Synchronous correlation intensity

The synchronous correlation intensity, (vi, V2), characterizes the degree of coherence between two signals that are measured simultaneously and is maximized when the variations of the two dynamic infrared dichroism signals are totally in phase with each other and minimized when the two signals are out of phase. Conversely, the asynchronous correlation intensity (vi, V2) characterizes the degree of coherence between two signals that are measured at two different instants that are separated in time by a correlation time x/2co. Thus, the maximum value of... 

Figure 10.2 Bidimensional correlation maps corresponding to changes in intensity of a band composed of one (bottom) or two peaks (top). Synchronous maps are located at the left and asynchromous to the right. The x- and y-axes correspond to the numbers of the point on the artificial curve and the z-axis is the correlational intensity. Roughly they represent a protein amide I band in a DjO buffer. Negative peaks are shaded...

The real and imaginary components, 3>(t i, V2) and F(vi, V2), of the cross-correlation function X(t) are referred to, respectively, as the synchronous and asynchronous correlation intensity. These quantities are related to the in-phase and quadrature spectra of dynamic dichroism by... 

Figure 1-10. A schematic contour diagram of a synchronous 2D IR correlation spectrum 31. Shaded areas represent negative correlation intensity.

The correlation intensity at the diagonal position of a synchronous 2D spectrum (Figure 1-10) corresponds to the autocorrelation function of perturbation-induced... 

Figure 1-14. A synchronous 2D IR spectrum of a thin film of atactic polystyrene in the CH-stretching vibration region at room temperature. Regular one-dimensional spectra of the same system are provided at the top and left of the 2D spectrum for reference. Shaded areas represent negative correlation intensity.

They are respectively referred to as the synchronous and asynchronous 2D infrared spectra. The synchronous spectrum characterizes the degree of coherence between the dynamic fluctuations of signals measured at two wavenumbers, and the correlation intensity becomes significant only if the reorientation rates of dipole transition moments are similar to each other. The asynchronous spectrum, however, characterizes the independent, uncoordinated out-of-phase fluctuations of the signals. Hence the asynchronous correlation intensity becomes non-vanishing only if the signals vary at difierent rates. 

The synchronous and asynchronous (i.e. quadrature) correlation intensities, V2) and (vi,V2), of the dynamic spectrum are given by... 

Figure 21.1 Schematic illustrations of (a) synchronous and (b) asynchronous 2D correlation spectra. White and gray areas in the contour maps represent positive and negative correlation intensities, respectively.

The explicit analytical expressions given by Equations (FI 6) and (F24), obtained for the synchronous and asynchronous spectrum, are well suited for the efficient machine computation of correlation intensities from discretely sampled and digitized spectral data. If a discretely sampled dynamic spectrum y(v -, t,) with the total of n points of wavenumber Vj is obtained for m times at each point of time tj, with a constant time increment, that is, t,+i - t, i = At, the integrations in Equations (FI6) and (F24) ean be replaced with summations. 

To extraa more information from the spearal data, 2D-COS can be employed. Basically, this analysis method ae-ates a pair of synchronous (vj,v2) and asynchronous F(vi,V2) 2D correlation spectra, where the spectral variables vi and V2 are wavenumbers. The synchronous 2D correlation intensity (vi,V2) represents the overall similarity or coincidental changes between two separate intensity variations measured at different spectral variables during variation of the external perturbation. The as3mchronous 2D correlation intensity 1 (vi,V2) may be regarded as a measure of dissimilarity or more strictly speaking, out-of-phase charaaer of the spectral intensity variations. 

Synchronous 2D correlation spectra represent coupled or related changes of spectral intensities, while asynchronous correlation spectra represent independent or separate variations [1007]. The 2D cross-correlation analysis enhances similarities and differences of the variations of individual spectral intensities, providing spectral information not readily accessible from ID spectra. 

Figure 16.39. Data showing correlation among fluorescence methods to determine humification degree of HA. A4AX is the humification index proposed by Zsolnay et al. (1999) it is calculated through the ratio between areas of the upper quarter of emission spectra (435-480nm) and the lower quarter (30( M45 nm) when excitation is made at 240nm. Iv is the humification index proposed by Kalbitz et al. (1999) it is calculated through the ratio of peak intensities in 465 and 399 nm measured in fluorescence synchronous-scan excitation spectra. A46S is the humification index proposed by Milori et al. (2002) it is calculated by fluorescence area of emission spectra when the excitation is made at 465 nm.

The functions, and ij/, are called the synchronous and asynchronous 2D intensity correlation functions, respectively. These functions represent the overall similarity and dissimilarity, respectively, between two intensity variations at vi and V2 caused by changing the magnitude of the perturbation. The results are plotted on two orthogonal axes (vi and V2) with the spectral intensity plotted on the third axis normal to the 2D spectral plane. Figures 3-31A and 3-3 IB illustrate schematic contour maps of a synchronous and an asynchronous 2D correlation spectrum, respectively, where + and - signs indicate the directions of the contour peaks relative to the 2D spectral plane. 

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