Dead time correction

Faraday collector, simultaneously with U, U and U during the first sequence. This shortens the analysis routine, consuming less sample. Ion beam intensities are typically larger in MC-ICPMS than in TIMS due to the ease with which signal size can be increased by introducing a more concentrated solution. While this yields more precise data, non-linearity of the low-level detector response and uncertainties in its dead-time correction become more important for larger beam intensities, and must be carefully monitored (Cheng et al. 2000 Richter et al. 2001). 

Integral intensities were obtained after dead-time corrections, background subtraction and normalization to averaged monitor counts. The Lp correction was applied in the usual way. Since the polarization ratio was not measured at BW5 so far, 90% linear horizontally polarized radiation was assumed for all scans. Calculations show that even a change in the beam polarization of 10% would effect the intensities of the highest order reflections of less than 1.5%. 

To determine the expressions for the optimised counting times, we write the expressions (10) and (11) in terms of count-rates and times (count rates are constant quantities for each Bragg reflection). We assume that the incident neutron flux is constant during a flipping ratio measurement, and that no dead-time correction is needed. In these conditions, we have the relations ... 

If no dead time correction is applied, then a linear calibration would not be possible, since the higher count rates between 10 and 10 Hz would be underestimated. This provides a way of determining the dead time empirically, i.e. by re-integrating the isotopic signals with different dead times until a linear calibration is obtained for a series of accurately known standards. 

Another limit source of uncertainty in isotope ratio measurements by mass spectrometry is the dead time of the ion detector for counting rates higher than 106cps, because a lower number of counts are usually registered than actually occur. Dead time correction of the detector is required if extreme isotope ratios are measured by channel electron multipliers and pulsed counting systems.86... 

It is common to prepare standards that contain approximately the same or slightly larger amounts of the element of interest than the amount estimated to be found in the sample. In this way errors associated with varying sample and standard instrumental dead-time corrections in the counting system are minimized. This is an important consideration when counting indicator radionuclides having half-lives short with respect to the time of counting. 

The curve (a) traces the outline of the peak obtained directly from the number of events recorded (Figure 31.5). The second curve (b) traces the outline of the peak obtained after correcting for coincidental events (dead time, shown by the shaded area). The centroids of peaks a and b are shown, and it can be seen that they occur at the same m/z value. Thus the dead-time correction alters only the abundances and not the m/z values of the ions. 

Dead time correction is made by empirical measurement of observed count rates as a function of increasing concentrations of activity. From these data, the dead time loss is calculated and a correction is applied to the measured data to compensate for the dead-time loss. Other techniques, such as use of buffers, in which overlapping events are held off during the dead time, use of pulse pile-up rejection circuits, and use of high-speed electronics, have been applied to improve the dead time correction. 

Guss et al (1988) measured data at four wavelengths about the copper K edge, i.e. 1.2359 A, 1.3771 A, 1.3790 A and 1.5416 A. Of particular note in the data reduction was the need for an empirical method for coincidence losses to be used, as the analytical dead time correction for the area detector was unreliable at the upper end of the range of counting rates. As a result, merging f -factors within the data set at each wavelength were reduced by 20-60%, for the empirical versus the analytical coincidence method of data correction. 

When the counting rate is extremely high, the counter may be missing some counts. Then a dead time correction is necessary, in addition to background subtraction see Sec. 2.21. 

COUNTER DEAD-TIME CORRECTION AND MEASUREMENT OF DEAD TIME... 

When dead-time correction is necessary, the net counting rate, called true net counting rate, is given by... 

The observed counting rate of a counter is 22,000 counts/min. What is the error in the true counting rate if the dead time is 300 fis and no dead-time correction is applied ... 

The factor F in Eq. 14.22 takes into account any other corrections (i.e., backscattering, foil self-absorption) that may be necessary (see Sec. 8.3). If dead-time correction is necessary, it should be applied to G. . 

The statistical nature of radioactive decay also leads to an uneven distribution of decays in time which is important when handling dead-time corrections and discussing required system time resolution. Let us first assume that a decay has occurred at time t = 0. What is then the differential probability that the next decay will take place within a short time interval, dr, after a time interval t has passed Two independ t processes must then occur in series. No decay may take place within the time interval from 0 to r, probability P 0),... 

The use of approximate matching between the mass bias solutions and the spiked sample solutions removes the necessity for making dead time corrections provided, that the matching includes both the isotopic ion abundances and their ratios. Arranging for just the isotopic ion abundance ratios to be matched in the mass bias and spiked sample solutions is not sufficient. 

Each stored XAS data point consists of the relative angle of the crystal monochromator, incident Iq, transmitted 7, and I2 (to monitor the spectrum of a energy reference) photon flux measurements, and the fluorescent counts, F, of the element of interest in the biological sample obtained from the channels of the fluorescence X-ray detector. With the use of the new solid state fluorescence detectors which require dead-time corrections, it is also necessary to store the total incoming count rate (ICR) seen by each detector element channel. 

Dead-time corrections have become necessary with the introduction of solid state detectors which suffer from count rate overload associated with the electronics. Dead-time losses can result in serious nonlinear distortions in the XAS data. Typically, one measures the number of photons before (ICR = n) and after (m) processing by the associated electronics, and the saturation curve is plotted. The curve is fit to an equation for dead-time derived from either the paralizable [m = /8n(l - nr)] or nonparalizable model [m = /3n expf-nr)], where t is the dead-time and /8n gives the true count rate. The dead-time t and the constant /8 are determined for each channel, and the correction is then applied to each data point to obtain the true count rate. 

Pulse processing also incorporates dead time correction. Dead time results from the inability of the detector electronics to process the pulses fast enough to match the volume of input signals. Therefore, the greater the incident intensity, the greater the losses would be during measurement. Dead time is typically 300-400 ns for modern spectrometers. 

The pile-up losses are corrected by electronic or computational means. Most spectroscopy amplifiers employ a pile-up detection and rejection circuit, which simply blocks further processing of the event and adds the dead time. The aforementioned dead-time correction principles apply. If pile-up events are not rejected, a calibration of the spectrometer for the losses in dependence of the dead time can be used. For more accurate results injection of events from a highly stable pulser provide a measure with the spectral data with the assumption that these events are subject to the same degree of pile-up as the photopeak events. 

The dead-time correction of the spectrometer is accurate in the given count rate range. This is necessary to obtain the accurate live time. 

---