{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T07:08:23Z","timestamp":1780470503045,"version":"3.54.1"},"reference-count":41,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2022,11,24]],"date-time":"2022-11-24T00:00:00Z","timestamp":1669248000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100009532","name":"Ministry of the Interior of the Czech Republic","doi-asserted-by":"publisher","award":["VI20192022173"],"award-info":[{"award-number":["VI20192022173"]}],"id":[{"id":"10.13039\/100009532","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Silicon photomultipliers are relatively new devices designed as a matrix of single-photon avalanche detectors, which have become popular for their miniature dimensions and low operating voltage. Their superior sensitivity allows detecting low-photon-count optical pulses, e.g., in ranging and LIDAR applications. The output signal of the photomultiplier is a non-stationary stochastic process, from which a weak periodic pulse can be extracted by means of statistical processing. Using the double-exponential approximation of output avalanche pulses the paper presents a simple analytical solution to the mean and variance of the stochastic process. It is shown that even for an ideal square optical pulse the rising edge of the statistically detected signal is longer than the edge of individual avalanche pulses. The knowledge of the detected waveform can be used to design an optimum laser pulse waveform or algorithms for estimating the time of arrival. The experimental section demonstrates the proposed procedure.<\/jats:p>","DOI":"10.3390\/s22239134","type":"journal-article","created":{"date-parts":[[2022,11,25]],"date-time":"2022-11-25T03:34:24Z","timestamp":1669347264000},"page":"9134","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Statistical Analysis of Silicon Photomultiplier Output Signals"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7034-9430","authenticated-orcid":false,"given":"Zdenek","family":"Kolka","sequence":"first","affiliation":[{"name":"Department of Radio Electronics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technicka 12, 616 00 Brno, Czech Republic"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3922-3979","authenticated-orcid":false,"given":"Peter","family":"Barcik","sequence":"additional","affiliation":[{"name":"Department of Radio Electronics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technicka 12, 616 00 Brno, Czech Republic"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2589-2722","authenticated-orcid":false,"given":"Viera","family":"Biolkova","sequence":"additional","affiliation":[{"name":"Department of Radio Electronics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technicka 12, 616 00 Brno, Czech Republic"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1016\/0263-2241(85)90024-7","article-title":"Recent developments in silicon avalanche photodiodes","volume":"3","author":"McIntyre","year":"1985","journal-title":"Measurement"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1016\/j.nima.2006.05.060","article-title":"Geiger-mode avalanche photodiodes, history, properties and problems","volume":"567","author":"Renker","year":"2006","journal-title":"Nucl. Instrum. Methods Phys. Res. Sect. A Accel. Spectrometers Detect. Assoc. Equip."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1016\/j.nima.2018.11.118","article-title":"Understanding and simulating SiPMs","volume":"926","author":"Acerbi","year":"2019","journal-title":"Nucl. Instrum. Methods Phys. Res. Sect. A Accel. Spectrometers Detect. Assoc. Equip."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Frach, T., Prescher, G., Degenhardt, C., De Gruyter, R., Schmitz, A., and Ballizany, R. (November, January 24). The digital silicon photomultiplier\u2014Principle of operation and intrinsic detector performance. Proceedings of the 2009 IEEE Nuclear Science Symposium Conference Record (NSS\/MIC), Orlando, FL, USA.","DOI":"10.1109\/NSSMIC.2009.5402143"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1950","DOI":"10.1109\/TNS.2015.2477716","article-title":"SPICE electrical models and simulations of silicon photomultipliers","volume":"62","author":"Villa","year":"2015","journal-title":"IEEE Trans. Nucl. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/JQE.2018.2802542","article-title":"High-Density Silicon Photomultipliers: Performance and Linearity Evaluation for High Efficiency and Dynamic-Range Applications","volume":"54","author":"Acerbi","year":"2018","journal-title":"IEEE J. Quantum Electron."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1309","DOI":"10.1109\/LPT.2013.2264049","article-title":"Fast timing silicon photomultipliers for scintillation detectors","volume":"25","author":"Yeom","year":"2013","journal-title":"IEEE Photonics Technol. