Discrimination threshold

However, the PLS-DA method requires sufficient calibration samples for each class to enable effective determination of discriminant thresholds, and one must be very careful to avoid overfitting of a PLS-DA model through the use of too many PLS factors. Also, the PLS-DA method does not explicitly account for response variations within classes. Although such variations in the calibration data can be useful information for assigning and determining uncertainty in class assignments during prediction, it will be treated essentially... 

Exposure of nonsmokers to 50 ppm for 6-8 hours results in carboxyhemoglobin levels of 8-10%. Several investigators have suggested that the results of behavioral tests such as time discrimination, visual vigilance, choice response tests, visual evoked responses, and visual discrimination threshold may be altered at levels of carboxyhemoglobin below 5%. ... 

When referring to an instrument, the term discriminate is used, i.e. the ability of a measuring instrument to respond to small changes in analyte concentration. This leads to the concept of discrimination threshold, which is defined as the largest change in a stimulus that produces no detectable change in the response of a measuring instrument,.. 

The Receiver Operator Characteristic curve (ROC curve) is a graphical plot of the sensitivity Sn versus false positive rate FPR for a binary classifier system as its discrimination threshold is varied. The ROC curve can also be represented equivalently by plotting the fraction of true positives (TP) versus the fraction of false positives (FP) (Figure C3). ROC analysis provides tools to select possibly optimal classification models. 

When a photon enters a detector, it may or may not produce a signal or it may produce a signal lower than the discriminator threshold and, therefore, it is not counted. This effect is accounted for by the detector efficiency h, defined as the ratio of the number of photons recorded to the number of photons that impinge upon the detector per unit time. Statistically, the probability that a photon has at least one interaction in the detector Nal crystal is 1 - e r, where m is the linear attenuation coefficient of Nal and r is the distance that the photon travels in the crystal. For an isotropic radioactive point source, the detector efficiency can be expressed as (Tsoulfanidis, 1983)... 

Sketch counting rate versus discriminator threshold, assuming that the electronie noise eonsists of pulses in the range 0 < K < 0.1 V and all the pulses due to the source have height equal to 1.5 V. 

The detector may affect the measurement in two ways. First, if the source is located outside the detector (which is usually the case), the particles may be scattered or absorbed by the detector window. Second, some particles may enter the detector and not produce a signal, or they may produce a signal lower than the discriminator threshold. 

Consider the differential pulse spectrum shown in Fig. 9.6 for which all pulses have exactly the same height Vq. To record this spectrum, one starts with the discriminator threshold set very high (higher than Vq) and then lowers the threshold by a certain amount AV (or A ) in successive steps. Table 9.1 shows the results of this measurement, where N(V is the number of pulses higher than or equal to V. A plot of these results is shown in Fig. 9.7. 

The leading-edge timing method determines the time of arrival of a pulse with the help of a discriminator, as shown in Fig. 10.20. A discriminator threshold is set and the time of arrival of the pulse is determined from the point where the pulse crosses the discriminator threshold. ... 

Figure 10.20 The time of arrival of the pulse is determined from the instant at which the pulse crosses the discriminator threshold.

The Na source is placed between two identical samples. Two XP 2020 photomultipliers equipped with scintillators are attached directly to the two samples. The pulses from the photomultipliers are used as start and stop pulses for the TCSPC module. The pulses from PMT 2 are delayed by a few nanoseconds so that a stop pulse arrives after the corresponding start pulse. Eaeh y quantum generates a large number of photons in the scintillator. Therefore, the PMT pulses are multiphoton signals, and the time resolution can be better than the transit time spread of the PMTs. Moreover, the amplitudes of the photomultiplier pulses are proportional to the energy of the particle that caused the scintillation. Therefore the amplitudes can be used to distinguish between the 511 keV events of the positron decay and the 1.27 MeV events from the Na. The discriminator thresholds for start and stop are adjusted in a way that the stop channel sees all, the start channel only the larger Na events. The rate of the Na events is of the order of a few kHz or below. 

If the discriminator threshold is set low enough an extremely high peak appears at very low amplitudes. This peak does not originate in the PMT but is caused by electronic noise of the preamplifier and noise pickup from the environment. Some typical pulse amplitude distributions are shown in Fig. 6.13. 

In some detectors a bump in the TCSPC instrument response function appears a few ns before the main peak. The size of the bump depends on the discriminator threshold. Normally the bump can be suppressed or reduced in size by increasing the discriminator threshold. The effect is probably caused by photoelectron emission from the first dynode. The corresponding pulses reach the anode prior to the photons from the cathode, and have a lower amplitude. Figure 6.20 shows an example for an H5773P-01 photosensor module. 

Fig. 6.30 R38909U, TCSPC instrument response in linear (left) and logarithmic scale (right). Time scale 100 ps/div., operating voltage -3 kV, preamphfier gain 20 dB, discriminator threshold - 80 mV. The IRF width is 28 ps, FWHM...

Fig. 6.31 R3809U MCP, count rate for 100 nA anode current and optimum discriminator threshold vs. supply voltage for a 20 dB, 1.6 GHz preamplifier...

The FWHM of the system response is between 200 ps and 350 ps. There is a weak secondary peak 1 ns to 2.5 ns after the main peak. A peak prior to the main peak can appear at low discriminator thresholds. The width of the response of the 0 and -50 versions does not noticeably depend on the CFD threshold and the CFD zero cross. This is an indication that the response is limited by the intrinsic speed of the semiconductor photocathode. 

Fig. 6.40 H5773P-0, TCSPC instrument response, time scale 500 ps/div. Maximum gain, preamplifier gain 20 dB, discriminator threshold -100 mV, -300 mV and -500 mV. Left. Linear scale. Right Logarithmic scale over 4 orders of magnitude...

The response function has a prepeak about 1 ns before and a secondary peak 2 ns after the main peak. The prepeak is caused by low amplitude pulses, probably by photoemission at the first dynode. It can be suppressed by properly adjusting the discriminator threshold. The secondary peak is independent of the discriminator threshold. 

Can dark counts be suppressed by increasing the Discriminator threshold ... 

The eommonly used MCPs and PMTs deliver single-electron pulses of 20 to 50 mV when operated at maximum gain. Although these pulses can be detected by the input diseriminators of most TCSPC modules, a preamplifier is recommended for several reasons. The most obvious one is that a good preamplifier, if it is con-neeted elose to the detector output, improves the noise immunity of the system. Moreover, with the amplifier the CFD ean be operated at a higher discriminator threshold, which improves the timing and the threshold stability. 

The preamplifier shown in Fig. 7.38 is a much better overload indieator than a rate meter. Monitoring the count rate is not safe because the discriminator threshold can be wrong, or the detector gain may be set too low to obtain any counts. Moreover, the count rate may break down at extreme overload. An inexperienced user may then increase the light intensity even more. In contrast, overload detection via the detector current responds properly in all these situations. 

As a practical example, Fig. 7.61 shows a CFD threshold scan for an XP2020RU PMT. The count rate versus discriminator threshold is shown left, the IRF right. Both figures are in linear scale. 

Figure 4.18 Calibration of the detector and amplifier gain using the pulse height selector. The amplifier output pulse height spectra are shown at gains of (a) 50, (b) 100, and (c) 150. The ratemeter counting rate as a function of gain setting is shown in (d) for a 4-V integral discriminator threshold. (Reprinted by courtesy of EG G ORTEC.)...

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