2.37), given by 

Under general laboratory conditions the main contribution to the noise comes from fluctuations of the probe-laser intensity, while the principal limit set by shot noise (Chap. 4) is seldom reached. The noise level is therefore essentially proportional to the transmitted intensity, which is given by the background term in (7.44). 

In the absence of window birefringence (that is, AZ r = AZ / = 0, O — 0) the signal-to-noise (S/N) ratio, which is, besides a constant factor a, equal to the signal-to-background ratio, becomes with (7.50) and (7.51a) for the dispersion signals 

In this case of ideal windows (br = bi = 0) the quality of the two polarizers, given by the residual transmission of the completely crossed polarizations ( = 0), limits the achievable S/N ratio. In saturation spectroscopy the S/N ratio is, according to (7.31), given by 

Signal-to-Noise (S/N) ratio which is, besides a constant factor a, equal to the signal-to-background ratio, becomes with (7.46) 

According to (10.23) the signal-to-background ratio is for saturation spectroscopy outside the laser resonator 

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The sensitivity of polarization spectroscopy compared with saturation spectroscopy is illustrated by Fig. 2.24a, which shows the same hfs transitions of I2... 

The higher sensitivity of polarization spectroscopy compared with conventional saturation spectroscopy results from the detection of phase differences rather than amplitude differences. This advantage is also used in a method that monitors the interference between two probe beams where one of the beams suffers saturation-induced phase shifts. This saturated interference spectroscopy was independently developed in different laboratories [271, 272]. The basic principle can easily be understood from Fig. 2.43. We follow here the presentation in [271]. 

The sensitivity of polarization spectroscopy compared with saturation spectroscopy is illustrated by Fig. 7.22a, which shows the same hfs transitions of I2 as in Fig. 7.12 taken under comparable experimental conditions. A section of the same spectrum is depicted in Fig. 7.22b with 9 7 0, optimized for dispersion-line profiles. 

A very new approach to improve the sensitivity of NMR spectroscopy is the injection of laser-polarized Xe isotopes into the sample volume of the NMR... 

The sensitivity of the saturated interference technique is comparable to that of polarization spectroscopy. While the latter can be applied only to transitions from levels with a rotational quantum number / > 1, the former works also for 7=0. An experimental drawback may be the critical alignment of the Jamin interferometer and its stability during the measurements. 

IR and Raman spectroscopies are very important tools for characterization of the chemical and physical nature of polymers. Due to the high sensitivity of IR spectroscopy to changes in the dipole moment of a given vibrating group, this technique is intensively used to identify polar groups. In contrast, Raman spectroscopy is especially helpful in the characterization of the homonuclear polymer backbone due... 

Especially for the application to biological relevant surfaces (e.g., adsorbed proteins) the sensitivity of polarized SHG to the chirality of the molecules (the "handedness" of their structures) is important (Verbiest et al. 1998). Recently, the second-order nonlinear optical analog to circular dichroism and optical rotatory dispersion spectroscopy has been successfully developed (Yee et al. 1994 Byers et al. 1994). 

The well known method of polarization spectroscopy (16) gains a substantial increase in sensitivity by observing the induced dicroism and birefringence of the gas sample rather than changes in absorption. 

The yellow disulfide radical anion and the briUiant blue trisulfide radical anion often occur together for what reason some authors of the older Hterature (prior to 1975) got mixed up with their identification. Today, both species are well known by their E8R, infrared, resonance Raman, UV-Vis, and photoelectron spectra, some of which have been recorded both in solutions and in solid matrices. In solution these radical species are formed by the ho-molytic dissociation of polysulfide dianions according to Eqs. (7) and (8). 8ince these dissociation reactions are of course endothermic the radical formation is promoted by heating as well as by dilution. Furthermore, solvents of lower polarity than that of water also favor the homolytic dissociation. However, in solutions at 20 °C the equilibria at Eqs. (7) and (8) are usually on the left side (excepting extremely dilute systems) and only the very high sensitivity of E8R, UV-Vis and resonance Raman spectroscopy made it possible to detect the radical anions in liquid and solid solutions see above. 

The obtained results are in agreement with our previous hypothesis [2-4] that absolute intensities and the distribution of relative intensities of IR bands in the spectra of adsorbed species are sensitive to the chemical activation of the corresponding bonds arising from polarization by adsorption sites. Hence, in addition to the low frequency shifts, intensites can be used as a criterion for chemical activation. Indeed, according to the fundamentals of IR spectroscopy, the intensities of IR stretching bands are proportional to the square of the dipole moment changes (dp) created by the stretching vibrations over the normal coordinates q of these vibrations [6] I °c [dp/d q]2. 

Until recently, previous studies for continuous monitoring of hepatic function with ICG utilized the absorption mode. However, new studies demonstrate that the highly sensitive fluorescence technique can equally be used [148-150]. In addition to high sensitivity, in-depth analysis of the emission, excitation and polarization properties of fluorescence spectroscopy furnishes additional functional information about the dye molecule. In this system, the fluorescence profile emanating from the clearance of injected biocompatible dye is monitored with a small photodetector. Fig. 8 shows the in vivo fluorescence detection apparatus developed for continuous monitoring of organ functions [147,148]. 

The INEPT (Insensitive Nuclei Enhanced by Polarization Transfer) experiment [6, 7] was the first broadband pulsed experiment for polarization transfer between heteronuclei, and has been extensively used for sensitivity enhancement and for spectral editing. For spectral editing purposes in carbon-13 NMR, more recent experiments such as DEPT, SEMUT [8] and their various enhancements [9] are usually preferable, but because of its brevity and simplicity INEPT remains the method of choice for many applications in sensitivity enhancement, and as a building block in complex pulse sequences with multiple polarization transfer steps. The potential utility of INEPT in inverse mode experiments, in which polarization is transferred from a low magnetogyric ratio nucleus to protons, was recognized quite early [10]. The principal advantage of polarization transfer over methods such as heteronuclear spin echo difference spectroscopy is the scope it offers for presaturation of the unwanted proton signals, which allows clean spec-... 

Levenson, M. D., and Eesley, G. L. 1979. Polarization selective optical heterodyne detection for dramatically improved sensitivity in laser spectroscopy. Appl. Phys. 19 1-17. Librizzi, R, Viapianni, C., Abbruzzetti, S., and Cordone, L. 2002. Residual water modulates the dynamics of the protein and of the external matrix in trehalose-coated MbCO An infrared and flash-photolysis study. J. Chem. Phys. 116 1193-1200. 

Dramatic improvements in instrumentation (lasers, detectors, optics, computers, and so on) have during recent years raised the Raman spectroscopy technique to a level where it can be used for species specific quantitative chemical analysis. Although not as sensitive as, for example IR absorption, the Raman technique has the advantage that it can directly measure samples inside ampoules and other kinds of closed vials because of the transparency of many window materials. Furthermore, with the use of polarization techniques, one can derive molecular information that cannot be obtained from IR spectra. Good starting references dealing with Raman spectroscopy instruments and lasers are perhaps [34-38]. 

An alternative experiment that measures the same vibrational fundamentals subject to different selection rules is Raman spectroscopy. Raman intensities, however, are more difficult to compute than IR intensities, as a mixed third derivative is required to approximate the change in the molecular polarizability with respect to the vibration that is measured by the experiment. The sensitivity of Raman intensities to basis set and correlation is even larger than it is for IR intensities. However, Halls, Velkovski, and Schlegel (2001) have reported good results from use of the large polarized valence-triple-f basis set of Sadlej (1992) and... 

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