Dead-Time Effect

Two models of dead-time behavior have been commonly used the paralysable model and the nonparalysable model (Knoll, 1979). Experimental data suggested that the paralysable model is suitable to describe the current detection system (Sun, 1985). For this model, the statistical relationship of the recorded count rate m to the true scintillation rate n is expressed as 

2 Relationship between Tracer Position and Detector Count Rate 

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Not only PMTs and other detectors such as avalanche photodiodes suffer from dead-time effects also the detection electronics may have significant dead-times. Typical dead-times of TCSPC electronics are in the range 125-350 ns. This may seriously impair the efficiency of detection at high count rates. The dead-time effects of the electronics in time-gated single photon detection are usually negligible. 

Time variations in the intensity of the flux during irradiation. This is an important consideration only when a single sample transfer system is used. Gas-filled BF3 neutron counter tubes are often used to monitor the neutron flux in order to normalize the data when the sample and the standard are not irradiated simultaneously. Gain shifts and dead-time effects associated with the use of neutron monitoring detectors also contribute to the errors associated with a single sample transfer system. 

In practice, decay of the spin coherence during the delay time t,i and finite optical depth flatten and broaden the anti-Stokes pulse, reducing the total number of anti-Stokes photons which can be retrieved within the coherence time of the atomic memory. For weak retrieve laser intensities, the total photon number per pulse increases with increasing laser power because the time required to read out the spin wave is longer than the characteristic decoherence time of our atomic memory ( 3gs, see Fig. 3 b). After accounting for dead-time effects, we find that once the retrieve laser power increases to 25 mW, all of the spin wave is retrieved in a time shorter than the decoherence time, resulting in a constant anti-Stokes number versus retrieve power. 

It is important to point out that even at 77 = 0 the observed value V = 0.942 0.006 is far from its ideal value of V = 0. One important source of error is the finite retrieval efficiency, which is limited by two factors. Due to the atomic memory decoherence rate 7C, the finite retrieval time Tr always results in a finite loss probability p 7c Tr. For the correlation measurements we use a relatively weak retrieve laser ( 2 mW) to reduce the number of background photons and to avoid APD dead-time effects. The resulting anti-Stokes pulse width is on the order of the measured decoherence time, so the atomic excitation decays before it is fully retrieved. Moreover, even as 7C —> 0 the retrieval efficiency is limited by the finite optical depth q of the ensemble, which yields an error scaling as p 1/ y/rj. The measured maximum retrieval efficiency at 77 = 0 corresponds to about 0.3. In addition to finite retrieval efficiency, many other factors reduce correlations, including losses in the detection system, background photons, APD afterpulsing effects, and imperfect spatial mode-matching. 

An implicit assumption in Eqs. (17) to (19) is that the probability D(E ) that a neutron of energy E is detected, is independent of t, which is not true if detector dead time effects are significant. 

Since the results obtained are independent of sample geometry and scattering power, sample attenuation, multiple scattering and detector dead time effects can all be eliminated as a possible cause of the observed anomalies. 

Furthermore, we also repeated the measurements on pure H2 using a new experimental setup, in which the distance between detectors and sample was increased from ca. 60 cm to 100 cm. With this procedure we also tested directly a conceivable influence of possible "dead-time" effects of the detectors for short times on the intensity of the //-signal. Also these additional measurements have clearly confirmed the results presented in Fig. 10 see inset. 

In the preceding section we identified the critical need for more effective control of processes with significant dead time. In this section we discuss a modification of the classical feedback control system which was proposed by O. J. M. Smith for the compensation of dead-time effects. It is known as the Smith predictor or the dead-time compensator. 

Before results from a new calibration are accepted, it is essential that the accuracy over the full calibration range is validated independently. Although the intensity response of a WD spectrometer is expected to be linear over six orders of magnitude (subject to corrections for counter dead-time effects), the accuracy of the calibration function is as sensitive as that for any other instrumental technique to the effects of bias, which are likely to be most significant in the analysis of samples at the extremes (low or high) of the calibration range. Discrepancies of this nature are sometimes caused by the use of inaccurate values in reference samples. These discrepancies can only be overcome satisfactorily by a critical evaluation of all calibration data. If the analysis of independently characterized reference materials cannot be used in this evaluation (because, for example, these samples have had to be used as primary calibration samples) then it is possible, though not entirely satisfactory, to evaluate the self-consistency of calibration data in order to identify discrepant points. 

