Absorption lineshape

Contrary to the point by point approach the diagonalization method consists of the generation of an entire lineshape function in one step. (13, 14, 57-60) Time-consuming calculations are carried out only once. The resulting set of complex numbers can be used for a simple calculation of the lineshape (absorption and dispersion modes) at any desired point on the frequency axis. Thus, the complex matrix from equation (147) can be diagonalized by a similarity transformation using an co-independent complex matrix W ... 

Lee S-Y 1998 Forward and inverse transforms between the absorption lineshape and Raman excitation profiles XVith int. Conf on Raman Spectroscopy ed A M Heyns (New York Wiley) pp 48-51... 

The exponential decay of the A population corresponds to a Lorentzian line shape for the absorption (or emission) cross section, a, as a fiinction of energy E. The lineshape is centred around its maximum at E. The fiill-width at half-maximum (F) is proportional to... 

The Time Dependent Processes Seetion uses time-dependent perturbation theory, eombined with the elassieal eleetrie and magnetie fields that arise due to the interaetion of photons with the nuelei and eleetrons of a moleeule, to derive expressions for the rates of transitions among atomie or moleeular eleetronie, vibrational, and rotational states indueed by photon absorption or emission. Sourees of line broadening and time eorrelation funetion treatments of absorption lineshapes are briefly introdueed. Finally, transitions indueed by eollisions rather than by eleetromagnetie fields are briefly treated to provide an introduetion to the subjeet of theoretieal ehemieal dynamies. 

For all of the eases eonsidered earlier, a C(t) funetion is subjeeted to Fourier transformation to obtain a speetral lineshape funetion I(co), whieh then provides the essential ingredient for eomputing the net rate of photon absorption. In this Fourier transform proeess, the variable co is assumed to be the frequeney of the eleetromagnetie field experienced by the molecules. The above considerations of Doppler shifting then leads one to realize that the correct functional form to use in converting C(t) to I(co) is ... 

It is equivalent, when an ftk spectrometer is used, to re-apodization of the data. Curve fitting is a method of modeling a real absorption band on the assumption that it consists of a series of overlapped peaks having a specific lineshape. Typically the user specifies the number of peaks to attempt to resolve and the type of lineshape. The program then varies the positions, sizes, and widths of the peaks to minimize the difference between the model and the spectmm. The largest difficulty is in knowing the correct number of peaks to resolve. Derivative spectra are often useful in determining the correct number (18,53,54). 

In the case of resonance absorption of synchrotron radiation by an Fe nucleus in a polycrystalline sample, the frequency dependence of the electric field of the forward scattered radiation, R(oj), takes a Lorentzian lineshape. In order to gain information about the time dependence of the transmitted radiation, the expression for R(oj) has to be Fourier-transformed into R(t) [6]. 

An application for multiplexed diode-laser sensors with a potentially large impact is for measurements of important parameters at several locations in a gas turbine combustion system. In this example, illustrated schematically in Fig. 24.1, the multiplexed diode lasers are applied for simultaneous absorption measurements in the inlet, combustion, afterburner, and exhaust regions. For example, measurements of O2 mass flux at the inlet may be determined at the inlet from Doppler-shifted O2 absorption lineshapes near 760 nm. Measurements of gas temperature and H2O concentrations in the combustion and afterburner regions may be determined from H2O lineshape measurements near 1.4 pm. Finally, measurements of velocity, temperature, and species concentrations (e.g., CO, CO2, unburned hydrocarbons) may be recorded in the exhaust for the determination of momentum flux (component of thrust) and combustor emissions. 

One important relationship which has survived from the earliest days of DNMR [1] and which is still used to estimate exchange rates is the relationship between the exchange rate which is the rate that just results in coalescence of the A and B signals into a broad, single, flat-topped absorption. From differentiation of the lineshape equation, it is possible to obtain the simple expression [1]... 

However, when the combination of concentration, N, and path length, /, is not small, the weak-absorber approximation is not valid, and the line-shape needs to be taken into account. The reason for this is that in the limit when absorption of light is already saturated at the center of the line, absorption due to added gas occurs only in the wings of the absorption line, which is sensitive to the lineshape. In the case of saturation at the center of the absorption line as shown in Fig. 14.8c, the absorption can be thought of as occurring in two regions, one from... 

The double quantum filter eliminates or at least suppresses the strong signals from protons that do not experience J-coupling, e.g. the solvent signal, which would otherwise dominate the spectrum and possibly be a source of troublesome tl noise. Compared to a phase-sensitive but non-DQ-filtered COSY with pure absorption lineshapes for the cross peaks but mixed lineshapes for the diagonal peaks, the phase-sensitive, DQ-filtered COSY has pure absoiption lineshapes throughout. 

The cross peaks in the 2D spectrum are a combination of absorption and dispersion lineshapes and consequently spectra are displayed in magnitude mode. 

The basic processing of ID and 2D data requires obligatory processing steps for transforming the raw data (FID) into a "readable spectrum, i.e. Fourier transformation and phase correction to produce a spectrum with absorptive lineshapes. Finally, a few additional step.s (calibration, peak picking, integration) as discussed in chapter 4 are required before the spectrum is eventually plotted. 

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