Measurement of SNR

If there are other sources of noise, SNR, will decrease below the value predirted by the number of interacting quanta so that DQE will fall below tj. From the measurement of SNR it will appear that fewer X-rays have been used to form die image than has actually been die case and DQE is a measure of that apparent lack of efiiciency. In fact, the quantity, SNR which, in the absence of additional noise sources is just the number of X-rays detected, is known as the number of noise-equivalent quanta or NEQ. 

To verify the modelling of the data eolleetion process, calculations of SAT 4, in the entrance window of the XRII was compared to measurements of RNR p oj in stored data as function of tube potential. The images object was a steel cylinder 5-mm) with a glass rod 1-mm) as defect. X-ray spectra were filtered with 0.6-mm copper. Tube current and exposure time were varied so that the signal beside the object. So, was kept constant for all tube potentials. Figure 8 shows measured and simulated SNR oproj, where both point out 100 kV as the tube potential that gives a maximum. Due to overestimation of the noise in calculations the maximum in the simulated values are normalised to the maximum in the measured values. Once the model was verified it was used to calculate optimal choice of filter materials and tube potentials, see figure 9. 

A simple expression for the signal-to-noise ratio (SNR) of a measurement of visibility amplitude involves several parameters relating to interferometer and source properties. The formula presented here provides the fundamental sensitivity limit. Contrast loss arising from instrumental jitter and seeing are summarised in a common factor system Strehl , which is the ratio of the number of photons which can be used for a coherent measurement to the... 

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... 

Figure 12. C02 Detection expected variation of SNR as a function of optical filter centre wavelength and bandwidth, assuming a mean optical power incident on the reference detector of 10 nW nm 1. Reference and measurement cells were assumed to be 1 m long and to contain 100% C02 gas at 1 Bar/20 °C.

Instrument performance must be sufficient to enable the collection of the selective glucose signature in a reliable manner relative to background noise. Ultimately, the SNR of the instrumentation defines the limit of detection for glucose and detailed experimental results are needed to establish the level of SNR that is necessary to measure glucose at clinically relevant concentrations. Tissue phantoms provide an excellent means to establish the relationship between the instrumental SNR and the limit of detection. Instrumentation must then be designed to provide this level of performance for spectral data collected noninvasively from living tissue. 

These devices have proved their capability to actually achieve the theoretical multiplex (SNR) advantage. This makes them very attractive for studies of light phenomena that have ultra-short (/ sec to psec) lifetimes or that involve measurements of very low SNR. 

The improvement in the instrumental SNR afforded by the use of polarization modulation has permitted CD detection to be applied to stopped-flow studies of biological reactions. The important information which can be obtained from such an approach has served as an impetus for the development of new instrumental approaches for the measurement of CD. These new approaches have allowed CD measurements to be extended to the time domain below that available with stopped-flow techniques. Presently, nanosecond, and even picosecond CD techniques have been developed, and it seems clear that extension to the sub-picosecond regime will follow. 

The application of multichannel light detection devices to the measurement of CD will significantly improve the technique and allow extension into areas not presently accessible by conventional, sequentially scanned CD. For example, multichannel devices will enable SNR improvements via spectral averaging. Alternately, a complete CD spectrum can be obtained on a transient species in the time domain required for a single wavelength... 

If the detector is the main source of noise, RB = 2 would be appropriate. If, however, the background is the main source of noise, then it is advisable to use a narrow bandwidth, RB < 1 (Schrader et al., 1981). The best approach to optimizing the conditions consists in measuring the SNR at different spectral bandwidths. Fig. 3.3-17 (Schrader, 1980) illustrates this problem. 

Figure 4.5. Spectra of 0.1 M Na2S04 dominated by background noise from the water and cell. At short measurement time, SNR is too low to permit observation of the S04 Raman band [see Eq. (4.21)].

The expression for Raman signal from Chapter 3 may be combined with Eq. (4.11) to arrive at the dependence of experimental SNR on various sample and measurement variables. SNR is a generally more important indicator of the utility of the measurement than raw signal, since SNR determines the detection limit and overall information content. In addition, SNR may be compared for spectra with quite different intensity units, such as dispersive/CCD and FT-Raman instruments. In the remainder of this chapter, we will derive SNR expressions for several situations, and define a figure of merit for SNR. 

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