The ratio factors R in O Eq. (30.35) are ideally unity, but small deviations and their uncertainties must be considered. Rg is the ratio of isotopic abundances for the unknown and standard, R, is the ratio of neutron fluences (including fluence drop off, self-shielding, and scattering), is the ratio of effective cross sections if the shape of neutron spectrum differs from the unknown sample to standard, Re is the ratio of counting efficiencies (differences due to geometry, y-ray self-shielding, and dead-time effects). 

Each ion current, lots, measured with an ICP-MS instrument is biased as a result of mass discrimination, variations in detector gain and detector efficiency, and other effects. These other effects, such as background, detector dead time effects (counting devices), interferences, and matrix effects, will not be discussed here, because they vary strongly depending on the type of mass spectrometer. Discussions on these topics can be found in Chapters 2 and 3 and in the literature [38-42]. An observed isotope amount ratio, or in other words an ion current ratio, Robs.i [Eq- (6.2)], calculated for two isotopes a and b is therefore also biased. This means that every measured or observed isotope amount ratio is biased or, to put it bluntly, these observed isotope amount ratios are wrong, unless they have been corrected for all effects mentioned above. 

Both geometries, however, suffer in that pulsing either the primary ion or the secondary ion beam limits the number of secondary ions of a specific m/q that can be recorded per analytical beam pulse. This is a direct result of the dead time effects/pulse pair resolution exhibited by detectors (see Section 4.2.4.2). In the case of Channel Plates (those most commonly used in TOF SIMS instruments), the pulse pair resolution approaches 10 ns, which is still greater than the primary ion pulse... 

These will suffer increased dead time effects on approaching the specified count rates (counting speed is limited). 

Such dead time effects can be corrected if the dead time of the counting system is known (t). This is described via Ihe relation ... 

Figure 4.19 Schematic example of the effect of dead time effects over the peak intensities recorded from an ion implanted substrate.

Measurement of Intense Signals When the signal count rate (frequency) approaches the dead time of the Electron Multiplier, there are several options that can be implemented to avoid the introduction of dead time effects. Such count rates are commonly noted when examining multiple secondary ion signals of very different intensities. 

Owing to the added constraints of Time of Flight mass filter-based SIMS instm-ments (these only use MCP detectors), additional options have had to be developed. The two most common approaches include the use of the Poisson statistic correction approach and the introduction of the Extended Dynamic Range (EDR) filter. The Poisson correction approach, apphed during data collection, is a statistic method that attempts to correct for the dead time effect suffered. Although effective, this method is applicable only over a limited intensity range, i.e. the maximum... 

Stationary mode describes the nse of an nn-scanned beam. Advantages of this mode lie in the fact that instantaneons dead-time effects are removed (see Section 4.2.3.3.3.2). Note Although this is also referred to as static made, this definition will not be used in this text so as to avoid confnsion with Static SIMS). 

Rastered mode describes scanning of a focnsed primary ion beam over some predefined area over the sample. In this mode, the beam spot size must be substantially smaller than the analyzed area and instantaneous dead-time effects associated with primary beam rastering must be considered (see Section 4.2.3.3.3.2). 

The shaped mode consists of forming an image of a primary beam aperture on the sample s surface (one form is referred to as Kohler illumination). Under this condition, the beam spot size remains independent of the primary ion current (the spot size is larger than under Gaussian mode). As the current density across the spot remains constant, rastering of the beam is then not necessary, although sometimes still applied. This mode of operation can be used when imaging in the microscope mode (see Section 5.3.2.2) and/or when carryout analysis where detector dead-time effects should be minimized (see Section 4.2.3.3.3.2). 

This frequency-type distribution is applied when describing events that have a non-symmetric probability of occurring around some mean value. Typical examples are in particle decay and particle detection. The event/nonevent is then expressed in units over which the signal decays, i.e. e , where n is some integer number. It was through an extension of this that dead time effects noted in primary ion-pulsed Time-of-Flight instruments can be partially corrected for (see Section 4.2.3.3.2.3). 

Brown and coworkers have tested avalanche photodiodes (APD) as replacements for PMTs. Preliminary tests were encouraging. Single photon counting was possible, though dead-time effects in the range of 1-2 /as limited the maximum count rate. Special active quenching circuitry has reduced this... 

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