On the Signal-to-Noise Ratio

Sandborg, M. and G. Alm-Carlsson, Influence of x-ray energy spectrum, contrasting detail and detector on the signal-to-noise ratio (SNR) and detective quantum efficiency (DQE) in projection radiography. Phys. Med. Biol., 1992. 37(6) p. 1245-1263. 

The locations of the maxima of the -field and the E-field are different depending on the mode chosen for the EPR experuuent. It is desirable to design the cavity in such a way that the B field is perpendicular to the external field B, as required by the nature of the resonance condition. Ideally, the sample is located at a position of maxuuum B, because below saturation the signal-to-noise ratio is proportional to Simultaneously, the sample should be placed at a position where the E-field is a minimum in order to minimize dielectric power losses which have a detrimental effect on the signal-to-noise ratio. 

Adaptive optics requires a reference source to measure the phase error distribution over the whole telescope pupil, in order to properly control DMs. The sampling of phase measurements depends on the coherence length tq of the wavefront and of its coherence time tq. Both vary with the wavelength A as A / (see Ch. 1). Of course the residual error in the correction of the incoming wavefront depends on the signal to noise ratio of the phase measurements, and in particular of the photon noise, i.e. of the flux from the reference. This residual error in the phase results in the Strehl ratio following S = exp —a ). 

Myopic deconvolution has enough flexibility to account for different cases depending on the signal-to-noise ratio of the measurements ... 

The next step is to determine the practical detection limit (pDL) based on the signal-to-noise ratio at the lowest level at which the analyst can get the HPLC system to function reproducibly on injections of a standard at a known concentration (S/N ratio of 3 1 is a rule of thumb). Then the practical quantitation limit (pQL) is determined usually at a level 2-5 times the pDL and the repeatability of the standard at this level is determined. This pQL usually results in analyte concentrations of nanograms or micrograms per milliliter. The repeatability of a 1.0 pg/mL clarithromycin standard preparation is shown in Table 2. ... 

Figure 7 demonstrates the effects of window functions on the signal to noise ratio of the 5r,r spectrum (for D-HMBC) and 5r,i spectrum. 5r,r spectra shown in fig. 7(c) revealed marked decrease of -noise in the range between 0.8 to 1.1 ppm. Processing of S r r spectral data, however, requires somewhat tedious phase adjustment of the Fi spectrum. In order to achieve this easily, it is recommended to take a ID-NMR spectrum at first under... 

Later, in Chapter 8, we will discuss power and sample size and see how to choose sample size in order to meet our objectives. We will also see in Section 3.3 how, in many circumstances, the calculation of the p-value is directly based on the signal-to-noise ratio. 

Again the test will be based on the signal-to-noise ratio. In this case the signal is the observed mean x of the column of differences while the noise is the standard error associated with that mean. For these data ... 

Switch to the subroutine and the phase program and start the experiment. The number of scans and shots per point depend on the signal-to-noise ratio. After the experiment is finished store the time trace. 

Reproducibility of the results depends strongly on the signal-to-noise ratio achieved. Therefore, whenever polarization transfer can give some sensitivity enhancement, use of INEPT (or other scheme) for T measurement would increase the precision and save experimental time. It is also possible to measure the relaxation times indirectly through measurements of 29Si satellites in 3H NMR spectra355, but application of the INEPT variant of such measurements is much more straightforward. 

As we continue to reduce the B0 field, moving the Sa position even closer to the 5b position, the two inner lines become very close to each other, but they never meet or cross. The outer lines become so weak that they may appear as tiny bumps, or they may disappear into the noise, depending on the signal-to-noise ratio of the spectrum. At this point of... 

To reach a limit on the value of qu of the order of 10-21 x qe (i.e. the existing limit on qn limit), we must be able to measure a phase shift Amin as small as 3.8 x 10-4 rad. The smallest measurable phase shift depends on the signal-to-noise ratio r of the interferometer. If C is the contrast of the signal, N the number of atoms detected per second, t the duration of the measurement and if we observe the linear part of the interference pattern, then... 

The limit of detection and the precision of quantitative analyses depend on the signal-to-noise ratio of the recorded spectra. The purpose of the optimization of a spectrochem-ical procedure is to increase the signal-to-noise ratio. This is discussed in the following section. 

The optical activity of vibrational transitions has been conducted. The infrared (IR) bands of a small molecule can easily be assigned with the performance of a normal coordinate analysis, and these can usually be well resolved. One of the problems associated with vibrational optical activity is the weakness of the effect. Instrumental limitations of infrared sources and detectors create additional experimental constraints on the signal-to-noise ratios. 

Figure 85. Plot of fractional saturation of the CD signal against (—)-a-pinene concentration for the oligomers 30 ( ) 31 ( ) 32 ( ). The CD signal at saturation, Ac, was obtained from nonlinear least-squares fitting of Ae vs (—)-a-pinene concentration using a 1 1 binding model. The lines are the nonlinear fits of the data to the 1 1 binding model. Error bars are based on the signal-to-noise ratio of the CD spectra. All measurement were recorded in a mixed solvent of 40 volume percent water in acetonitrile (by volume) at 295 K. [oligomer] = 4.2 fiM.

EDS offers two modes of examination stationary and scanning. In the stationary mode, the probe stays at one location until the collection of X-ray photons is complete. The dwell time of the probe for EDS analysis is determined by the number of X-ray photon counts received by the detector. Elemental detection relies on the signal-to-noise ratio. As discussed in Chapter 4, the... 

The peak deconvolution presented in Fig, 4.27(B) is not unique, i.e. another set of components or other equations of adsorption isotherm than Langmuir can produce very similar spectra. The significance of the peak deconvolution depends on the signal to noise ratio, which is a serious problem in the IR method. 

Fig. 4.9 Illustration ofthe effect of the time spent acquiring the FID on the signal-to-noise ratio (SNR) in the spectrum. In (a) the FID has decayed to next to nothing within the first quarter ofthe time, but the noise carries on unabated for the whole time. Shown in(b) is the effect of halving the time spent acquiring the data the SNR improves significantly. In (c) we see that taking the first quarter ofthe data gives a further improvement in the SNR.

In flow analysis with spectrophotometric detection, the Schlieren effect is generally the ultimate limitation on the signal-to-noise ratio and hence on the detection limit. Furthermore, it can lead to systematic measurement deviations, thus degrading accuracy. 

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