Gaussian absorption line

Figure 2.5 Typical (gaussian) absorption line showing a HWHM (half width at half maximum) of Av and a Lamb dip (dashed curve)...

FIGURE 4.4 Line shapes. Lorentzian (broken lines) and Gaussian (solid lines) line shapes and their first derivatives are given. The outermost vertical lines delimit full width at half height (FWHH) of the absorption lines. 

Let us establish the required relationships more precisely. Consider a narrow idealized rectangular absorption line AT(x) = rect(x/2 AxL) having half-width AxL and centered at x = 0. Its variance is easily found to be <7l = (2 Axl/3)2. Its area is 2 AxL. Now, let us assume that this line is being used to measure an instrument response function exp( —x2/2cr2) that has Gaussian shape and variance ... 

Figures 5-11 illustrate the restoration process in the presence of a drifting base line. These data are methane absorption lines taken with a four-pass Littrow-type diffraction grating spectrometer. For these data 2048 data points were taken. The impulse response function was approximated by a gaussian. The true width of these lines is approximately 0.02 cm-1.

The system used for amplification and detection of an ESR signal is such that the first derivative of the absorption line is recorded. The shape of an ESR line in solution is usually Lorentzian [Equation (3.86)]. The Lorentzian shape resembles a Gaussian (except that it falls off more slowly). Differentiation of the Gaussian shape (3.89) gives — 2cd(v — v0)exp[-d(v - v0)2], which has the form of the u=l harmonic-oscillator function [(1.133) and (1.137)] with x — y v0. Thus the first-derivative of an absorption resembles Fig. 1.1b with the origin at v0. (See also Problem 8.22.)... 

For an intermediate value of rc the absorption spectrum takes a certain form between the Lorentzian and Gaussian. Thus, the value of tc deckles the spectrum for substances. It is to be noted here that if tc becomes smaller than about 10 s sec the spectrum generally becomes so narrow that a pronounced narrowing of the absorption line is abruptly observed. 

Gaussian Laser Profile-Voigt Atom Profile. This case turns out to be a better approximation of our experimental situation, i.e., the laser FWHM is fairly broad compared to the absorption line width and the absorption profile of atoms in an atmospheric combustion flame is described by a Voigt profile. Here the laser is assumed to have a Gaussian spectral profile as well as a Gaussian atomic absorption profile. In this case, convolution of two Gaussian functions is still a Gaussian function. Evaluation of the ratio n2/nT, and the fluorescence radiance. Bp, allows determination of the half width of the fluorescence excitation profile, 6X... 

The resonant absorption lines of Fig. 20 are well described by a Gaussian distribution... 

Fig. 1 Top Behavior of the electronic linear chiroptical response in the vicinity of an excitation frequency. Re = real part (e.g., molar rotation [< ]), Im = imaginary part (e.g., molar ellipticity [0]). Without absorption line broadening, the imaginary part is a line-spectrum (5-functions) with corresponding singularities in the real part at coex. A broadened imaginary part is accompanied by a nonsingular anomalous OR dispersion (real part). A Gaussian broadening was used for this figure [37]. Bottom Several excitations. Electronic absorptions shown as a circular dichroism spectrum with well separated bands. The molar rotation exhibits regions of anomalous dispersion in the vicinity of the excitations [34, 36, 37]. See text for further details...

Figure 1 Experimental and simulated EPR spectra of oxidized CooA at pH 7.4. Experimental conditions temperature, 2 K microwave frequency, 35.106GHz microwave power, 20p,W 100 kHz field modulation amplitude, 0.4 mT time constant, 128 ms scan time, 4 min. Lower traces, in absorption line-shape (due to rapid-passage conditions), are the experimental spectrum (blue) and a digital integration of the simulated spectrum (red). Upper traces in first-derivative lineshape are a digital derivative of the experimental spectrum (blue) and the simulated spectrum (red). Simulation parameters component (a) g = [2.60, 2.268, 1.85], (b) g = [2.47, 2.268, 1.90] Gaussian single-crystal linewidths (half-width at half-maximum) W = [500, 200, 400] MHz. Simulated spectra for (a) and (b) are added in the ratio 2 1 to give the summed spectrum shown...

Fig. 35. Characteristic line shape for a) Lorentzian and b) Gaussian absorption curve, together with functions for absorption and first derivative curves...

In Figures 3.3-S.7 we plot the absorption line shapes as a function of the detuning from the Ei — Eg resonance at different times in the history of the Gaussian pulse linking Eo) to IE2), with f = 0 being the pulse maximum. The Eo) and IE2) states are coupled nonradiatively to some continuum channels representing the P space. 

Spectrally, the gaussian source is a blackbody with a brightness temperature of lOOK and an emission line at 60cm . The point source corresponds to a blackbody at 2000 K, and the elliptical source is a blackbody at 50 K and an absorption line at 80cm . The spectra of the three sources is shown in Fig. 5.2 (right). 

The spectral results of the simulation are shown in Fig. 5.7 (left) for the central pixel of the gaussian source (blue), the point source (green) and the central pixel of the elliptical source (red). It can be observed that the emission and absorption line positions are detected but present a sine-shape this is due to the boxcar function... 

Three different sources are available point source, gaussian source and elliptical source. The common parameters are x pos and y pos (in arcseconds), the temperature (in Kelvins), the cut-on and cut-off wavenumbers, the emission wavenumber (to place an emission line across the spectrum) and the absorption wavenumber (to place an absorption line across the spectrum). The specific parameters are ... 

The half-width Av can be evaluated if the absorption line profile is assumed to be triangular. Since a line profile is a Gaussian distribution, this becomes a good approximation. Under these conditions, the relation... 

Fig. 3.19a,b. Transition probability J (co) of an atom traversing a laser beam (a) with a rectangular intensity profile /(jc) and (b) with a Gaussian intensity profile for the case y< /T = vld. The intensity profile I((o) of an absorption line is proportional to P(co)... 

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