SNR, Signal-to-Noise Ratio

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]. 

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. 

In fig. 2 an ideal profile across a pipe is simulated. The unsharpness of the exposure rounds the edges. To detect these edges normally a differentiation is used. Edges are extrema in the second derivative. But a twofold numerical differentiation reduces the signal to noise ratio (SNR) of experimental data considerably. To avoid this a special filter procedure is used as known from Computerised Tomography (CT) /4/. This filter based on Fast Fourier transforms (1 dimensional FFT s) calculates a function like a second derivative based on the first derivative of the profile P (r) ... 

Materials for MO Media. The materials classes best suited for MO media are RE-TM alloys, Co/Pt multilayers, and ferrites. The quality of disks is mainly characterised by the signal-to-noise ratio (SNR). 

Fig. 16. Maximum achievable signal-to-noise ratio (SNR) on read-out of different writable optical data storage systems as a function of the writing energy (laser power) (121). SQS = Organic dye system (WORM) PC = phase change system (TeSeSb) MO = magnetooptical system (GbTbFe). See text.

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... 

Figure 2b and Eq. (10) show that the Wiener inverse-filter is close to the direct inverse-hlter for frequencies of high signal-to-noise ratio (SNR), but is strongly attenuated where the SNR is poor ... 

Fig. 3.25 Left signal-to-noise ratio (SNR) of the Mbssbauer spectra of a basalt taken with MIMOS II (full SI-PIN detector system black data-points) and MIMOS IIA (1/4 of full SDD system red data-points) respectively. Right XRF spectra of low Z elements measured with MIMOS IIA (SDDs) at —20°C. The Compton scattered 14.4 keV line (at 13.8 keV) and the resonant 14.4 keV Mossbauer line are well separated...

The most fundamental aspect of a sensitivity discussion of remote detection is the fact that it is inherently a point-by-point technique. Each spectrum recorded by the detector does not contain any information other than its amplitude. Conceptually, a remote NMR experiment is very similar to a 2D NMR experiment with a z filter between encoding and detection, which causes all transverse magnetization to dephase. For 2D NMR experiments, it has been shown that the signal-to-noise ratio (SNR) per square root time, which will be denominated as sensitivity in the following, is the same as in the ID case when neglecting T2 relaxation [20, 21]. To compare the sensitivity of a remotely detected spectrum [Figure 2.6.4(b)] with an equivalent experiment with direct detection [Figure 2.6.4(a)], we can use an expression similar to the discussion in Ref. [20] ... 

The diffusion time to is the evolution time for the encoded magnetization pattern, and its useful range is ultimately limited by Ti and the signal-to-noise ratio (SNR). For experiments with water at room temperature, tD can often be as long as several seconds, probing pore sizes of up to several hundreds of microns. 

As shown above, limits can be estimated on two ways from blanks and from cabbration data. Modern analytical methods such as spectrometry and chromatography use a third way to an increasing extent the estimation of detection limit by means of the signal-to-noise ratio SNR. 

It is intuitively obvious that this phenomenon should also exist in systems having steady states (e.g., in a system described by quartic potential that has been intensively studied in the context of stochastic resonance), but it is more natural to investigate the resonant properties of signal-to-noise ratio (SNR) in those cases [113]. 

Another important point in the design of a detector is the signal to noise ratio (snr). It was shown, that electrode noise is proportional to the electrode area. 

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