## Optimization of multi-photon event discrimination levels using Poisson statistics

Optics Express, Vol. 12, Issue 1, pp. 84-89 (2004)

http://dx.doi.org/10.1364/OPEX.12.000084

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### Abstract

In applications where random multi-photon events must be distinguishable from the background, detection of the signals must be based on either analog current measurement or photon counting and multi-level discrimination of single and multi-photon events. In this paper a novel method for optimizing photomultiplier (PMT) pulse discrimination levels in single-and multi-photon counting is demonstrated. This calibration method is based on detection of photon events in coincidence to short laser pulses. The procedure takes advantage of Poisson statistics of single- and multi-photon signals and it is applicable to automatic calibration of photon counting devices on production line. Results obtained with a channel photomultiplier (CPM) are shown. By use of three parallel discriminators and setting the discriminator levels according to the described method resulted in a linear response over wide range of random single- and multi-photon signals.

© 2004 Optical Society of America

## 1. Introduction

1. R. J. Ellis and A. G. Wright: “Optimal use of photomultipliers for chemiluminescence and bioluminescence applications,” Luminescence **14**, 11–18 (1999). [CrossRef] [PubMed]

2. J. T. Soini, J. M. Soukka, E. Soini, and P. E. Hänninen, “Two-photon excitation microfluorometer for multiplexed single-step bioaffinity assays,” Rev. Sci. Instrum. **73**, 2680–2685 (2002). [CrossRef]

4. J. T. Soini, J. M. Soukka, N. J. Meltola, A. E. Soini, E. Soini, and P. E. Hänninen, “Ultra Sensitive Bioaffinity Assay for Micro Volumes,” Single Molecules **1**, 203–206 (2000). [CrossRef]

5. PerkinElmer Optoelectronics data sheet, “Channel Photomultipliers, Overview and Specifications” (PerkinElmer Optoelectronics, 2001), http://optoelectronics.perkinelmer.com/content/RelatedLinks/cpm_brochure.pdf.

## 2. Calibration method

*P*(

*n*) for the photomultiplier to detect a pulse of

*n*photoelectrons is thus

*µ*is the mean number of photoelectrons emitted from the photocathode.

*µ*can be estimated by using a priori information that a part of the excitation light pulses do not lead to detection of any photons. Assuming that the total number of detected single- and multi-photon pulses during a measurement is

*N*(as detected using one discriminator with level set optimally for single-photons), and

_{C1}*N*laser pulses are registered at the same time, the probability of

_{L}**not**detecting any photons is

*N*and the estimated numbers of single- and multi-photoelectron events

_{L}µ*N*(

_{L}P*n*) can now be calculated.

*N*, discriminator 3 detects events of three or more photoelectrons

_{C2}*N*and so on. The measurement can be repeated and the levels adjusted until registered and estimated event numbers match, i.e.

_{C3}*N*≈

_{Cj}*N*̂

*, where the estimates (denoted with ^) are*

_{cj}## 3. Experimental setup

2. J. T. Soini, J. M. Soukka, E. Soini, and P. E. Hänninen, “Two-photon excitation microfluorometer for multiplexed single-step bioaffinity assays,” Rev. Sci. Instrum. **73**, 2680–2685 (2002). [CrossRef]

4. J. T. Soini, J. M. Soukka, N. J. Meltola, A. E. Soini, E. Soini, and P. E. Hänninen, “Ultra Sensitive Bioaffinity Assay for Micro Volumes,” Single Molecules **1**, 203–206 (2000). [CrossRef]

## 4. Results and discussion

*µ*≈0.09. In that case the photoelectron distribution was narrow and well separated from noise background, and it was straightforward to set the discrimination voltage of DSC1. Higher concentrations resulted in wider photoelectron distribution and higher pulses, in average. Multiple peaks that would correspond to multi-photoelectron pulses were not observed. Consequently, it is not possible to register individual multi-photon events with good accuracy with this type of detector.

4. J. T. Soini, J. M. Soukka, N. J. Meltola, A. E. Soini, E. Soini, and P. E. Hänninen, “Ultra Sensitive Bioaffinity Assay for Micro Volumes,” Single Molecules **1**, 203–206 (2000). [CrossRef]

## References and Links

1. | R. J. Ellis and A. G. Wright: “Optimal use of photomultipliers for chemiluminescence and bioluminescence applications,” Luminescence |

2. | J. T. Soini, J. M. Soukka, E. Soini, and P. E. Hänninen, “Two-photon excitation microfluorometer for multiplexed single-step bioaffinity assays,” Rev. Sci. Instrum. |

3. | P. Hänninen, A. Soini, N. Meltola, J. Soini, J. Soukka, and E. Soini, “A new microvolume technique for bioaffinity assays using two-photon excitation,” Nature Biotechnol. |

4. | J. T. Soini, J. M. Soukka, N. J. Meltola, A. E. Soini, E. Soini, and P. E. Hänninen, “Ultra Sensitive Bioaffinity Assay for Micro Volumes,” Single Molecules |

5. | PerkinElmer Optoelectronics data sheet, “Channel Photomultipliers, Overview and Specifications” (PerkinElmer Optoelectronics, 2001), http://optoelectronics.perkinelmer.com/content/RelatedLinks/cpm_brochure.pdf. |

**OCIS Codes**

(030.5260) Coherence and statistical optics : Photon counting

(030.5290) Coherence and statistical optics : Photon statistics

(040.5250) Detectors : Photomultipliers

**ToC Category:**

Research Papers

**History**

Original Manuscript: December 2, 2003

Revised Manuscript: December 20, 2003

Published: January 12, 2004

**Citation**

Juri Soukka, Arho Virkki, Pekka Hänninen, and Juhani Soini, "Optimization of multi-photon event discrimination levels using Poisson statistics," Opt. Express **12**, 84-89 (2004)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-1-84

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### References

- R. J. Ellis and A. G. Wright: �??Optimal use of photomultipliers for chemiluminescence and bioluminescence applications,�?? Luminescence 14, 11-18 (1999). [CrossRef] [PubMed]
- J. T. Soini, J. M. Soukka, E. Soini, and P. E. Hänninen, �??Two-photon excitation microfluorometer for multiplexed single-step bioaffinity assays,�?? Rev. Sci. Instrum. 73, 2680-2685 (2002). [CrossRef]
- P. Hänninen, A. Soini, N. Meltola, J. Soini, J. Soukka, and E. Soini, �??A new microvolume technique for bioaffinity assays using two-photon excitation,�?? Nature Biotechnol. 18, 548-550 (2000). [CrossRef]
- J. T. Soini, J. M. Soukka, N. J. Meltola, A. E. Soini, E. Soini, and P. E. Hänninen, �??Ultra Sensitive Bioaffinity Assay for Micro Volumes,�?? Single Molecules 1, 203-206 (2000). [CrossRef]
- PerkinElmer Optoelectronics data sheet, �??Channel Photomultipliers, Overview and Specifications�?? (PerkinElmer Optoelectronics, 2001), <a href="http://optoelectronics.perkinelmer.com/content/RelatedLinks/cpm_brochure.pdf">http://optoelectronics.perkinelmer.com/content/RelatedLinks/cpm_brochure.pdf</a>.

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