Line profile measurements

For very accurate line profile measurements, a heterodyne technique has been developed 240) which can be briefly explained as follows the light, scattered into a cone within the angle 0 b9 (50< 1 °). is focused onto the cathode of a photomultiplier. The photocurrent is proportional to the square of the incoming light amplitude but cannot follow the rapid light frequency. Any beat frequencies, however, resulting from interference between the... 

An interesting development of the IPDA has recently been reported by Benjamin et al. (22). They use a high gain ( 10 ) MCP combination coupled with a rapid readout of the PDA to allow detection of individual photons. Centroiding of the photon pulse allows spatial resolutions less than the pixel width. Also, a P-46 phosphor is used for fast time response. This system may be quite useful for line profile measurements in the EUV, where low counting rates can be tolerated. 

The contents of Chap. 4, which covers spectroscopic instrumentation and its application to wavelength and intensity measurements, are essential for the experimental realization of laser spectroscopy. Although spectrographs and monochromators, which played a major rule in classical spectroscopy, may be abandoned for many experiments in laser spectroscopy, there are still numerous applications where these instruments are indispensible. Of major importance for laser spectroscopists are the different kinds of interferometers. They are used not only in laser resonators to realize single-mode operation, but also for line-profile measurements of spectral lines and for very precise wavelength measurements. Since the determination of wavelength is a central problem in spectroscopy, a whole section discusses some modern techniques for precise wavelength measurements and their accuracy. 

ToF-SIMS was applied to perform line-profile measurements of the element distribution [26]. The qualitative sputter profile is given in Figure 11.5a. It shows Ga2N, GaO, Cl, and A1 signals as a function of sputter depth and shows an approximately homogenous distribution of impurities in both the HVPE and MOVPE sublayers. The Ga2N and A1 signal slopes mark the GaN-sapphire interface. 

Figire 20 Force (solid line) and absolute current (dashed line) profiles measured simultaneously are a function of vertical piezo displacement for the Pt-coated tip over a FcCuSH SAM. Only approach data are shown. Adapted from Tivanski, A. V. Li, J. K. Walker, G. C. LangrnuirZm, 24, 2288-2293. 25... 

The Voigt line shape closely describes line profiles measured undermost laboratory and atmospheric conditions. 

Figure 4.16. Free-surface velocity profiles measured on 1400° C molybdenum. The free-surface velocity profile is characterized by an 0.05 km/s amplitude elastic precursor, a plastic wave front, and a spall signal (characteristic dip) upon unloading. The dashed lines represent the expected free surface velocity based on impedance-match calculation [Duffy and Ahrens, unpublished].

Figure 3 Optical profiler measurements of a region on the unpolished back of a silicon wafer line scan (a) and 3D display (b) (Courtesy of WYCO Corp.).

FIGURE 20.12 (a) Top part shows variations of elastic modulus profile measured in different locations of the polypropylene (PP)-ethylene-propylene-diene terpolymer (EPDM) blend. The locations are shown by white dots in the blend phase image placed at the bottom. Vertical white dashed lines show the components borders and the elastic modulus value for this location. Vertical black dotted lines indicate the locations where elastic modulus E gradually changes between PP (E ) and EPDM (E )- These values are indicated with black arrows on the E axis, (b) LvP curves for PP-matrix, EPDM-domains, and one of interface locations. The approach curves are seen as solid black lines and the retract curves as gray lines. 

Figure 5.24(B) shows a line profile extracted from the map of Figure 5.24(A) by averaging over 30 pixels parallel to the boundary direction corresponding to an actual distance of about 20 nm. The analytical resolution was 4 nm, and the error bars (95% confidence) were calculated from the total Cu X-ray peak intensities (after background subtraction) associated with each data point in the profile (the error associated with A1 counting statistics was assumed to be negligible). It is clear that these mapping parameters are not suitable for measurement of large numbers of boundaries, since typically only one boundary can be included in the field of view.

The effect of instrumental broadening can be eliminated by deconvolution (see p. 38) of the instrumental profile from the measured spectrum. If deconvolution shall be avoided one can make assumptions on the type19 of both the instrumental profile and of the remnant line profile. In this case the deconvolution can be carried out analytically, and the result is an algebraic relation between the integral breadths of instrumental and ideal peak profile. From such a relation a linearizing plot can be found (e.g., measured peak breadths vs. peak position ) in which the instrumental breadth effect can be eliminated (Sect. 8.2.5.8). 

We now consider in somewhat more detail a simplified approach based on the curve of growth . For this, we ignore fine details of the observed line profile and use the equivalent width (EW) defined in Fig. 3.4, WA = f RdX or Wv = f Rdv, where R(AX) or R(Av) is the relative depression below the continuum at some part of the line. The curve of growth is a relationship between the equivalent width of a line and some measure of the effective number of absorbing atoms. Equivalent... 

Measurement of integrated absorption requires a knowledge of the absorption line profile. At 2000-3000 K, the overall line width is about 10-2 nm which is extremely narrow when compared to absorption bands observed for samples in solution. This is to be expected, since changes in molecular electronic energy are accompanied by rotational and vibrational changes, and in solution collisions with solvent molecules cause the individual bands to coalesce to form band-envelopes (p. 365). The overall width of an atomic absorption line is determined by ... 

The error in this estimate compared to the equatorial value of GM/Rc2 is always less than 4% for a spin frequency v < 600 Hz (Bhattacharyya et al. 2003). Bhattacharyya et al. (2003) also find that future high-precision measurements could detect a signature of frame-dragging if there are two horns in the line profile. The ratio of the depth of the low energy (red) horn to the depth of the high energy (blue) horn increases quickly with the increase of a/M, but it either decreases or slowly increases with the increase of other parameters. Hence a precise measurement of a line profile could demonstrate the existence of frame-dragging. 

Table 13.3 Draw-resonance ratio measured under specific experimental conditions0 for the three polymers shown in Table 13.1 [13]. From Some effects of the rheological properties of PET on spinning line profile and structure developed in high-speed spinning , Perez, G., in High-Speed Fiber Spinning, Ziabicki, A. and Kawai, H. (Eds), 1985, pp. 333-362, copyright (1985 John Wiley Sons, Inc.). Reprinted by permission of John Wiley Sons, Inc.

Section IV explains a new approach to high resolution spectroscopy based on various kinds of saturation effects. Some of the experiments are performed inside the laser resonator, which implies the presence of coupling phenomena between the absorbing molecules under investigation and the laser oscillation itself. These feedback effects can be used for high-precision frequency stabilization and to measure frequency shifts and line profiles with an accuracy never... 

Several other laser lines have already been used in a similar way 2-90) to measure absorption coefficients and absolute wavelengths of absorption lines, as well as the line profiles and possible fine structures of many polyatomic molecules. By substituting different isotopes, the isotopic shift of absorption lines has been studied Table 2 shows some of the molecules investigated by the laser line absorption technique, together with the exciting laser wavelengths and some remarks about the kind of measurements performed. 

Uncompetitive inhibitors can bind to the enzyme-substrate complex only, but not to the free enzyme molecule. The Lineweaver-Burk plots in such cases give parallel straight lines for activity-substrate concentration profiles, measured at different concentrations of the inhibitor (Figure 8.4), according to equation ... 

---