Spectral widths

When the operator suspects the presence of an aliased signal, the testing procedure for such aliasing also depends on the type of quadrature detection being used. For either type of quadrature phase detection system, the sw parameter can be significantly increased. The position of the putative aliased resonance then changes in relation to the rest of the signals. 

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Pump-probe absorption experiments on the femtosecond time scale generally fall into two effective types, depending on the duration and spectral width of the pump pulse. If tlie pump spectrum is significantly narrower in width than the electronic absorption line shape, transient hole-burning spectroscopy [101. 102. 103. 104. 105. 106. 107. 108. 109. 110. 111. 112 and 113] can be perfomied. The second type of experiment, dynamic absorption spectroscopy [57, 114. 115. 116. 117. 118. 119. 120. 121 and 122], can be perfomied if the pump and probe pulses are short compared to tlie period of the vibrational modes that are coupled to the electronic transition. 

One variation in dye laser constmction is the ring dye laser. The laser cavity is a reentrant system, so that the laser light can circulate in a closed loop. The ring stmcture provides a high degree of stabiUty and a narrow spectral width. The spectral width of a conventional dye laser on the order of 40 GH2 is narrowed to a value as small as a few MH2. Such systems offer very high resolution in spectroscopic appHcations. 

Finally, instmmental broadening results from resolution limitations of the equipment. Resolution is often expressed as resolving power, v/Av, where Av is the probe linewidth or instmmental bandpass at frequency V. Unless Av is significantly smaller than the spectral width of the transition, the observed line is broadened, and its shape is the convolution of the instrumental line shape (apparatus function) and the tme transition profile. 

Fig. 3.4. The isotropic Q-branch width (a) and rotational shift (b) calculated in the models of strong (1) and weak (2) collisions as a function of r E = ojqte and T = 1/tj correspondingly. The straight lines are perturbation theory estimates of spectral width and shift...

Consider the dependence of the spectral width on the dimensionless parameter T, which in the framework of impact theory linearly increases with increase in density. Then, according to the theory expounded in the preceding section, the extremum is at the point... 

Q-branch rotational structure 179-82 spectra of nitrogen in argon 180 spectral collapse theory 150 spectral width 107 strong collision model 188 cumulant expansions 85-91... 

Experiments on the sky. Two experiments have been carried out at the sky, using two laser installations built for the American and French programmes for Uranium isotope separation, respectively AVLIS at the Lawrence Livermore Nat l Lab (California) in 1996 and SILVA at CEA/Pierrelatte (Southern France) in 1999. The average power was high pa 2 x 175 W, with a pulse repetition rate of 12.9 and 4.3 kHz, a pulse width of 40 ns and a spectral width of 1 and 3 GHz. Polarization was linear. The return flux was < 5 10 photons/m /s (Foy et al., 2000). Thus incoherent two-photon resonant absorption works, with a behavior consistent with models. But we do need lower powers at observatories ... 

Figure 22. Returned flux at 330 nm as a function of the power balance between the two beams at 589 nm and 569 nm. Circles spectral width at L>2 = 1 GHz. Squares spectral width at L>2 = 3 GHz. Filled symbols pulse repetition rate = 4.3 kHz open symbols rep rate= 12.9 kHz.

In the example given in the preceding secdon, the number of words of data storage was 15,000 and the spectral width was 7500 Hz, so an acquisition time of 15,000/(2 X 7500) = 1.0 s was required after each pulse. 

The resoludon is controlled not only by such factors as field homogeneity and intrinsic nature of the compound (such as the presence of exchange or restricted rotadon), but also by the sampling rate. With a spectral width of 7500 Hz on a 500-MHz instrument, the sampling rate was 1/(2(7500)) s, i.e., 0.066 ms. An acquisition dme of 1.0 s requires 1.0 s/0.066 ms s 15,000 data points of computer memory. 

A poor digital resolution will result in loss of some of the fine structure of an NMR signal. To increase the digital resolution, we need either to maintain the same number of data points but reduce the spectral width or, alternatively, to maintain the spectral width but increase the number of data points. Which method would you prefer for achieving a better signal-to-noise ratio ... 

If the spectral width is inadequate to cover every peak in the spectrum, then some peaks in the downfield or upfield region may fold over and appear superimposed on the spectrum. How can you identify these folded signals ... 

Figure 1.30 (a) Normal NMR spectrum resulting from the correct selection of spectral width, (b) When the spectral width is too small, the peaks lying outside the spectral width can fold over. Thus a and b represent artifact peaks caused by the fold-over of the a and b signals. 

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