Absorption component spectra

Figure 6.10 Absorption component spectra (left panels) and total shape spectra (right panels) reconstructed by the FPT for normal breast as per in vitro MRS data from Ref. [31].

Figure 6.16 Converged absorption component spectra (left panels) and total shape spectra (right panels) as reconstructed by the FPT at Np = 1500. The upper panels (i) and (iv) correspond to normal breast tissue, the middle panels (ii) and (v) to fibroadenoma and the lower panels (iii) and (vi) to malignant breast, derived from in vitro data in Ref [31].

Figure 6.21 Absorption component spectra for normal stromal prostate as reconstructed by the FPT at Np = 54 (top panel (i)) and Np = 800 (bottom panel (ii)), based on in vitro MRS data from Ref. [54].

Figure 4.1 Time and frequency domain data in signal processing in the noiseless case using the fast Fourier transform (FFT) and fast Pad6 transform (FPT). Top panel (i) the input FID (to avoid clutter, only the real part of the time signal is shown). Middle panel (ii) absorption total shape spectrum (FFT). Bottom panel (iii) absorption component (lower curves FPT) and total (upper curve FPT) shape spectra. Panels (ii) and (iii) are generated using both the real and imaginary parts of the FID.

Absorption Component Shape Spectra Absorption Total Shape Spectrum... 

Figure 4.8 Absorption component shape spectra (left) and absorption total shape spectra (right) from the FPTf 1 near full convergence for signal lengths Np = 180,220,260. On panel (iv) for Np = 180, the total shape spectrum reached full convergence, despite the fact that on panel (i) for the corresponding component shape spectra, the 11th peak is missing and the 12th peak is overestimated.

FIGURE 14. (Reproduced from Ellison 2000). Portion of the Lya forest between zabs = 3.277 and 3.607 in the Keck spectrum of Q1422+231 shown in Figure 13. There are more than 50 individual absorption components in each 100 A-wide stretch of spectrum. 

We present the absorption component shape spectra and the total shape spectra as reconstructed by the FPT for the normal breast data in Figure 6.10 at three partial signal lengths Np = 1000,1500, and 2000. The top right panel (iv) indicates that at Np = 1000, the absorption total shape spectrum has converged. In contrast, for the component shape spectrum (top left panel (i)), there is only one peak (phosphoethanolamine. A = 5) at 3.22 ppm that has been overestimated, whereas phosphocholine, (A = 4) has not been detected. 

FADE COMPONENT SHAPE SPECTRA (Left), TOTAL SHAPE SPECTRA (Right) PARTIAL SIGNAL LENGTHS Np = 1000,1500, 2000 Absorption Component Shape Spectra Absorption Total Shape Spectrum... 

The Pad6-reconstructed absorption component shape spectra for the normal glandular prostate are shown in Figure 6.18 at Np = 54 and Np = 800. The upper panel reveals that at Np = 54, only 12 of fhe 27 resonances were resolved. These correctly resolved peaks were mainly at the two extremes of the spectrum (lactate and alanine at 1.33 and 1.49 ppm and myoinositol... 

The converged absorption component shape spectrum (top panel (i)) and total absorption shape spectrum (lower panel (ii)) for prosfafe cancer between 2.40 and 3.70 ppm at Np = 800 are compared in Figure 6.26. Strikingly, the serrated peaks on the total shape spectrum only suggest the number of underlying resonances. The converged componenf specfrum is essential to visualize the actual number and structure of resonances. For example, from the small polyamine peaks, it would be difficult to know that there are actually two components. 

In Fig. 10, we plot the absorption rate Wn as a function of 8 for p 0.95 and different ft. When ft / 2A the absorption rate exhibits the familar Mollow absorption spectrum [38] with small dispersive structures at 8 = fl The absorption rate changes dramatically when ft = 2A. Here, the dominant features of the rate are emissive and absorptive components at 8 = ft, indicating that at 8 = —ft the weaker field is absorbed, whereas at 8 = ft is amplified at the expense of the strong field. The weaker field is always absorbed (amplified) at 8 = —ft (8 = ft) independent of the ratio r = Ti/I between the spontaneous emission rates 14 and 14. We illustrate this in Fig. 11, where we plot the absorptive rate for different values of r. The absorptive (emissive) peak remains absorptive (emissive) independent of the ratio r. 

Since the absorption component of the FM signal is recorded as a derivative spectrum, a method for extraction of the Doppler profiles form the FM absorption signal is also needed. North et al. [69] first suggested using a resursive relationship in order to extract this information. In a more recent paper, they settled on a method that expands the FM absorption signal in a Taylor series [67], and then used both intergation and differentiation with respect to dto in order to obtain two solutions, one for <5(cu0),... 

Figure 7. Spectropolarimetry of the lOpm silicate feature [41] (a) upper panel along the line of sight to the source AFGL 2136. The middle-box shows the polarization spectrum is composed of an emissive component (long-dashed line) and an absorptive component (short-dashed line). Note the change in PA of polarization across the feature (right-hand box) (b) lower panel along the line of sight to the source AFGL 2591. Note that a purely absorptive component is sufficient to account for the polarization spectrum. Note also, the feature at 11.2pm attributed to crystalline olivine.

Spectrophotometry [ISV] (1881) n. An analytical instrumental technique for measuring color values by the relative intensity of the component spectrum colors. Broadly, a technique which, by measuring the absorption (or reflection) of electromagnetic... 

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