Efficiency of the Detectors

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) 

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Let the rate of the event under study be R. It will be proportional to the cross section for the process under study, a, the incident electron current, Iq, the target density, n, the length of the target viewed by the detectors,, the solid angles subtended by the detectors, Aoi and A012 the efficiency of the detectors, and... 

NAA is a quantitative method. Quantification can be performed by comparison to standards or by computation from basic principles (parametric analysis). A certified reference material specifically for trace impurities in silicon is not currently available. Since neutron and y rays are penetrating radiations (free from absorption problems, such as those found in X-ray fluorescence), matrix matching between the sample and the comparator standard is not critical. Biological trace impurities standards (e.g., the National Institute of Standards and Technology Standard Rference Material, SRM 1572 Citrus Leaves) can be used as reference materials. For the parametric analysis many instrumental fiictors, such as the neutron flux density and the efficiency of the detector, must be well known. The activation equation can be used to determine concentrations ... 

Similarly to Eq. (2.6), fCis a proportionality constant containing fixed operating conditions, for example incident electron current density, transmission of the analyzer at the kinetic energy Ea, efficiency of the detector at the kinetic energy Ea, and the probability of the Auger transition XYZ. 

Quantitative Analysis. The efficiency of the detector is such that almost 100% of the X-rays entering it will produce a pulse, but the pulse processing speed limits the rate at which X-rays can be counted. If the count rate is less than a few thousand counts per second, then most of the incoming pulses are processed, but as the count rate rises an increasing fraction of the pulses are rejected. The live time during an analysis when the detector was counting is thus less than the elapsed time, and the EDS system records both times in order that the true count rate may be measured. 

SPC techniques are hardly affected by additive noise and multiplicative noise is absent. However, subtractive noise due to the collection efficiency and transmission of optics and the quantum efficiency of the detector do play a role. In addition, at high count rates, the efficiency goes down due to pileup effects. 

In most applications, the electrochemical compounds are usually oxidized, yielding one or more electrons per molecule reacted. The oxidized form is usually unstable and reacts further to form a stable compound that flows past the carbon electrode surface. Unfortunately, this is not always the case, with the stable oxidized form occasionally building up at the surfaces of the carbon electrode. This creates sensitivity problems and decreases the efficiency of the detector. However, the problem is usually overcome by regularly cleaning the carbon electrode surfaces, removing any oxidizable products. Eluents for EC detection must be electrochemically conductive, which is achieved by the addition of inert electrolytes (to maintain a baseline current) such as phosphate or acetate. All solvents and buffers used in preparation of an eluent must be relatively pure and selected so as to not undergo electrochemical changes at the applied electrode potentials. 

The result of our effort to develop the best possible detector for MES is as follows. Our detector has a resolution of approximately 2 KeV (fwhm) at 15 KeV as shown in Figure 6. There is virtually no deterioration in performance over a period of several months. The overall efficiency of the detector when used for MES with 14-KeV y-radiation is such that a 0.001-inch thick sample of stainless steel type 302 (natural isotopic abundance) gives a spectrum with the peak height some 400% of the base line, Figure 7. (For comparison, when we started we were quite content with 50%.) With our 10-mc Co-57 source, the data acquisition rate in the peak is approximately 500 counts/min. This means that in a matter of a minute or less one obtains a recognizable spectrum. As a bonus, the observance of 6-KeV x-rays yields an effect of approximately 50% of the baseline. To accomplish this, we interpose a plastic filter between the source and the sample to absorb most of the 6-KeV radiation from the source (which does not contribute to the effect but is elastically... 

When a luminescence spectrum is obtained on an instrument such as that used to produce the spectra in Figure 7.23, it will depend on the characteristics of the emission monochromator and the detector. The transmission of the monochromator and the quantum efficiency of the detector are both wavelength dependent and these would yield only an instrumental spectrum. Correction is made by reference to some absolute spectra. Comparison of the absolute and instrumental spectra then yields the correction function which is stored in a computer memory and can be used to multiply automatically new instrumental spectra to obtain the corrected spectra. The calibration must of course be repeated if the monochromator or the detector is changed. 

It is the usual practice, therefore, to irradiate a standard containing a known amount of the element to be determined along with the samples and to count both standards and samples with the same detector system. In this case the absolute value of the flux, the constancy of the flux, and the detection efficiency of the detector do not enter into the determination. By combining the standard activation equations for both standard and sample, the following equation results ... 

Obtaining product energy distributions from the intensities of chemiluminescence spectra is relatively straightforward, requiring a knowledge of the appropriate transition probabilities and the spectral efficiency of the detector. One complication that can arise in the analysis of chemiluminescence data is the possibility of cascading an emitting state... 

Correction for efficiency of the detector, number of events generated by a single photon, detector proportionality, etc, all of which must be precise and reproducible. 

An identical absorption efficiency of the detector is assumed in these calculations for 0.5 A and 1.5 A A s. Hence, to exploit these benefits of changing A truly needs an efficient detector in each wavelength range. For example, at 0.9 A film is 40% efficient and the IP 80% whereas at 0.33 A wavelength film is only 8% efficient in absorbing photons whereas the IP is 44% efficient. 

The absorption efficiency of the detector/film also reduces with A according to a factor exp(— fit). Photographic film, for example, reduces in absorption efficiency between 1.54A and 0.9 A by a factor of —1.35 (see figure 5.21). In table 5.4 the absorption efficiencies of various detectors as a function of wavelength are compared. Note that for film the Br... 

Another problem with RS measurements is that the corresponding thermometry is subject to calibration. This implies careful evaluation of the experimental parameters (quantum efficiency of the detector, collection efficiency, laser energy, total number density, solid angle of the collection optics, optical path length, and so on), but a typical procedure relies on the ratio between the measured RS signal and a reference signal obtained from a gas of known RS cross section and temperature. 

Detector effects. The detector may affect the measurement in two ways. First, the size and thickness of the detector window (Fig. 8.1) determine how many particles enter the detector and how much energy they lose, as they traverse the window. Second, particles entering the detector will not necessarily be counted. The fraction of particles that is recorded depends on the efficiency of the detector (see Sec. 8.4.2). 

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