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1229","DOI":"10.1364\/OL.37.001229","article-title":"Silicon photomultiplier detector for atmospheric lidar applications","volume":"37","author":"Riu","year":"2012","journal-title":"Opt. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Candan, C., Tiken, M., Berberoglu, H., Orhan, E., and Yeniay, A. (2021). Experimental study on km-range long-distance measurement using silicon photomultiplier sensor with low peak power laser pulse. Appl. Sci., 11.","DOI":"10.3390\/app11010403"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1364\/BOE.4.000659","article-title":"Silicon photomultipliers for improved detection of low light levels in miniature near-infrared spectroscopy instruments","volume":"4","author":"Zimmermann","year":"2013","journal-title":"Biomed. Opt. Express"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"B25","DOI":"10.1364\/JOSAB.31.000B25","article-title":"Measurement of photon correlations with multipixel photon counters","volume":"31","author":"Kalashnikov","year":"2014","journal-title":"J. Opt. Soc. Am. B"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1016\/j.nima.2010.03.169","article-title":"Characterisation studies of silicon photomultipliers","volume":"620","author":"Eckert","year":"2010","journal-title":"Nucl. Instrum. Methods Phys. Res. Sect. A Accel. Spectrometers Detect. Assoc. Equip."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1109\/JSTQE.2014.2346489","article-title":"Silicon photomultipliers signal-to-noise ratio in the continuous wave regime","volume":"20","author":"Adamo","year":"2014","journal-title":"IEEE J. Sel. Top. Quantum Electron."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1016\/j.nima.2018.11.119","article-title":"Overview on the main parameters and technology of modern Silicon Photomultipliers","volume":"926","author":"Piemonte","year":"2019","journal-title":"Nucl. Instrum. Methods Phys. Res. Sect. A Accel. Spectrometers Detect. Assoc. Equip."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1109\/TNS.2013.2283231","article-title":"Silicon photomultipliers electrical model extensive analytical analysis","volume":"61","author":"Marano","year":"2014","journal-title":"IEEE Trans. Nucl. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/j.nima.2011.07.034","article-title":"Extensive electrical model of large area silicon photomultipliers","volume":"654","author":"Condorelli","year":"2011","journal-title":"NUclear Instruments Methods Phys. Res. Sect. A Accel. Spectrometers. Detect. Assoc. Equip."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/j.nima.2018.09.030","article-title":"SiPM readout electronics","volume":"926","author":"Ciciriello","year":"2019","journal-title":"Nucl. Instrum. Methods Phys. Res. Sect. A Accel. Spectrometers Detect. Assoc. Equip."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"336","DOI":"10.1109\/TNS.2012.2234135","article-title":"Simulating silicon photomultiplier response to scintillation light","volume":"60","author":"Jha","year":"2013","journal-title":"IEEE Trans. Nucl. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1016\/j.nima.2018.01.059","article-title":"Characterization of silicon photomultipliers and validation of the electrical model","volume":"887","author":"Peng","year":"2018","journal-title":"Nucl. Instrum. Methods Phys. Res. Sect. A Accel. Spectrometers Detect. Assoc. Equip."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.nima.2015.08.024","article-title":"Timing resolution performance comparison of different SiPM devices","volume":"801","author":"Dolinsky","year":"2015","journal-title":"Nucl. Instrum. Methods Phys. Res. Sect. A Accel. Spectrometers Detect. Assoc. Equip."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.optlastec.2012.12.024","article-title":"Lidar with SiPM: Some capabilities and limitations in real environment","volume":"49","author":"Agishev","year":"2013","journal-title":"Opt. Laser Technol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"102290L","DOI":"10.1117\/12.2264935","article-title":"Evaluation of performance of silicon photomultipliers in lidar applications","volume":"10229","author":"Vinogradov","year":"2017","journal-title":"Photon Count. Appl. 2017"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2771","DOI":"10.1109\/TNS.2021.3121871","article-title":"Novel Model for Analysis and Optimization of Silicon Photomultiplier-Based Scintillation Systems","volume":"68","author":"Sommer","year":"2021","journal-title":"IEEE Trans. Nucl. Sci."