System and method of extending the linear dynamic range of event counting
A method and apparatus for photon, ion or particle counting described that provides seven orders of magnitude of linear dynamic range (LDR) for a single detector. By explicitly considering the log-normal probability distribution in voltage transients as a function of the number of photons, ions or particles present, the binomial distribution of observed counts for a given threshold, the mean number of photons, ions or particles can be determined well beyond the conventional limit.
1. A method of measuring a photon flux, comprising:
providing:
a digital processor;
a detector disposed to receive the photon flux, having an output voltage; and
an analog-to-digital converter (ADC), for digitizing a sample of a detector output voltage, an ADC output communicating with the digital processor;
the method further comprising:
synchronizing a sampling time of the ADC with a light pulse from a pulsed light source;
obtaining, by the ADC, a plurality of digitized samples of the detector output voltage;
accepting, by the digital processor, the plurality of digitized samples of the detector output voltage; and
configuring the digital processor to process the plurality of digitized samples of the detector output voltage by:
(a) calculating an average value of a number of times the digitized detector output voltage exceeds a threshold; when the average value is less than about 1, outputting the average value as the photon flux; and,
(b) when the average value calculated in (a) is greater than about 1, outputting an average value of the digitized detector output voltage as the photon flux.
2. The method of claim 1 , further comprising:
determining the threshold as greater than the detector voltage output when the pulsed source is not emitting photons and less than the detector voltage output for a single photon.
3. The method of claim 1 , wherein a source of the photon flux is a laser.
4. The method of claim 1 , further comprising:
equating the photon flux determined by step (a) with the photon flux determined by step (b) when the average value of the number of times the digitized detector output voltage exceeds the threshold is about 1.
5. The method of claim 1 , wherein the output photon flux value is one of: (a) the average number of times per pulse the digitized detector output voltage exceeds the threshold or (b) the average value of the digitized detector output voltage multiplied by a gain.
6. The method of claim 5 , wherein the gain is determined by computing a ratio of the value determined by step (a) to the value determined by step (b) when the average value determined by step (a) is about 1.
7. The method of claim 1 , wherein the detector is a photomultiplier tube (PMT).
8. The method of claim 1 , wherein the detector is an avalanche photodiode (APD).
9. A method of measuring a particle flux, comprising:
providing:
a digital processor;
a detector disposed to receive particle flux, having a pulse output voltage; and
an analog-to-digital converter (ADC), having a sampling rate, for digitizing a detector output voltage, the ADC output communicating with the digital processor;
the method further comprising:
obtaining, by the ADC, a plurality of digitized samples of the detector output voltage;
accepting, by the digital processor, the plurality of digitized samples of the detector output voltage; and
configuring the digital processor to process the plurality of digitized samples of the detector output voltage by:
(a) calculating an average value of a number of times the digitized detector output voltage exceeds a threshold;
when the average value is less than about 1, outputting the average value as the particle flux; and,
(b) when the average value calculated in (a) is greater than about 1, outputting an average value of the digitized detector output voltage as the particle flux.
10. The method of claim 9 , further comprising: equating the particle flux determined by step (a) with particle flux determined by step (b) when the average value of the number of times the digitized detector output voltage exceeds the threshold is about 1.
11. The method of claim 9 , wherein a source of the particle flux is an output of a mass spectrometer.
12. The method of claim 9 , wherein a source of the particle flux is an output of a scanning electron microscope.
13. The method of claim 9 , wherein the detector is an electron multiplier tube.
14. The method of claim 9 , wherein the threshold is greater than the detector voltage output for Johnson noise and less than the detector voltage output for a single particle.
15. The method of claim 9 , wherein output particle flux value is one of: (a) the average number of times the digitized detector output voltage exceeds the threshold or (b) the average value of the digitized detector output voltage multiplied by a gain.
16. The method of claim 15 , wherein gain is determined by computing a ratio of the value determined by step (a) to the value determined by step (b) when the value determined in step (a) is about 1.