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Photon counting imaging is a well-established low light level imaging technique where an image is assembled from individually detected photons. Originally developed for astronomy due to its sensitivity, it now has applications in many diverse fields of science and technology, including bioluminescence,\cite{Roncali2008,Baubet2000} optical tomography,\cite{Schmidt2000} DNA sequencing,\cite{Previte2015} lidar,\cite{McCarthy2009} quantum information science and encryption,\cite{Hadfield2009} and optical communications both on earth and in space.\cite{Boroson2013,Hemmati2014,Hemmati2007} More information about single-photon detection technology can be found in recent reviews.\cite{Hadfield2009,Buller2010,Eisaman2011,Seitz2011} Importantly, photon counting imaging allows the timing of photon arrival, and in life sciences photon counting imaging is often used for Fluorescence Lifetime Imaging Microscopy (FLIM), which has emerged as a key technique to image the environment and interaction of specific probes in living cells \cite{Becker2012,Berezin2010,Borst2010} with single-molecule sensitivity, molecular specificity, sub-cellular sub-micrometer resolution, and real-time data collection with negligible cytotoxicity.\cite{Fischer2011}  In conventional photon counting imaging, photon events on the phosphor screen of a microchannel plate (MCP)-based image intensifier are imaged with a charge-coupled device (CCD) or a complementary metal-oxide-semiconductor (CMOS) camera at high frame rates, and many frames are accumulated to build up an image.\cite{Suhling2002,Suhling1999,Dick1989,Jenkins1987,Bergamini2000,Bergamini2000a,Uslenghi2004,Boksenberg1985,Vallegra1995,Vallegra1997,Hirvonen2014_ol,Hirvonen2015_njp,Hirvonen2015_spie} image.\cite{Suhling2002,Suhling1999,Dick1989,Jenkins1987,Bergamini2000,Bergamini2000a,Uslenghi2004,Boksenberg1985,Vallegra1995,Vallegra1997,Hirvonen2014_ol,Hirvonen2015_njp, Hirvonen_2015}  However, single photon detection is also possible with electron-bombarded (EB) sensors, where the single photoelectron liberated from the photocathode is accelerated directly into the CCD or CMOS sensor, without going through a multiplication process and without being converted into light on a phosphor.\cite{Spring1998} The resulting photon events are smaller and dimmer than MCP-intensified photon events, but have a narrow, voltage-dependent pulse height distribution and avoid distortion of the image due to the coupling of the MCP to the camera, spectral matching of the camera sensitivity and the phosphor and image lag due to the phosphor decay time.\cite{Hirvonen2014_rsi} A characteristic feature of the photon counting imaging technique is the possibility of using a centroiding technique, where the true position of a photon event that covers several pixels can be determined with subpixel accuracy.\cite{Hutchings2007,Suhling2002,Suhling1999,Dick1989,Jenkins1987,Bergamini2000,Bergamini2000a,Uslenghi2004,Boksenberg1985,Vallegra2011,Bellis1991,Bulau1986,Carter1997,Kawakami1994,Srivastava2009,Michel1997,Blazit2008,Tremsin2003} The centroiding algorithms for photon counting imaging were originally developed for implementation in hardware,\cite{Boksenberg1985,Kempka2004,Fordham1989} and in their simplest incarnation the edges of the photon events are ignored. In the advent of faster computers the centroiding is nowadays done in software, but the algorithms employed in photon counting imaging are still usually simple, one-iteration algorithms based on a center-of-mass calculation. 
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