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Jha, A.K., Kupinski, M.A., and Van Dam, H.T. (2011, January 23\u201329). Monte Carlo simulation of silicon photomultiplier output in response to scintillation induced light. Proceedings of the 2011 IEEE Nuclear Science Symposium Conference Record, Valencia, Spain.","DOI":"10.1109\/NSSMIC.2011.6154662"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Tontini, A., Gasparini, L., and Perenzoni, M. (2020). Numerical model of spad-based direct time-of-flight flash lidar CMOS image sensors. Sensors, 20.","DOI":"10.3390\/s20185203"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/j.nima.2014.12.010","article-title":"Analytical model of SiPM time resolution and order statistics with crosstalk","volume":"787","author":"Vinogradov","year":"2015","journal-title":"Nucl. Instrum. Methods Phys. Res. Sect. A Accel. Spectrometers. Detect. Assoc. Equip."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/j.nima.2011.11.086","article-title":"Analytical models of probability distribution and excess noise factor of solid state photomultiplier signals with crosstalk","volume":"695","author":"Vinogradov","year":"2012","journal-title":"Nucl. Instrum. Methods Phys. Res. Sect. A Accel. Spectrometers. Detect. Assoc. Equip."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1109\/TNS.2011.2179314","article-title":"A comprehensive model to predict the timing resolution of SiPM-based scintillation detectors: Theory and experimental validation","volume":"59","author":"Seifert","year":"2012","journal-title":"IEEE Trans. Nucl. Sci."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Incoronato, A., Locatelli, M., and Zappa, F. (2021). Statistical modelling of spads for time-of-flight lidar. Sensors, 21.","DOI":"10.3390\/s21134481"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"12031","DOI":"10.1109\/JSEN.2019.2938018","article-title":"Modeling the Nonlinear Response of Silicon Photomultipliers","volume":"19","author":"Rosado","year":"2019","journal-title":"IEEE Sens. J."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Morciano, A., Perenzoni, M., and D\u2019Amico, S. (2021, January 15\u201317). Signal-to-Noise Ratio in Pulsed Mode SiPMs for LiDAR Applications. Proceedings of the 2021 International Conference on IC Design and Technology, ICICDT 2021, Dresden, Germany.","DOI":"10.1109\/ICICDT51558.2021.9626464"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1117\/1.OE.57.3.031306","article-title":"Peak detection approaches for time-correlated single-photon counting three-dimensional lidar systems","volume":"57","author":"Tolt","year":"2018","journal-title":"Opt. Eng."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.nima.2018.11.083","article-title":"Characterisation of SiPMs","volume":"926","author":"Klanner","year":"2019","journal-title":"Nucl. Instrum. Methods Phys. Res. Sect. A Accel. Spectrometers. Detect. Assoc. Equip."},{"key":"ref_34","unstructured":"(2022, September 20). Biasing and Readout of ON Semiconductor SiPM Sensors. Available online: https:\/\/www.onsemi.com\/pub\/Collateral\/AND9782-D.PDF."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Barbarino, G., de Asmundis, R., De Rosa, G., Mollo, C.M., Russo, S., and Vivolo, D. (2011). Silicon Photo Multipliers Detectors Operating in Geiger Regime: An Unlimited Device for Future Applications, IntechOpen.","DOI":"10.5772\/21521"},{"key":"ref_36","first-page":"1276","article-title":"Electrical characterization of silicon photo-multiplier detectors for optimal front-end design","volume":"2","author":"Corsi","year":"2006","journal-title":"IEEE Nucl. Sci. Symp. Conf. Rec."},{"key":"ref_37","unstructured":"(2022, September 20). RB-Series SiPM Sensors. Available online: https:\/\/www.onsemi.com\/pdf\/datasheet\/microrb-series-d.pdf."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.nima.2017.10.031","article-title":"Performance of SiPMs in the nonlinear region","volume":"912","author":"Rosado","year":"2018","journal-title":"Nucl. Instrum. Methods Phys. Res. Sect. A Accel. Spectrometers. Detect. Assoc. Equip."},{"key":"ref_39","unstructured":"Girard, O., Haefeli, G., Kuonen, A., Pescatore, L., Schneider, O., and Stramaglia, M.E. (2022, September 20). Characterisation of Silicon Photomultipliers Based on Statistical Analysis of Pulse-Shape and Time Distributions. Available online: https:\/\/arxiv.org\/abs\/1808.05775."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Parzen, E. (1999). Stochastic Processes, SIAM.","DOI":"10.1137\/1.9781611971125"},{"key":"ref_41","unstructured":"Gronwall, C., and Gustafsson, F. (2022, September 20). Modelling of Laser Radar Systems. Technical Report. Available online: http:\/\/www.control.isy.liu.se\/research\/reports\/2006\/2743.pdf."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/23\/9134\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:26:13Z","timestamp":1760145973000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/23\/9134"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,24]]},"references-count":41,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2022,12]]}},"alternative-id":["s22239134"],"URL":"https:\/\/doi.org\/10.3390\/s22239134","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,11,24]]}}}