The correction for dead time is required because the photon counting process is non-linear. A photon pulse generated by the photomultiplier and amplifier has a finite width of about 30 nanoseconds (ns). Thus, two or more photons arriving within 30 ns merge into a single pulse, which is registered as one count. The probability for missed counts increases with the count rate, and as the count rate increases, the registered counts eventually saturate. The maximum operating count rate for the Brewer instrument is limited to about 2 million counts per second (MHz). Under this condition, the average photon spacing is about 15 times the photon pulse width, and correction for dead time can be accurately made. Prior to every measurement, targeted radiation is sampled, and if the count rate is too high, the appropriate neutral density filter is inserted to reduce the count rate below 2 MHz. If the count rate is low (< 0.5 MHz), the thickness of the neutral density is reduced, if possible.
The correction assumes the following model:
where N is the measured photon count rate. No is the corrected photon count rate. t is the dead time.
With knowledge of t, it is possible to solve iteratively for No from N. At maximum measured count rate (N = 2 MHz), the correction required is about + 6.5% for an instrument with dead time of 30 ns.
As discussed in Section 6.3.2, the slit mask of the Brewer spectrophotometer is designed to measure dead time quickly and automatically by using a mask position where two slits (slit #2 and slit #4) are opened together. This allows a two-source linearity measurement by counting the photons with two slits opening individually, as well as with both opening together. Three equations are described for N2, N4 and N2+4, where N2 = number of photons counted with slit #2 opened, N4 = number of photons counted with slit #4 opened, and N2+4=number of photons counted with both slits opened. From these three equations, three unknowns (No2, No4, and t) can be solved iteratively since it is known that No2 + No4=No2+4. Results of this internal two-source test compare very well with conventional, but more cumbersome, tests using two external radiation sources.
In operation, the dead time is measured and recorded on a daily basis using two intensity settings, and the results are used as an indicator of instrument performance. Measured dead times for the two intensity levels should agree and should remain fairly stable with time. These tests are useful to warn operators of possible problems associated with the setting or stepping of the slit mask, as well as photon counting circuitry.
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