Critical signal-to-noise ratio

Flaws under this dimension will be under the critical signal-to-noise ratio of 2 1 for a given film system class and for instance for the borderline film of class C5 a flaw must be already -21 % deeper for perception than for the film of class C4. 

But the main advantage of the SNR concept in modern analytical chemistry is the fact that the signal function is recorded continuously and, therefore, a large number of both background and signal values is available. As shown in Fig. 7.9, the principles of the evaluation of discrete and continuous measurement values are somewhat different. The basic measure for the estimation of the limit of detection is the confidence interval of the blank. It can be calculated from Eq. (7.52). For n = 10 measurements of both blank and signal values and a risk of error of a = 0.05 one obtains a critical signal-to-noise ratio (S/N)c = fo.95,9 = 1.83 and a = 0.01 (S/N)c = t0.99,9 = 2.82. The common value (S/N)c = 3 corresponds to a risk of error a = 0.05... 0.02 in case of a small number of measurements (n = 2... 5). When n > 6, a... 

The detectability of critical defects with CT depends on the final image quality and the skill of the operator, see figure 2. The basic concepts of image quality are resolution, contrast, and noise. Image quality are generally described by the signal-to-noise ratio SNR), the modulation transfer function (MTF) and the noise power spectrum (NFS). SNR is the quotient of a signal and its variance, MTF describes the contrast as a function of spatial frequency and NFS in turn describes the noise power at various spatial frequencies [1, 3]. 

Fig.5 shows the noise influence on CCF for both types of pulses and different b values. This influence is weak, especially for q(t) type of signals. For s(t) signals growth of 2-factor critically increases the signal to noise ratio. For q(t) signals this effect is much weaker and depends on quantity of periods in pulses. 

However unlike H which is the most abundant of the hydrogen isotopes (99 985%) only 1 1% of the carbon atoms m a sample are Moreover the intensity of the signal produced by nuclei is far weaker than the signal produced by the same number of H nuclei In order for NMR to be a useful technique in structure deter mination a vast increase in the signal to noise ratio is required Pulsed FT NMR pro vides for this and its development was the critical breakthrough that led to NMR becoming the routine tool that it is today... 

Heteronuclear-shift-correlation spectra, which are usually presented in the absolute-value mode, normally contain long dispersive tails that are suppressed by applying a Gaussian or sine-bell function in the F domain. In the El dimension, the choice of a weighting function is less critical. If a better signal-to-noise ratio is wanted, then an exponential broadening multiplication may be employed. If better resolution is needed, then a resolution-enhancing function can be used. 

The relatively small mass differences for most of the elements discussed in this volume requires very high-precision analytical methods, and these are reviewed in Chapter 4 by Albarede and Beard (2004), where it is shown that precisions of 0.05 to 0.2 per mil (%o) are attainable for many isotopic systems. Isotopic analysis may be done using a variety of mass spectrometers, including so-called gas source and solid source mass spectrometers (also referred to as isotope ratio and thermal ionization mass spectrometers, respectively), and, importantly, MC-ICP-MS. Future advancements in instrumentation will include improvement in in situ isotopic analyses using ion microprobes (secondary ion mass spectrometry). Even a small increase in precision is likely to be critical for isotopic analysis of the intermediate- to high-mass elements where, for example, an increase in precision from 0.2 to 0.05%o could result in an increase in signal to noise ratio from 10 to 40. 

There is also a lot of criticism on Taguchi s method, especially with respect to the data analysis part. Some of this criticism focuses on the use of Taguchi s quality criteria the signal-to-noise ratios [15]. A good example of the drawback of these signal-to-noise ratios is given in Chapter 6. 

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