Band-widths

In practice, only a limited number of views are available the scanned sector is typically 180 or 360°, and the angular increment 2°. Moreover the frequency band-width of the employed pulses is very limited, typically one octave. The resolving power of the system is then limited. A typical numerical signal is composed of 1024 samples at a sampling period of 50 nsec. 

Finally, if one has a condition with incoherent radiation of a small band width Av exciting a broad absorption band with a(v + A ) one finds ... 

In experimental measurements, sueh sharp 5-funetion peaks are, of eourse, not observed. Even when very narrow band width laser light sourees are used (i.e., for whieh g(co) is an extremely narrowly peaked funetion), speetral lines are found to possess finite widths. Let us now diseuss several sourees of line broadening, some of whieh will relate to deviations from the "unhindered" rotational motion model introdueed above. 

Ring-shaped ground, band width b, radius... 

Although the power spectral density contains information about the surface roughness, it is often convenient to describe the surface roughness in terms of a single number or quantity. The most commonly used surface-finish parameter is the root-mean-squared (rms) roughness a. The rms roughness is given in terms of the instrument s band width and modulation transfer function, M(p, q) as... 

Different values of will result if the integral limits (i.e., band width) or modulation transfer function in the integral change. All surface characterization instruments have a band width and modulation transfer function. If rms roughness values for the same surface obtained using different instruments are to be compared, optimally the band widths and modulation transfer functions would be the same they should at least be known. In the case of isotropic surface structure, the spatial frequencies p and q are identical, and a single spatial frequency (/>) or spatial wavelength d= /p) is used to describe the lateral dimension of structure of the sample. 

The modulation transfer function of the optical scatterometer is nearly unity. The spatial frequency band width, using 0.633-nm photons from a He-Ne laser, is typically 0.014—1.6 jim corresponding to a spatial wavelength band width 70— 0.633 pm. This corresponds to near normal sample illumination with a minimum... 

The importance of instrument band width is illustrated by considering the rms roughness of the two samples of Figure 2. If the rms roughness is calculated over the... 

The significance of instrument band width and modulation transfer function was discussed in connection with Equation (3) to characterize the roughness of nominally smooth surfaces. The mechanical (stylus) profilometer has a nonlinear response, and, strictly speaking, has no modulation transfer function because of this. The smallest spatial wavelength which the instrument can resolve, 4nin> given in terms of the stylus radius rand the amplitude aoi the structure as... 

R, D. Jacobson, S. R. Wilson, G. A. Al-Jumaily, J. R, McNeil, and J. M. Bennett. Microstructure Characterization by Angle-Resolved Scatter and Comparison to Measurements Made by Other Techniques. To be published in AppL Opt. This work discusses the band width and modulation transfer function of the scatterometer, stylus profilometer, optical pro-filometer, and total integrated scattering systems, and gives results of mea suring several surhices using all techniques. 

To demonstrate the effect in more detail a series of experiments was carried out similar to that of volume overload, but in this case, the sample mass was increased in small increments. The retention distance of the front and the back of each peak was measured at the nominal points of inflection (0.6065 of the peak height) and the curves relating the retention data produced to the mass of sample added are shown in Figure 7. In Figure 7 the change in retention time with sample load is more obvious the maximum effect was to reduce the retention time of anthracene and the minimum effect was to the overloaded solute itself, benzene. Despite the reduction in retention time, the band width of anthracene is still little effected by the overloaded benzene. There is, however, a significant increase in the width of the naphthalene peak which... 

The results from the overload of the more polar solute are similar to that for the aromatic hydrocarbons, but the effect of the overloaded peak on the other two appears to be somewhat less. It is seen that there is little change in the retention of anisole and acetophenone, although the band width of acetophenone shows a slight increase. The band width of benzyl acetate shows the expected band broadening... 

The general understanding of the electronic structure and the bonding properties of transition-metal silicides is in terms of low-lying Si(3.s) and metal-d silicon-p hybridization. There are two dominant contributions to the bonding in transition-metal compounds, the decrease of the d band width and the covalent hybridization of atomic states. The former is caused by the increase in the distance between the transition-metal atoms due to the insertion of the silicon atoms, which decreases the d band broadening contribution to the stability of the lattice. 

The key elements of database setup discussed in this section are analysis parameter sets, data filters (i.e., band-widths, averaging, and weighting), limits for alerts and alarms, and data-acquisition routes. 

Here, W is a cut-off of the order of the 7t-band width, introduced because the right-hand side of Eq. (3.13) is formally divergent. As in the discrete model, the spectrum of eigenstates of Hct for A(a)= Au has a gap between -Ao and +Alh separating the empty conduction band from the completely filled valence band. 

The quantitative determination of a component in gas chromatography using differential-type detectors of the type previously described is based upon meas urement of the recorded peak area or peak height the latter is more suitable in the case of small peaks, or peaks with narrow band width. In order that these quantities may be related to the amount of solute in the sample two conditions must prevail ... 

It is generally accepted that the maximum increase in band width that can be tolerated due to any extraneous dispersion process is a 5% increase in standard deviation (or a 10% increase in peak variance). 

Part of the absorption spectrum of an aqueous solution of neodymium(iii) -configuration/ - is shown in Fig. 10-4. The situation shown there is quite typical of the whole of the lanthanoid series i.e. we could have chosen any/" configuration equally well to illustrate the main characteristics of the spectra of lanthanoid complexes. We shall focus on three main features splittings, band widths and absolute excitation frequencies. 

Since then, the vibrational spectrum of Ss has been the subject of several studies (Raman [79, 95-100], infrared [101, 102]). However, because of the large number of vibrations in the crystal it is obvious that a full assignment would only be successful if an oriented single-crystal is studied at different polarizations in order to deconvolute the crystal components with respect to their symmetry. Polarized Raman spectra of samples at about 300 K have been reported by Ozin [103] and by Arthur and Mackenzie [104]. In Figs. 2 and 3 examples of polarized Raman and FTIR spectra of a-Ss at room temperature are shown. If the sample is exposed to low temperatures the band-widths can enormously be reduced (from several wavenumbers down to less than 0.1-1 cm ) permitting further improvements in the assignment. 

Figure 2. Two-dimensional representation of Case 1 dwell calculation. The helical wind angle is A and the band width of the roving is B. ...

BAND WIDTH is the width of the roving on the surface of the mandrel. CIRCUMFERENCE is the circumference of the mandrel. 

P 42] Typically, a flow rate of 150 pi min was used [71]. A 0.1 M furan solution containing 0.1 M NaCl04 and 5 mM NaBr was used as reaction medium. Reaction was carried out at room temperature. Interdigitated band electrodes with 100 pm wide gaps and 500 pm band widths were tested in a 800 pm deep Perspex micro reactor. 

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